Prospects for the b b̄H, H → τ+τ− observability
for masses below 200 GeV
with ATLAS detector at LHC
Tadeusz Szymocha
The Henryk Niewodniczański Institute of Nuclear Physics,
Polish Academy of Sciences,
Kraków, Poland
A thesis submitted for the Doctor of Philosophy in Physics degree
prepared under the supervision of prof. dr hab. Elżbieta Richter-Was
˛
Kraków, August 2007
A
I would like to thank prof. dr hab. Michał Turała and prof. dr hab. Piotr Malecki for the invitation to the ATLAS
experiment and the possibility to participate in this challenging project. I would like to thank my supervisor prof.
dr hab. Elżbieta Richter-Was
˛ for her guidance over years of my Ph.D. studies.
Most of the work presented in these theses was done at the IFJ PAN ATLAS group. I would like to thank all
members for kind atmosphere, especially dr Anna Kaczmarska, dr Krzysztof Korcyl and dr Marcin Wolter for
fruitful discussions and common work over various projects. I also acknowledge the help of Łukasz Janyst in
solving many programming issues.
I have benefited from my stays at the ATLAS groups of University Paris VI (especially from valuable advice
of dr Frédéric Derue concerning implementation of an algorithm within Athena framework) and LAPP Annecy
(especially from the help of dr Fabien Tarrade in getting familiar with off-line reconstruction at the ATLAS
experiment).
This work was performed within a scope of the Higgs Working Group of the ATLAS experiment. I am
grateful to several ATLAS students and senior colleagues for the very inspiring and friendly atmosphere in
the group, in particular to Michael Heldmann, Kyle Cranmer, Silvia Resconi and Markus Schumacher. I also
profited from several very constructive comments from Donatella Cavalli, the expert on H → ττ reconstruction
with ATLAS experiment.
Last but not least, I would like to thank my whole family for their encouragement and support through my
whole education time.
This work was partially supported by:
• Polish State Committee for Scientific Research (KBN) grant 2 P03B 001 22;
• Polish - French Collaboration 01-103 (cf. 95-81) within IN2P3;
• Ministry of Science and Higher Education grant N202 064 31/3876;
• Ministry of Science and Higher Education grant 132/CER/2006/03.
A
The process of understanding nature has led scientists to create theories that in the possibly simplest way (with a
minimal number of free parameters) would describe a variety of phenomena. Our present knowledge is collected
in, so called, the Standard Model (SM). Unfortunately, this theory is not complete. The electroweak symmetry
breaking mechanism and the hierarchy problem are two open questions of this theory. Some answers can be
given by the discovery of the Higgs boson or the supersymmetry.
In order to verify experimentally the proposed theories, the new accelerator, the Large Hadron Collider
(LHC) at CERN, is being constructed, where the Higgs boson and/or the supersymmetry are expected to be
discovered. The supersymmetry offers an elegant solution to the hierarchy problem by natural cancellation of
fermionic and bosonic contributions to the loop diagrams. Since supersymmetric theory has in general case
a large number of parameters, the Minimal Supersymmetric Standard Model (MSSM) was proposed with a
minimal number of new parameters.
At the protons center of mass energy of 14 TeV, the main production mechanism for the Higgs boson is gluon
fusion. However, there is another process, with small cross-section in the SM, but highly enhanced in the MSSM:
the associated Higgs boson production with bottom quarks. In these theses the analysis of this production process
with Higgs boson decay into tau lepton pair at the ATLAS detector at the LHC is presented. The Higgs boson
decay into tau leptons was chosen as it has a smaller level of background than more frequent (90% of total) decay
into bb̄ pairs.
The results of the Higgs boson searches are usually presented in plane of the MSSM parameters mA and tan β
in various benchmark scenarios, for which other MSSM parameters are fixed. We have performed an analysis for
one of the possible production mode and completed scan of the MSSM parameter space. After including results
of the analysis presented here, we were able to extend region where Higgs boson can be found with more than
5σ significance for the mass range 120 GeV − 200 GeV.
The efficient reconstruction and identification of τ leptons (their hadronic decays) play an important role
in physics analysis. As an important part of the performed analysis the dedicated reconstruction algorithm and
identification tools were developed and their performance was discussed.
The searches presented in this dissertation were guided by the following theses:
• revisiting the analysis of the signal and background in fast simulation for three mass points: 120 GeV,
150 GeV and 200 GeV and taking into account not only semi-leptonic decay of the τ lepton pair, but also
introducing the leptonic one, which was considered negligible so far;
• development of an algorithm for reconstruction and identification of hadronic τ decays;
• application of the algorithm to the signal reconstruction and interpretation of results of the fast simulation
versus the full simulation;
• interpretation of results within the MSSM model and determination of the observability potential.
C
Acknowledgments
i
Abstract
iii
Contents
v
List of Figures
ix
List of Tables
xi
Chapter I
Introduction
Chapter II
The ATLAS experiment
II.1
II.2
II.3
II.4
II.5
II.6
II.7
II.8
II.9
Chapter III
III.1
III.2
III.3
III.4
Chapter IV
IV.1
IV.2
IV.3
IV.4
1
Introduction . . . . . . . . . . . . .
Physics Goals for Performance . . .
Inner Detector . . . . . . . . . . . .
II.3.1
Pixel Detectors . . . . . . . .
II.3.2
Semiconductor Tracker . . .
II.3.3
Transition Radiation Tracker .
Calorimeters . . . . . . . . . . . . .
II.4.1
Electromagnetic calorimeter .
II.4.2
Hadronic calorimeter . . . . .
Muon System . . . . . . . . . . . .
Magnets . . . . . . . . . . . . . . .
Trigger and Data Acquisition . . . .
ATLAS Data and Computing Model
II.8.1
Event Data Model . . . . . .
II.8.2
Grid environment . . . . . .
Summary . . . . . . . . . . . . . .
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3
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21
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The Higgs Boson Physics
The Higgs Mechanism in the Standard Model . . . . . . . . . . . . . .
The Higgs Mechanism in the Minimal Supersymmetric Standard Model
Experimental limits . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The observability of the bb̄H, H → ττ process
Introduction . . .
Events generation
Events simulation
Events selection .
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vi
C
IV.5
IV.6
Acceptance for signal and background events . . .
Expected number of events and the mass resolution
IV.6.1
Analysis streams with b-jet tag and b-jet veto
IV.6.2
Events in the mass window . . . . . . . . .
IV.7
Sensitivity in ℓℓETmiss versus ℓ had ETmiss channel . .
IV.8
Interpretation in the MSSM model . . . . . . . . .
IV.9
Summary . . . . . . . . . . . . . . . . . . . . . .
Chapter V
V.1
V.2
V.3
V.4
V.5
V.6
V.7
Chapter VI
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30
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95
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Theoretical predictions for signal process
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Different production mechanisms: sensitivity to the kinematics . . . . . . . . . . .
Selection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mass reconstruction for signal events . . . . . . . . . . . . . . . . . . . . . . . . .
Different Monte Carlo approaches for Yukawa induced bb̄ → H production process
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The tau1P3P Algorithm
VI.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VI.2
Identification of τ leptons at Tevatron . . . . . . . . . . . . . . . . . . .
VI.2.1
Detectors overview . . . . . . . . . . . . . . . . . . . . . . . . .
VI.2.2
Reconstruction of hadronic τ decays at Tevatron . . . . . . . . .
VI.2.3
Identification of hadronic τ decays at Tevatron . . . . . . . . . .
VI.3
Identification of Tau Leptons with CMS . . . . . . . . . . . . . . . . .
VI.4
Identification of Tau Leptons with ATLAS . . . . . . . . . . . . . . . .
VI.4.1
The tauRec package . . . . . . . . . . . . . . . . . . . . . . . .
VI.4.2
The tau1P3P algorithm . . . . . . . . . . . . . . . . . . . . . . .
VI.5
Hadronic τ decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VI.6
Reconstruction of the hadronic τ’s . . . . . . . . . . . . . . . . . . . .
VI.6.1
The leading hadronic track . . . . . . . . . . . . . . . . . . . .
VI.6.2
The τ1P and τ3P hadronic τ’s . . . . . . . . . . . . . . . . . . .
VI.6.3
The energy scale of τ1P and τ3P . . . . . . . . . . . . . . . . . .
VI.6.4
The calorimetric observables . . . . . . . . . . . . . . . . . . .
VI.7
Performance for signal and background samples . . . . . . . . . . . . .
VI.7.1
True hadronic τ′ s from qq̄ → Z → ττ and qq̄ → W → τν events .
VI.7.2
Fake hadronic τ′ s from di-jet events . . . . . . . . . . . . . . . .
VI.7.3
Fake hadronic τ′ s from qq̄ → Z → ττ and qq̄ → W → τν events .
VI.8
Optimization with multivariate techniques . . . . . . . . . . . . . . . .
VI.8.1
PDE-RS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VI.8.2
Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . .
VI.8.3
Support Vector Machine . . . . . . . . . . . . . . . . . . . . . .
VI.9
Performance of 1 prong and 3 prong τ-jets identification . . . . . . . .
VI.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter VII
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Results from the Full Simulation
VII.1 Introduction . . . . . . . . .
VII.2 Analysis framework . . . . .
VII.3 The reconstruction efficiency
VII.3.1
Isolated electrons . . .
VII.3.2
Isolated muons . . . .
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vii
VII.3.3
τ-jet candidates . . . . . . . . . . .
VII.3.4
Comparison with the fast simulation .
VII.4 The ETmiss reconstruction . . . . . . . . . .
VII.4.1
Two methods of ETmiss estimation . .
VII.4.2
ETmiss calibration . . . . . . . . . . .
VII.4.3
ETmiss resolution . . . . . . . . . . .
VII.5 Invariant mass of the di-τ system . . . . . .
VII.5.1
The mass resolution using ETν . . . .
VII.5.2
The mass resolution using ETmiss . . .
VII.6 Acceptances and expected number of events
VII.7 Summary . . . . . . . . . . . . . . . . . .
Chapter VIII
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Conclusions
111
Appendix A
A.1
A.2
A.3
A.4
A.5
Appendix B
B.1
B.2
Appendix C
C.1
Bibliography
Energy calibration for τ-jets in fast simulation . . . . . . . .
Reconstruction of ETmiss in fast simulation . . . . . . . . . .
Calculation of invariant mass of reconstructed τ leptons pair
The mass reconstruction for background events . . . . . . .
List of variables . . . . . . . . . . . . . . . . . . . . . . . .
98
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113
113
115
115
119
120
121
Acceptance and expected number of events for the mass point mH = 150 GeV . . . . . 121
Acceptance and expected number of events for the mass point mH = 200 GeV . . . . . 128
135
List of abbreviations and names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
137
viii
C
ix
List of Figures
II-1
II-2
Overall layout of the ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic view of the ATLAS inner detector . . . . . . . . . . . . . . . . . . . . . . . . . .
7
7
III-1
III-2
III-3
The Standard Model Higgs boson branching ratio as a function of the Higgs boson mass mhS M
The Standard Model and Minimal Supersymmetric Standard Model Higgs boson widths . .
The branching ratio of the MSSM h, H and A Higgs bosons for non-SUSY decay modes as a
function of their mass for tan β = 30 and vanishing mixing . . . . . . . . . . . . . . . . . .
The confidence level for the signal plus background hypothesis CL s , as a function of test
mass mH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The excluded region at 95% confidence level in (mA , tan β) plane for the no-mixing (left) and
scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
mmax
h
15
15
III-4
III-5
IV-1
IV-2
IV-3
IV-4
IV-5
IV-6
IV-7
IV-8
V-1
V-2
V-3
V-4
VI-1
VI-2
VI-3
VI-4
VI-5
VI-6
VI-7
18
19
20
The Feynman diagrams for associated production of the Higgs boson with two high-pT bottom quarks: gg → bb̄H and qq̄ → bb̄H . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
The MSSM parameter space with 5 σ discovery contour for the ATLAS experiment searches
of associated Higgs production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Distributions of variables used for events selection in ℓℓETmiss channel . . . . . . . . . . . . 28
Distributions of variables used for events selection in ℓ had ETmiss channel . . . . . . . . . . 29
The Gaussian fit to reconstructed mττ distribution for bb̄H process . . . . . . . . . . . . . . 38
The mass of h and H bosons vs mass of A boson for tan β = 10 and tan β = 30 and the total
width of different Higgs bosons in the MSSM model . . . . . . . . . . . . . . . . . . . . . . 48
The discovery limit for three mass points 120 GeV, 150 GeV and 200 GeV for ℓℓETmiss , ℓ had ETmiss
and both final states combined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
The MSSM parameter space with new 5 σ discovery contour evaluated in these theses . . . 50
The alternative to bb̄H process Feynman diagrams for bottom quark fusion: bb̄ → H and
gb → bH processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Higgs
The pT
distribution for three production mechanisms: gg → H, gg → bb̄H and qq →
qqH in ℓℓETmiss and the transverse momenta distribution of the lepton from the leptonic τ
decay and of the ρ hadron from the hadronic τ decay in ℓ had ETmiss for the gg → H production
The characteristic kinematical distributions before respective selection in ℓℓETmiss for different production processes: gg → H , gg, qq̄ → bb̄H and qq → qqH . . . . . . . . . . . . .
Higgs
The pT
distribution in ℓℓETmiss for the three production mechanisms . . . . . . . . . . . .
The tauRec likelihood discriminant distribution and the rejection against QCD jets versus
τ-jet efficiency in different pT windows . . . . . . . . . . . . . . . . . . . . . . . . . . . .
P
P
Fraction of energy carried by the π± , π0 with respect to the visible transverse energy
for hadronic one-prong and three-prong decay modes . . . . . . . . . . . . . . . . . . . . .
The cone separation between the most energetic π±lead and ETtruth directions for a one-prong
and three-prong, and between ETtruth direction and energy weigted barycenter for three-prong
The efficiency, as a function of track transverse momenta, for accepting a given track as a
good quality one . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The efficiency for labeling a given track as electron-track for true electron tracks and nonelectron tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The separation ∆R between the true direction of the barycenter of the visible decay products
of the τ and the reconstructed direction of the hadronic τ . . . . . . . . . . . . . . . . . . .
The energy scale of all τ1P and τ3P compared to the τ visible decay products . . . . . . . .
53
55
58
61
70
72
72
73
74
75
78
x
L  F
VI-8
VI-9
VI-10
VI-11
VI-12
VI-13
VI-14
VI-15
VI-16
VI-17
VI-18
VI-19
VI-20
VII-1
VII-2
VII-3
VII-4
VII-5
VII-6
VII-7
VII-8
A-1
A-2
A-3
A-4
A-5
A-6
The energy scale of all τ1P and τ3P compared to the τ visible decay products for the qq̄ →
Z → ττ sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distributions of discriminating variables for τ1P candidates . . . . . . . . . . . . . . . . .
Distributions of discriminating variables for τ3P candidates . . . . . . . . . . . . . . . . .
The ETtruth distribution of the visible products of analyzed hadronic τ decays . . . . . . . . .
The reconstruction efficiency, as a function of ETtruth , for true one-prong and three-prong,
normalized respectively to one-prong or three-prong hadronic τ decays . . . . . . . . . . .
The reconstruction efficiency, as a function of ETtruth , for true one-prong and three-prong,
normalized to all hadronic τ decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ETtruth distribution of the analyzed hard-process partons from the QCD jets sample . . .
The reconstruction+identification efficiency for τ1P and τ3P candidates in a function of ETtruth
e f low
The ET
distribution of fake τ1P and τ3P from the QCD ISR in qq̄ → W, Z events . . . . .
Schematic view of the Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Normalized distributions of the discriminating function XNN and the Support Vector Machine
for signal and background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Best values of two SVM parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background rejection as a function of signal efficiency for three analysis methods: PDE-RS,
Neural Network and Support Vector Machine for τ1P and τ3P . . . . . . . . . . . . . . . . .
The overall identification efficiency for true electrons from the bb̄A process and Higgs boson
at mass 120 GeV for ℓℓETmiss , as a function of pseudorapidity η and transverse momentum pT
The overall identification efficiency for true muons from bb̄A process and Higgs boson at
mass 120 GeV for ℓℓETmiss , as a function of pseudorapidity η and transverse momentum pT .
The overall (reconstruction + identification) efficiency for 1 prong τ candidates from the bb̄A
process and Higgs boson at mass 120 GeV versus η and pT . . . . . . . . . . . . . . . . . .
The overall (reconstruction + identification) efficiency for 3 prong τ candidates from bb̄A
process and Higgs boson at mass 120 GeV versus η and pT . . . . . . . . . . . . . . . . . .
Fit to the relative difference of ETmiss and ETν x-component in (-0.4,0.4) window for ℓℓETmiss .
The difference between ETν for non-interacting particles according to Monte Carlo truth and
reconstructed ETmiss for bb̄A, mA = 120 GeV for ℓℓ ETmiss and ℓ had ETmiss as well as for
Z → ττ combined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The reconstructed invariant mass of τ lepton pair for the signal bb̄A at mass 120 GeV after
generic selection for ℓℓETmiss and ℓ had ETmiss . . . . . . . . . . . . . . . . . . . . . . . . .
The reconstructed invariant mass of τ lepton pair for the signal bb̄A at mass 120 GeV and
tan β = 10 after consecutive cuts for ℓℓETmiss . . . . . . . . . . . . . . . . . . . . . . . . . .
The calibration factor as function of raw jet transverse momentum praw
T for τ − jets and for
b-jets and light-jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
jet
jet
The ratio of pT /pτ−had
as a function of pT and as a function of η before and after energy
T
calibration for τ-jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ratio ETmiss /ETν is shown for different production processes: gg → H, bb̄H and qqH in
ℓ had ETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The reconstructed invariant mass of the ττ system mττ in ℓℓETmiss channel and different production modes: gg → H, bb̄H and qqH, if the true neutrino or ETmiss was used for mττ
reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The reconstructed invariant mass of the ττ system mττ in ℓ had ETmiss channel and different
production modes if the true neutrino or ETmiss was used for mττ reconstruction . . . . . . .
The reconstructed mass of the ττ system in ℓℓETmiss and ℓ had ETmiss for the Z/γ∗ → ττ events
78
80
81
83
84
85
86
88
89
91
92
92
93
97
98
98
99
101
102
104
105
113
114
115
117
118
119
xi
List of Tables
II-1
Performance parameters of the inner detector . . . . . . . . . . . . . . . . . . . . . . . . .
6
III-1
III-2
The expected SM and MSSM particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neutral Higgs boson couplings to fermions and gauge bosons in the MSSM normalized to
the SM Higgs boson couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
Summary on the σ × BR for the signal and background samples used in the analysis . . . .
The efficiencies ε and rejection R used in this analysis . . . . . . . . . . . . . . . . . . . .
The cumulative acceptance after consecutive selections for signal mH = 120 GeV events in
ℓℓETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptance after consecutive cuts for background events in ℓℓETmiss channel
The cumulative acceptance after consecutive selections for signal mH = 120 GeV events in
ℓ had ETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptance after consecutive cuts for background events in ℓ had ETmiss channel
The cumulative acceptance after consecutive cuts for tt¯ background events in ℓ had ETmiss
channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptance after consecutive cuts for tt¯ background events in ℓℓETmiss channel
Expected number of signal mH = 120 GeV and background events for an integrated luminosity 10 f b−1 after consecutive cuts in ℓℓETmiss channel . . . . . . . . . . . . . . . . . . . .
Expected number of signal mH = 120 GeV and background events for an integrated luminosity 10 f b−1 after consecutive cuts in ℓ had ETmiss . . . . . . . . . . . . . . . . . . . . . .
Resolution of the reconstructed invariant mass of the τ system for signal events in ℓℓETmiss
channel. Results from gaussian fit in mass window mH = 120 GeV ± 20 GeV . . . . . . . .
Resolution of the reconstructed invariant mass of the τ system for signal events in ℓ had ETmiss
channel. Results from gaussian fit in mass window mH = 120 GeV ± 20 GeV . . . . . . . .
Expected number of signal and background events within mass window mH = 120 GeV ±
20 GeV for an integrated luminosity 10 f b−1 after consecutive cuts in ℓℓETmiss channel . . . .
Expected number of signal mH = 120 GeV and background events for an integrated luminosity 10 f b−1 after consecutive cuts in ℓ had ETmiss channel . . . . . . . . . . . . . . . . . .
√
The signal significance in terms of the signal (S) to square root background (B), S / B for
10 f b−1 in different mass points. Values for cross-section of bb̄H and gg → H processes are
shown for SM predictions and do not include the MSSM signal enhancement . . . . . . . .
The improvement of combined significance from both ℓℓETmiss and ℓ had ETmiss channels relative to significance of ℓ had ETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . .
The tan β reach for 30 f b−1 and discovery sensitivity of 5σ for the bb̄A/H/h and gg → H
processes combined. Given is also improvement of combined significance with respect to
ℓ had ETmiss mode alone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The signal significance at given tan β . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
25
Cross-sections for signal processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptances of the selection criteria in ℓℓETmiss for three different production
mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptances of the selection criteria in ℓ had ETmiss for three different production mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Resolution of the reconstructed invariant mass of the ττ system in ℓℓETmiss channel for different Higgs boson production mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . .
Resolution of the reconstructed invariant mass of the ττ system in ℓ had ETmiss channel for
different Higgs boson production mechanisms . . . . . . . . . . . . . . . . . . . . . . . . .
55
IV-1
IV-2
IV-3
IV-4
IV-5
IV-6
IV-7
IV-8
IV-9
IV-10
IV-11
IV-12
IV-13
IV-14
IV-15
IV-16
IV-17
IV-18
V-1
V-2
V-3
V-4
V-5
17
31
32
33
33
34
35
39
40
41
41
43
44
46
47
49
50
57
57
59
60
xii
L  T
V-6
V-7
V-8
V-9
V-10
V-11
V-12
VI-1
VI-2
VI-3
VI-4
VI-5
VI-6
VI-7
VI-8
VI-9
VI-10
VI-11
VI-12
VI-13
VI-14
VII-1
VII-2
VII-3
VII-4
VII-5
VII-6
B-1
B-2
B-3
Cross-section for signal production with bb̄H Yukawa coupling in ℓℓETmiss and ℓ had ETmiss
mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptance of the selection criteria in ℓℓETmiss for different approaches of
modelling production process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptance of the selection criteria in ℓ had ETmiss for different approaches
of modelling production process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Resolution of the reconstructed invariant mass of the ττ system in ℓℓETmiss channel for different approaches of modeling production process . . . . . . . . . . . . . . . . . . . . . .
Resolution of the reconstructed invariant mass of the ττ system in ℓ had ETmiss channel for
different approaches of modelling production process . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptance in the mass window mH = 120 GeV ± 20 GeV in ℓℓETmiss for
different approaches of modeling production process . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptance in the mass window mH = 120 GeV ± 20 GeV in ℓ had ETmiss for
different approaches of modelling production process . . . . . . . . . . . . . . . . . . . . .
The τ decay branching ratios, based on 108 simulated τ decays from Z → ττ events . . . . .
The reconstruction quality of the visible decay products of the hadronic τ-candidates from
the qq̄ → Z → ττ sample, (η, φ) coordinates . . . . . . . . . . . . . . . . . . . . . . . . . .
chrgEMtrk
Formulas used for calculating resET
and resETneuEM for τ1P and τ3P energy scale . .
e f low
Acceptance inside specified windows for the ET /ETtruth . . . . . . . . . . . . . . . . . .
Acceptances for different selections at the particle level, extracted from the fully simulated
qq̄ → Z → ττ events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reconstruction efficiencies with respect to all analyzed hadronic τ decays . . . . . . . . . .
The cumulative acceptance of identification selection for true τ1P and τ3P candidates in the
|η| < 1.5 range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Total efficiency with respect to all hadronic τ decays, based on the democratic mixture of
qq̄ → Z → ττ and qq̄ → W → τν samples . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reconstruction efficiency for fake hadronic τ candidates matched to the hard-process partons
Probability for reconstructing τ1P or τ3P from hard-process parton . . . . . . . . . . . . .
The cumulative acceptances of the fake τ1P and τ3P in the |η| < 1.5 pseudorapidity range . .
The cumulative acceptances of the τ1P and τ3P in the |η| < 1.5 pseudorapidity range for the
dijet35 samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptances of the fake τ1P and τ3P in the |η| < 1.5 pseudorapidity range . .
Background rejection for varying identification efficiency obtained with use of different multivariate analysis methods: PDE-RS, Neural Network and Support Vector Machine . . . . .
Calibration factors for ETmiss components for bb̄A sample. . . . . . . . . . . . . . . . . . .
Mass resolution after consecutive cuts for signal events in ℓℓ ETmiss channel. ETν is used
instead of ETmiss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mass resolution after consecutive cuts for signal events in ℓ had ETmiss channel. ETν is used
instead of ETmiss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mass resolution after consecutive cuts for signal events in ℓℓ ETmiss and ℓ had ETmiss channels
Acceptance of signal events for fast and full simulation . . . . . . . . . . . . . . . . . . . .
Expected number of signal events for fast and full simulation . . . . . . . . . . . . . . . . .
61
62
62
63
63
64
64
71
75
77
77
82
83
84
85
86
86
87
87
89
93
101
103
104
106
107
108
The cumulative acceptance after consecutive selections for signal mH = 150 GeV events in
ℓℓETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Expected number of signal mH = 150 GeV events for an integrated luminosity 10 f b−1 after
consecutive cuts in ℓℓETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
The cumulative acceptance after consecutive selections for signal mH = 150 GeV events in
ℓ had ETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
xiii
B-4
B-5
B-6
B-7
B-8
B-9
B-10
B-11
B-12
B-13
B-14
B-15
B-16
Expected number of signal mH = 150 GeV events for an integrated luminosity 10 f b−1 after
consecutive cuts in ℓ had ETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Resolution of the reconstructed invariant mass of the τ system for signal events in ℓ had ETmiss
channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Resolution of the reconstructed invariant mass of the τ system for signal events in ℓ had ETmiss
channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Expected number of signal and background events within mass window mH = 150 GeV ±
30 GeV for an integrated luminosity 10 f b−1 after consecutive cuts in ℓℓETmiss channel . . . .
Expected number of signal and background events within mass window mH = 150 GeV ±
30 GeV for an integrated luminosity 10 f b−1 after consecutive cuts in ℓ had ETmiss channel .
The cumulative acceptance after consecutive selections for signal mH = 200 GeV events in
ℓℓETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Expected number of signal mH = 200 GeV events for an integrated luminosity 10 f b−1 after
consecutive cuts in ℓℓETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cumulative acceptance after consecutive selections for signal mH = 200 GeV events in
ℓ had ETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Expected number of signal mH = 200 GeV events for an integrated luminosity 10 f b−1 after
consecutive cuts in ℓ had ETmiss channel . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Resolution of the reconstructed invariant mass of the τ system for signal events in ℓ had ETmiss
channel. Results from gaussian fit in mass window mH = 200 GeV ± 40 GeV . . . . . . . .
Resolution of the reconstructed invariant mass of the τ system for signal events in ℓ had ETmiss
channel. Results from gaussian fit in mass window mH = 200 GeV ± 40 GeV . . . . . . . .
Expected number of signal and background events within mass window mH = 200 GeV ±
40 GeV for an integrated luminosity 10 f b−1 after consecutive cuts in ℓℓETmiss channel . . . .
Expected number of signal and background events within mass window mH = 200 GeV ±
40 GeV for an integrated luminosity 10 f b−1 after consecutive cuts in ℓ had ETmiss channel .
124
125
125
126
127
129
130
131
131
132
132
133
134
xiv
L  T
C I
I
The search for the Higgs boson is a primary goal of the high energy physics today. The Higgs boson was
introduced to the theory as a consequence of invoking the Higgs mechanism to break the electroweak symmetry.
The interaction between a particle and the Higgs field would result in observable mass of this particle and
interaction between Higgs fields themselves - the mass of the Higgs boson. At present, the Higgs boson is the
only particle predicted in the Standard Model (SM) but not yet discovered.
However, the SM is faced with the hierarchy problem and with problem of divergent Higgs boson mass. The
most elegant solution to these problems is to assume more general symmetry, called the supersymmetry, that
exists between bosons and fermions. The addition of a minimal number of new parameters to the SM leads to
proposition of the Minimal Supersymmetric Standard Model (MSSM). In this model 2 Higgs doublets create
5 physical Higgs bosons: h, H, A and H ± . At the tree level, the Higgs sector of the MSSM is determined by
only two parameters, typically chosen to be: mA - mass of the CP-odd Higgs boson and tan β - ratio of the
vacuum expectation values of the two Higgs doublets. The divergence of Higgs boson mass, due to higher order
loop corrections, solved in the SM by unnatural "fine tuning" of the tree level parameters, can be removed in
the MSSM. When the supersymmetry is exact, the corrections to the Higgs boson mass from particle and its
supersymmetric partner loops cancel each other.
Some theoretical considerations, assuming that the SM is valid only up to cutoff energy Λ, beyond which
new physics appears, allow to set limits on the Higgs boson mass. The requirements that electroweak vacuum
is stable and that the SM remains perturbative until Planck scale (1019 GeV ∗ ) set upper and lower bounds of
130 GeV < mH < 190 GeV on the Higgs boson mass. In case the new physics appears at 1 TeV scale, the bounds
are weakened to 50 GeV < mH < 800 GeV [1].
The on-going experiments at the existing collider (Tevatron) are stretched to their limits in order to find a
plausible answer concerning Higgs boson existence. The new accelerator, Large Hadron Collider (LHC), placed
at the European Laboratory for Particle Physics (CERN) will operate at 7 times higher energy and around 10
times higher luminosity and dedicated detectors: A Toroidal LHC ApparatuS (ATLAS) and Compact Muon
Spectrometer (CMS) are designed to find the Higgs boson or exclude its existence in most of the existing theoretical models. The results published after the second phase of running of the Large Electron-Positron collider
(LEP-2) set the limit of mhS M = 114.4 GeV for the SM Higgs boson [2] and the limit of mhMS S M > 92.8 GeV,
mA > 93.4 GeV, tan β < 0.7 or tan β > 2.0 for the MSSM [3].
According to the SM predictions, the main Higgs boson production channel at the LHC energies will be
the gluon fusion. However, in these theses we will concentrate on the Higgs boson production associated with
b-quarks (bb̄H), strongly enhanced in the MSSM model (for large tan β values), with Higgs boson decay into τ
lepton pair. The main advantage of this decay mode is a considerably smaller level of the QCD jets background
than in more frequent decay into bb̄ pair.
Chapters IV, V, VI, VII and appendices represent original work of the author of these theses or the development to which he contributed significantly. The work of the author consisted of:
∗
In these theses we use units, for which c = ~ = 1, where c is the speed of light and ~ is the reduced Planck constant.
2
C I. I
• Large statistics of Monte Carlo simulation for signal (gluon-gluon fusion, Vector Boson Fusion and three
approaches for the Yukawa induced bb̄H process at mass points 120 GeV, 150 GeV and 200 GeV) and
various background samples (bb̄Z, Z/γ∗ , bb̄W, single W, W + jets, tt¯) with the use of software for the fast
simulation of the detector response. The studies of various Monte Carlo approaches to assess expected
backgrounds are an important part of this analysis. The simulated data were used for analyzes presented
in Chapter IV and V, partial results were published in [4, 5];
• Development of the analysis code, executed on the fast simulation data and evaluation of contribution to
the combined significance of final states, where τ pair decays leptonically (ℓℓ ETmiss ) or semi-leptonically
(ℓ had ETmiss ) for low mass region. These results are presented in Chapter IV and published in [6];
• Significant contribution to the development of an algorithm for the reconstruction of hadronic τ decays (called the tau1P3P), code C++ implementation in offline software of the ATLAS Collaboration
(Athena), benchmarking and validation of the performance. These results are presented in Chapter VI and
published in [7, 8];
• Significant contribution to the optimization of the tau1P3P algorithm with multivariate methods, especially with Neural Network. These results are presented in Chapter VI and published in [9];
• Preparation of the full simulation of signal bb̄A, A → ττ (at mA = 120 GeV) data and the reconstruction
of the Z → ττ background samples in the grid environment. These data were used in Chapter VII;
• Development of the analysis code with the use of the Analysis framework (the EventView package)
executed on the fully simulated data produced during ATLAS Data Challenges. This code was used to
derive results in Chapter VII. This Chapter represents original work of author starting from the preparation
of the MC events samples, development of the analysis code to the discussion of results.
To summarize, the results of these theses have been partially published in five ATLAS Physics or Communications Notes [5–9] and one article published in a journal [4]. The results presented here have been discussed
during various meetings of the Higgs and Tau Working Groups of the ATLAS Collaboration and included in
conference reports and publications discussing experiment potential for the hadronic tau identification.
These theses are organized in Chapters. After Introduction, in Chapter II the ATLAS detector is described
with its physics potential evaluated. In Chapter III the physics aspects of the Higgs mechanism are summarized
and the present limits for the Higgs boson mass are discussed. Chapter IV describes studies of the bb̄H process
based on the fast simulation of the ATLAS detector, evaluation of the signal and background rates as well as the
signal significance for this channel at low Higgs boson mass range. Finally, the results of the complete scan of the
MSSM parameter space are presented. Chapter V discusses the analysis of impact of various approaches to modeling associated production of Higgs boson with b-quarks on acceptance and expected event rates. Chapter VI
starts with a description of Tevatron experiments and their methods for the reconstruction and the identification
of hadronic τ decays. The techniques used by experiments placed there could be accommodated in LHC collaborations as well. The main part of this chapter consists of a description of the new algorithm for the reconstruction
of hadronic τ decays, suitable for processes having visible τ-jets in range of 20-70 GeV. The algorithm described
in Chapter VI was used in the analysis of fully simulated data samples of bb̄A at mA = 120 GeV and Z → ττ processes and results were presented in Chapter VII. These theses conclude with Chapter VIII. Appendices included
at the end contain more technical details or extension of subjects discussed in the main part of these theses.
Let us emphasize that these theses was completed at the time of a very rapid development and unstable
performance of the ATLAS offline software. Both the design of the algorithms and the event data model were
significantly modified every few months, with no backward compatibility preserved. It made completing analysis
with large statistics data samples extremely difficult. Certain confusion was also raised by the fact that algorithms
performance was often much worse than the nominal one (from the well tuned for the fortran version of the
reconstruction software) and it seemed not well justified to adjust expected detector potential for the Higgs
boson observability to these very temporary performance figures. In spite of the mentioned above constraints,
the whole analysis chain was performed, leading to important results accepted by the ATLAS collaboration.
C II
T ATLAS 
II.1 Introduction
The European Laboratory for Particle Physics (CERN) placed near Geneva, Switzerland, has undertaken a project
of building a new machine called the Large Hadron Collider. In its basic work mode the LHC will accelerate
two beams of protons to energy of 7 TeV each. There are also plans for collisions of heavy ions (Pb-Pb). The
particles will be kept in a ring of circumference ∼ 27 km by superconducting dipole magnets generating field of
8.36 T. The LHC will be capable of colliding particles every 25 ns and of reaching luminosity of 1033 cm−2 s−1
in the first phase, that should give an insight into new physics at TeV scale. Ultimately running at luminosity of
1034 cm−2 s−1 is foreseen.
The searches for the new physics will be performed on five detectors which presently undergo final integration: A Toroidal LHC ApparatuS (ATLAS), Compact Muon Spectrometer (CMS), Large Hadron Collider beauty
(LHCb) experiment, A Large Ion Collider Experiment (ALICE) and a detector TOTEM for the diffractive physics
and the luminosity measurements.
The ATLAS detector is a general purpose detector. The overall layout of the detector is shown in Figure II-1
and Figure II-2. Its total dimensions exceed 46 m in length and 22 m in diameter [10]. The main physics goals
comprise searches for origin of mass (Higgs boson), a supersymmetry and detailed studies of the top quark
properties. The more detailed description of the designed detector performance and physics program is published
in ATLAS Technical Design Report (TDR) [11]. In the next sections of this chapter the detector set-up, as
documented in TDR, will be summarized, as it was the base for physics simulations and analysis presented here.
The CMS is also a general purpose detector, but with different principles which guided design optimization. It has smaller overall dimensions (21 m length and 16 m diameter vs 46 m and 22 m in ATLAS), higher
mass (12 500 tons vs 7 000 ton), stronger magnetic field (4 T vs 2 T) and an excellent electromagnetic calorimeter, based
crystals (energy resolution in the central part of electromagnetic calorimeter
√ on PbWO4 scintillating
√
3%/ E ⊕ 0.3% vs 10%/ E ⊕ 0.2%). The physics program of the CMS collaboration is very close to that of
ATLAS: primary goals are the search for Higgs boson and the evidence of supersymmetry [12].
The mixing between three quark families is represented via the Cabibbo-Kobayashi-Maskawa (CKM) [13]
unitary matrix. The standard parametrization of the matrix contains three angles and one complex phase. The
presence of the complex elements leads to the violation of the CP symmetry in weak interactions. The LHCb
experiment [14] is dedicated to a study of the CP violation phenomena in the sector of B mesons. The precise
measurements will enable to test the SM predictions and to look for the effects of new physics beyond SM.
The other interesting topic will be studies of rare decay modes of B mesons where the new physics may lead to
measurable deviations from the SM prediction. Owing to better acceptance in forward direction and a dedicated
trigger a factor of two better yield of bb̄ events is expected compared to the ATLAS or the CMS.
The ALICE detector is relatively small and is supposed to study physics of strongly interacting matter at
extreme energy density, where new a state of matter - quark-gluon-plasma - is expected. This physics can be
studied in heavy ions (Pb-Pb) collisions at 5.5 TeV per nucleon that are foreseen to take place during dedicated
one month operation of the accelerator per year [15].
4
C II. T ATLAS 
The TOTEM detector will measure the total proton-proton cross-section and study elastic scattering and
diffractive dissociation at LHC. It will be set-up close to the beam axis, close to the CMS experiment interaction
point. It consists of two types of detectors. The first is a set of telescopes of “Roman pots”, placed symmetrically
on both sides of the intersection region for detection of protons scattered at very small angles in elastic or quasielastic reactions. The second is a forward inelastic detector, covering about 4 pseudorapidity units in the forward
cones (3 < |η| < 7) with full azimuthal acceptance. It will measure the overall rate of inelastic reactions [16].
In the ATLAS collaboration the following coordinate system is adopted. The beam direction defines the zaxis and (x,y) plane is the plane transverse to the beam direction. The positive x-axis is defined as pointing from
the interaction point to the center of the LHC ring and the positive y-axis is pointing upwards. The azimuthal
angle φ is measured around the beam axis and the polar angle θ is the angle from the beam axis. Other variables
are defined in Appendix A.5.
II.2 Physics Goals for Performance
At the LHC collider the multipurpose detectors, ATLAS and CMS, have to fulfill various criteria [11]:
• large acceptance in pseudorapidity η with almost full coverage in azimuthal angle φ;
• efficient tracking for momentum measurements of leptons with high transverse momenta pT as well as
electron, photon, τ-lepton and heavy flavour quarks identification;
• very good electromagnetic calorimetry for electron/photon identification and energy measurements as well
as full-coverage hadronic calorimetry for accurate jet and missing transverse energy ETmiss measurements;
• accurate muon momentum measurements, especially for high luminosity;
• fast trigger with low pT thresholds for accumulation of data with high efficiency for all processes of interest
at the LHC.
As it will be shown in the next sections, the ATLAS detector fulfills these criteria. However, we should remember
that for various reasons not all the parts of the detector will be ready and commissioned from the very beginning.
This will have a direct impact on physics, which will be studied with early data. For example, the outer endcaps of transition radiation trackers covering 2.0 < |η| < 2.4 will be staged. Also a large part of the trigger and
data acquisition processors will not be available, so we will have to limit the first level of trigger output rate
from 75 kHz to around 35 kHz. This will be done by raising trigger thresholds on multi-jets, ETmiss , transverse
e(µ)
momentum of electron e or muon µ: pT and will affect mainly the B-physics program [17].
It is expected that the ATLAS detector will give us the opportunity to exclude or discover new physics phenomena. The primary task will be the search for the Higgs boson. In the Standard Model (SM) and its extensions
(for example the Minimal Supersymetric Standard Model (MSSM)) the Higgs boson can be discovered, if exists,
in complete region of the parameter space.
The ATLAS detector can also investigate supersymetric particle spectrum and is able to discover squarks
and gluinos up to masses of ∼ 2.0 T eV for 10 f b−1 , rising the limit to ∼ 2.5 T eV for 100 f b−1 [18, 19]. Another
example is the search aimed into the discovery of new heavy boson Z’. The search for direct production at
Tevatron and virtual effects at LEP excluded region of Z’ mass below 800 GeV. The discovery potential of the
LHC for luminosity of 100 f b−1 is around 5 T eV [20, 21].
We expect that with the first few weeks of the collected data with integrated luminosity of 100 pb−1 300 pb−1 , the measurements of the SM processes can be done (cross-sections and event features for minimum
bias, QCD-jets, W, Z boson, tt¯- production, etc.). We will gather dedicated control samples for measurements of
specific backgrounds (e.g. tt¯ j j as background to irreducible tt¯bb̄ in tt¯H → tt¯bb̄ channel).
During the first year of operation, the main task will be to commission and to calibrate the ATLAS detector
in situ. The Z → ℓℓ process will be used to set the absolute electron and muon scales in the electromagnetic
calorimeter and tracking detectors respectively. The tt¯ events might be used to establish absolute scale for jets,
ETmiss and to understand the b-tagging performance. Very likely the initial luminosity of only 1031 − 1032 cm−2 s−1
will be available at the beginning, extending the time needed to gather statistics of 10 f b−1 [17].
II.3. Inner Detector
5
II.3 Inner Detector
The most inner part of the ATLAS detector constitutes the inner detector, which is comprised in the solenoidal
magnetic field of 2 T. It has three systems of detectors built in different technologies:
• Pixel detectors are based on semiconductor silicon detectors formed in micron-size pixels;
• Semi-Conductor Tracker (SCT) also uses semiconductor detectors; however, sensors are forming a few
centimeter-long strips;
• Transition Radiation Tracker (TRT) is based on transition radiation that is radiated by particles passing
through gaseous medium.
The inner detector parameters are summarized in Table II-1.
II.3.1
Pixel Detectors
The pixel detector system should provide information for the pattern recognition of tracks close to the interaction
point. This largely determines the ability of the inner detector to find secondary vertices. In order to achieve
these criteria, semiconductor detectors were chosen because they have a good spatial resolution and a very fast
response time. In the case of the ATLAS detector, they are reversed-biased n+ − on − n junctions. The ionizing
particles, while passing through this detector, produce electron-hole pairs along their track. An external electric
field separates them before they recombine. Electrons drift towards anode and holes to the cathode producing
electronic signal.
The pixel detectors are formed into 3 coaxial barrels. The first layer at a distance of ∼ 4 cm has η coverage
|η| < 2.5. The next two layers, positioned at 10 and 13 cm, cover region |η| < 1.7. At each side of the interaction
point there are also 3 disks that will give position measurement for particles strongly bent in the magnetic field
or traversing detector for higher η.
The basic module of pixel detectors is the same in a barrel and at the disks. Each module is 62.4 mm long and
21.4 mm wide, with 61440 pixel elements giving resolution of 12 µm in Rφ direction and 66 µm in z direction in
the barrel and 12 µm in Rφ and 77 µm in z in the disk section.
The pixels deliver three position measurements of high precision for the determination of impact parameter
and secondary vertex of short living particles like B-mesons or τ leptons.
II.3.2
Semiconductor Tracker
The Semiconductor Tracker is the next layer of tracking detector and is divided into a barrel and end-cap parts.
The barrel of the SCT consists of 8 layers of silicon micro-strip detectors covering |η| < 1.4. In the end-cap part
there are 9 wheels on each side of the interaction point covering 1.4 < |η| < 2.5.
The basic module is comprised of four detectors (hybrids). The two rectangle shape detectors are connected
to form a strip and glued together back-to-back with two other detectors at 40 mrad angle in order to measure the
z position. The sensor area has the size the of 80 µm × 12 cm in Rφ and z direction respectively.
The modules in the end-caps will form a ring around the beam axis. The strips are separated from each other
depending on the position on the ring varying from 54, 4 µm to 94 µm. The spatial resolution of 16 µm in Rφ
direction and 580 µm in z direction should be achieved.
The SCT will give 8 position points per track. This information will be used for momentum, impact parameter, vertex position and pattern recognition measurements.
6
II.3.3
C II. T ATLAS 
Transition Radiation Tracker
The Transition Radiation Tracker is build from straw detectors. Their small dimensions and the isolation of
active wires in small gas volumes allow them to work in high multiplicity track environment expected at LHC
experiments. Straw tubes are particle detectors based on the same principle as a proportional counter. The basic
set-up of the proportional counter is a cylinder with conducting walls and a thin wire of typical 15 − 50 µm
diameter. The cylinder is filled with a suitable gas and a positive potential is applied to the wire. Straw tubes
also operate in the proportional mode, e.i. when ionizing particle passes the proportional counter electrons are
released and they drift to the anode wire. In the vicinity of the wire they encounter a strong electrical field
and are accelerated to the energy that allows them to ionize another molecule. The additional electrons from
secondary ionization are also accelerated and after obtaining sufficient energy they can ionize another molecule.
The resulting cascade process is called gas amplification. The charge produced in that process is proportional
to the number of electrons initiating the gas amplification. A current is induced on the anode wire that can be
detected by sensitive electronics.
The TRT barrel consist of ∼ 36 layers of 4 mm diameter straw tubes having a 30 µm diameter of 0.6 µm
gold-plated wolfram wire. The modules operate in gas mixture in proportions of 70/27/3 (Xe/CO2 /O2 ). The TRT
should deliver measurements of ∼ 36 points (with 170 µm resolution per straw) for charged particle tracks with
|η| < 2.5 and pT > 0.5 GeV.
Table II-1: Performance parameters of the inner detector [11].
System
Position
Resolution
σ (µm)
Pseudorapidity η
coverage
Pixels
B-layer
2 barrel layers
3 end-cap disks
Rφ - 12, z - 66
Rφ - 12, z - 66
Rφ - 12, z - 77
|η| < 2.5
|η| < 1.7
1.7 < |η| < 2.5
Silicon strips
4 barrel layers
9 end-cap wheels
on each side
Rφ - 16, z - 580
Rφ - 16, z - 580
|η| < 1.4
1.4 < |η| < 2.5
Axial barrel straw
Radial end-cap
170 (per straw)
170 (per straw)
|η| < 0.7
0.7 < |η| < 2.5
TRT
II.3. Inner Detector
7
Magnets
Inner Detector
Electromagnetic calorimeter
Muon detectors
Hadronic calorimeter
Figure II-1: Overall layout of the ATLAS detector.
SCT
TRT
Pixels
Figure II-2: Schematic view of the ATLAS inner detector [11].
8
C II. T ATLAS 
II.4 Calorimeters
The inner detector is situated in the calorimetric system of the ATLAS detector. There are two main subsystems:
electromagnetic and hadronic. Both are sampling calorimeters, which means that they absorb energy in highdensity steel and periodically sample the shape of the resulting particle shower, inferring the energy of the
original particle from this measurement.
II.4.1
Electromagnetic calorimeter
The electromagnetic (EM) calorimeter absorbs energy from particles that interact electromagnetically, which
include charged particles and photons. It has high precision, both in the amount of energy absorbed and in the
precise location of the energy deposited. The energy-absorbing materials in the ATLAS detector are lead and
stainless steel, with liquid argon (LAr) as the sampling material. A cryostat around the EM calorimeter keeps it
sufficiently cool.
The EM calorimeter covers pseudorapidity region |η| < 3.2 and has a special, accordion shape to create electromagnetic shower inside detector. Just in front of EM calorimeter, there is a presampler calorimeter installed,
which is used to find correction for the energy lost up to EM calorimeter (Inner Detector, cryostats, coils, etc.).
It is divided into a central (barrel) part (|η| < 1.475) and two end-caps (1.375 < |η| < 3.2). Each of the endcaps calorimeters form two coaxial rings. Outer wheel is covering (1.375 < |η| < 2.5) and inner (2.5 < |η| < 3.2).
In the region of |η| < 2.5 the EM calorimeter has 3 sections: strips, middle and the back. Together, total
thickness of the EM calorimeter varies from 24 radiation length (X0 ) for the EM barrel part at η = 0, to 35 X0
in the end-caps at η = 2.5. The strips have constant thickness of ∼ 4X0 , while the middle section absorbs almost
all particles energy ∼ 16X0 . The granularity of sub-detector in ∆η × ∆φ is following: 0.003 × 0.1 in the strips,
0.025 × 0.025 in the middle and 0.05 × 0.025 in the back section. This division of detector is useful for particle
identification and separation (e/γ/π). The fine granularity is also a base for reconstruction of hadronic τ-jets, as
described in Chapter VI.
Usually, the energy resolution is parametrized as
∆E
a
c
= √
,
⊕b⊕
E
E[GeV]
E[GeV]
(II.1)
where a represents the statistical fluctuations in the shower development, b is constant term which is dominated
by different response to electromagnetic and hadronic shower components, but also reflects uncertainties in
the energy measurements due to mis-calibration, cracks, longitudinal leakage, etc., c corresponds to the noise
(electronic noise, pile-up) and ⊕ express customary notation for the addition in square, so Equation II.1 reads as
follows:
s
a2
c2
∆E
.
=
+ b2 + 2
E
E[GeV]
E [GeV]
The contribution from the pile-up and electronic noise was found to be small (below 0.3% for 50 GeV photons) [22]. Thus, the energy resolution of EM calorimeter, confirmed with test beam data, is parametrized usually
as:
•
∆E
E
=
√ 10%
E[GeV]
⊕ 0.2% in EM barrel part,
•
∆E
E
=
√ 12%
E[GeV]
⊕ 0.5% in EM end-cap part,
where ∆E is the energy resolution and E - the particle energy [10].
II.5. Muon System
II.4.2
9
Hadronic calorimeter
The hadronic (HAD) calorimeter absorbs energy from particles that pass through the EM calorimeter, but interact
via the strong force (neutral hadrons). It is less precise both in the energy magnitude and in the localization
(within about 0.1 × 0.1 only in ∆η × ∆φ). The energy-absorbing material is steel with scintillating tiles that
sample the energy deposited.
The tile calorimeter has 8 meters in diameter and covers 12 meters along the beam axis. The far-forward
sections of the hadronic calorimeter are contained within the EM calorimeter’s cryostat and use liquid argon as
well.
The hadronic calorimeter is divided into 3 sections in z direction: the central and two extended barrels. The
granularity of a hadronic barrel part is ∆η × ∆φ = 0.1 × 0.1 in region of |η| < 3 and 0.2 × 0.2 for 3 < |η| < 4.9.
This granularity will affect the expected energy resolution:
•
∆E
E
=
√ 52%
E[GeV]
⊕ 3.0% in HAD barrel part,
•
∆E
E
=
√ 75%
E[GeV]
⊕ 5.0% in HAD end-cap part,
where term c from Equation II.1 was found to be small in the hadronic calorimeter during fits to the year 1998
test beam measurements [10, 23].
The hadronic calorimeter is designed to stop as much hadronic shower in its volume as possible and to limit
shower propagation into the muon system.
II.5 Muon System
The muon detectors are placed outside the inner detector and calorimeters. In the magnetic field of air-core
toroids muon tracks are bent and transverse momentum can be calculated. We distinguish two sub-systems,
according to their functionality.
The first part of the muon system are precision chambers - Cathode Strip Chambers (CSC) and Monitored
Drift Tubes (MDT). The CSC is built from multi-wire proportional chambers, where charge induced on cathode
wires gives position measurement. The MDT is a system of proportional drift tubes with diameter of 30 mm,
where position is obtained from electron drift time to anode. Tubes are set up in 2-3 layers per each chamber.
The trigger detectors constitute the second part which covers region |η| < 2.4, and in the barrel part are
built from Resistive Plate Chambers (RPC) while in the end-caps regions from Thin Gap Chambers (TGC). The
trigger is based on a coincidence of signal in the first layer (station) and a range of wires in the second or third
station. Such coincidences define trigger Region of Interest (RoI), which size in ∆η × ∆φ plane is ∼ 0.1 × 0.1 and
where a muon with at least 10 GeV could be spotted [10, 11].
II.6 Magnets
There are two magnet systems in the ATLAS detector. The main task of the central solenoid is to provide the
inner detector with 2 T magnetic field. In order not to introduce additional material, the central solenoid and
electromagnetic calorimeter share common vacuum vessel. This part of the system has length of 5.3 m and inner
diameter of 2.46 m.
Outside the calorimeters start superconducting air-core toroids which supply the muon spectrometer with
magnetic field. They consist of a 26 m long barrel part with an inner bore of 9.4 m and outer diameter of 19.5 m,
and two end-caps with lengths 5.6 m and inner bores of 1.26 m, inserted at each end of the barrel. Each toroid
has eight flat coils symmetrically arranged around the beam axis generating peak field of 4 T. The magnetic field
is perpendicular to the muon trajectories in broad η range and its total bending power, integrated between the
first and the last muon chambers, increases from about 3 Tm at η = 0 to about 8 Tm at |η| = 2.8 [10, 11].
10
C II. T ATLAS 
II.7 Trigger and Data Acquisition
The signal from New Physics will have to be extracted from the well known Standard Model physics processes.
There is even more than 8 orders of magnitude difference in the expected cross-sections between the signal and
the background, so it is crucial to very selectively filter events that possibly contain new physics.
The main function of the trigger system is to reduce data stream from 40 MHz (from bunch interactions) to
100 Hz feasible to write out to permanent storage. The trigger system consists of three levels, each depending on
the decision of the previous one.
The first level trigger (LVL1) is based on very simple quantities from dedicated set of detectors (muon trigger
chambers, calorimeters at low granularity). The simple algorithm implemented in hardware electronic decides
whether to pass an event to a higher level. It also builds Region of Interest - the region of detector, which should
be read-out by the second level of trigger in order to have more detailed information about the event.
The second level trigger (LVL2) verifies LVL1 decision by reprocessing information from the detectors
in a given RoI (muon or calorimeter system) and can evaluate additional features basing on information from
SCT/Pixel and TRT detectors.
The third level trigger (LVL3) is usually called an Event Builder and at this level complete event with information from all detectors is constructed. It processes the selection according to algorithms similar to the off-line
ones.
The relevant for the analysis presented in these theses is a τ-trigger. The so called “Trigger menu” consists of
two types of selections with τ signatures: τ60i and τ35i + xE45. The first one requires isolated τ-jet with at least
60 GeV deposited in EM calorimeter . The second one selects τ-jets with at least 35 GeV of transverse momenta
and the missing ET < 45 GeV [11].
II.8 ATLAS Data and Computing Model
II.8.1
Event Data Model
The ATLAS detector will produce enormous amount of data. In order to efficiently handle the information readout from the detector, the Event Data Model with four levels of data format was proposed.
The raw data is usually referred to the byte stream output of the high level trigger (LVL3). The expected
size of this data will be 1.5 MB per event and will be produced at the rate of 150-200 Hz. The events will not be
usually ordered in time, due to parallel processing and different time needed by high level trigger algorithms for
event processing.
Two additional steps will be performed for data processing. The first one will build the Event Summary Data
(ESD) as an output of reconstruction. The basic objects at this level will be calorimeter clusters, hits and tracks
from the inner detector, energy deposition in cells of the calorimeter, combined muon tracks, candidates for
electrons, photons and τ-s. It will allow particle identification, track re-fitting, jet calibration and other studies. It
is foreseen that ESD size will take 500 kB per event.
The second step will process the Analysis Object Data (AOD) from the ESD. The AOD will be a reduced
event representation of ESD data. It will contain candidates for specific object (γ, τ − jet, etc.) and more detailed
information on quantities used for its identification, like neural network weights, likelihood values, etc. It is
expected that it will take 100 kB per event.
The decreasing event size after each level of reconstruction process allows a user to process more the AOD
than the ESD or the raw events in the same time.
Additionally, the ATLAS Collaboration defined Tag Data (TAG) format. The TAG data are meta-data describing event contents that will enable faster and efficient access to this event later, during user analysis. It will
contain simple, trigger-like information, e.g. event with 2 leptons with pT above 10 GeV threshold. The assumed
average TAG data size is 1 kB per event [24].
II.9. Summary
II.8.2
11
Grid environment
The idea of Grid [25] is to use distributed resources: processors, storage and network, as one system. It is now
possible due to the development of fast networks (2.5-10 Gbps) and additional software, called “middle-layer”,
installed at all computing centers (also called “sites”). The main task of a middle-layer is to provide interface
between heterogeneous hardware deployed at sites, and software run on them.
The Grid resources are grouped in Virtual Organizations (VO). Usually VO are formed by communities
of researches that work on a common project. The ATLAS VO gathers institutes participating in the ATLAS
experiment that are willing to share their computational resources with other members of the collaboration.
A grid job must be described in the Job Description Language, with information about a program to be
executed, required input files, desired machine architecture, memory, disk space, etc. A dedicated grid service,
called Resource Broker (RB) decides on the basis of this information where to execute a user job to optimize
overall performance of the system. Usually the decision is based on physical location of the data, which is
dependent on the data distribution model.
The LHC experiments developed a hierarchical data distribution model, with CERN being its Tier 0, 11 large
national laboratories with sufficient manpower to operate 365 days per year, 7 days a week and 24 hours per day,
as well as with resources for keeping a part of the raw, the ESD and the AOD data, forming Tier 1. A number
of small institutes around the world will constitute Tier 2 sites which will be responsible for maintaining a local
copy of the AOD data for physics studies.
It is expected that the ATLAS experiment itself will produce 1.3 PB of raw data per year. Together with
reconstructed events and MC data, 10 PB per year will be required. This amount of data can not be stored or
processed in one institute or laboratory (e.g. CERN) only. Since grid environment offers computing and storage
power “on demand”, it is considered as a reasonable solution for the operation model.
The enormous processing power offered by the Grid can be also used to resolve computing requirements of
particle physics today. Thousands of processors may run common tasks for the whole collaboration. These steps
are generation of physics events, simulation and digitization. The two last actions are time consuming but can be
easily split into parallel jobs. The reconstruction phase, the ESD and the AOD production, should also be done
centrally. The last step, the user analysis, is quite specific for each process considered, and should be run by the
physicist doing given analysis.
II.9 Summary
The physics goals set for new high energy physics experiments require building a detector with large acceptance
in pseudorapidity and almost full coverage in azimuthal angle. It should also have an efficient tracking system
and excellent calorimeters resolution.
The ATLAS detector consists of a number of detectors arranged in layers around the beam axis. The closest
to the interaction point are position and tracking detectors (Pixels, SCT and TRT). Next are calorimeters that,
by absorption of particle, measure its energy. The most distant are detectors of particles that were not absorbed
earlier - the muon chambers. In order to obtain as full η coverage as possible, additional detectors are placed
along the beam direction in form of layers of rings.
All these detectors should enable precise measurements of particle position, momentum and energy deposition with high granularity and resolution in search of new physics: quest for Higgs boson, hints for supersymmetry or other scenarios for New Physics.
The amount of data expected to be registered during run-time of the experiment, together with Monte Carlo
samples used for physics studies, require unprecedented storage, computer power and fast networks for data
processing and transfer that at present can be offered only by the grid environment.
12
C II. T ATLAS 
C III
T H B P
III.1 The Higgs Mechanism in the Standard Model
The Standard Model is a theory that combines our knowledge about the strong and electro-weak interactions of
elementary particles. It describes particles and forces known from experiments in the language of the gauge field
theory, where fermion fields correspond to particles and gauge fields are responsible for interactions [26].
The basic principle of the SM is the gauge invariance. Usually, we describe a system by writing down its
Lagrangian. The Lagrangian is invariant under the gauge transformation, if a substitution:
ψ(x) → ψ′ (x) = e−iα(x) ψ(x) ,
where ψ(x) is the field, α(x) - the phase and the i - the imaginary unit, leaves the Lagrangian unchanged or the
change is a full derivative.
The SM is based on the S U(3)color × S U(2)L × U(1)Y group. The first term describes a strong interaction
while two others contain electroweak force. Since the gauge bosons of one group do not transform under gauge
symmetries of the other, we can write down the Lagrangian as:
Y
1 j
1
1
j
LS = ψ̄iγµ ∂µ + ig1 Bµ + ig2 T j Wµ + ig3 λaGaµ ψ − Bµν Bµν − Wµν W jµν − GaµνGaµν ,
(III.1)
2
4
4
4
j
where one Bµ , three Wµ and eight Gaµ fields are gauge bosons, Y, T j (j=1,2,3) and λa (a=1,2,...,8) are the group
generators corresponding to U(1)Y , S U(2)L and S U(3)color groups, three gm (m=1,2,3) are the gauge couplings
and γµ are Dirac matrices. The weak hypercharge is defined as a doubled difference of electric charge Q and the
weak isospin Iz : Y = 2(Q − Iz ).
The observed masses of fermions and bosons require that the gauge symmetry is spontanously broken. This
is achived by writing the full lagrangian as:
L = LS + LS S B ,
where LS is defined by Equation III.1 and LS S B is a term responsible for the spontaneous symmetry breaking
!
φ+
and the mass generation. In the SM it is done by introducing a new iso-doublet of scalar fields φ =
,
φ0
called the Higgs field [27] and writing LS S B that it includes interactions of the scalar field with gauge bosons
and fermions:
LS S B = (Dµ φ)† (Dµ φ) − VHiggs (φ) − LYukawa ,
where
j
Dµ = ∂µ + ig1 Y2 Bµ + ig2 T j Wµ
is a covariant derivative,
14
C III. T H B P
VHiggs = µ2 (φ† φ) + λ(φ† φ)2
is the Higgs potential energy term with interaction of the scalar field with itself, µ and λ are free parameters and
LYukawa = g f [ψ̄R (φ† ψL ) + (ψ̄L φ)ψR ]
describes the interaction between Higgs and fermion fields. The ψ(L,R) (ψ̄(L,R) ) are left-handed and right-handed
fermionic fields (and their conjugate) respectively and g f is a constant coupling of Yukawa interaction.
In the case of µ2 < 0, the Higgs self-interaction term, VHiggs , has a "mexican-hat" shape with the minimum
2
µ
value at |φ2 | = − 2λ
≡ − ν2 . The ground state, the vacuum, corresponds to a particular value of the Higgs field
which is compatible with the minimum. Since the Higgs field of the vacuum ground state is in general not
invariant under S U(2) × U(1), the gauge symmetry is spontaneously broken. However it must be invariant under
U(1) of electromagnetism. So only the neutral component of the Higgs doublet can assume the non-zero vacuum
expectation value. Without loss of generality we can choose the vacuum as


 0 
hφi =  √ν 
2
2
The physical particles are obtained by mixing fields from the Lagrangian: the charged W bosons are the
linear combination of Wµ1 and Wµ2 :
Wµ± =
√1 (Wµ1
2
± iWµ2 ),
and neutral bosons, photon and Z, are the combination of Bµ and Wµ3 :
!
!
!
Bµ
cos θW sin θW
Aµ
,
=
Wµ3
− sin θW cos θW
Zµ
where θW is the weak mixing angle. It gives also a relationship between the W and Z masses: mW = mZ cos θW .
The SM Higgs boson is a CP-scalar and its couplings to fermions (f) and gauge bosons (V) are related to
their mass (m f and mV for fermions and bosons respectively) and are given by:
gh f¯ f =
√
2 mf
,
v
2m2V
v ,
ghVV =
√
where v = ( 2G F )−1/2 = 246 GeV and G F = 1.16639(2) · 10−5GeV −2 is the Fermi constant of the weak
interaction. At the tree level, due to quadratic Higgs fields term in the lagrangian, the Higgs boson mass is
expressed as:
p
mh = −2µ2 ,
which is a free parameter of the theory.
The SM Higgs branching ratio and its width can be calculated and are shown in Figure III-1 and Figure III-2 [28] respectively∗ . In the low Higgs boson mass region, below 200 GeV, the decays into ττ is ca.
10%. At the mass point of 2mW (ca. 160 GeV) the BR(H → ττ) drops to ca. 1%, while at 2mZ (ca. 180 GeV) to
ca. 1 per mill. The natural Higgs boson width in the same mass range does not exceed 1 GeV. It increases rapidly
for higher masses, reaching ca. 600 GeV at mh = 1 T eV.
Despite the experimental success [29], the SM has a number of weaknesses. First, the SM introduces masses
of particles, but does not include gravity, so it must be only a low energy limit of more general theory. Second, the
hierarchy problem - there is an enormous gap between the electroweak scale of 250 GeV and the Planck (gravity)
scale MP = (G N )−1/2 = 1.22 · 1019 GeV, where G N is the Newton constant, with no interaction
between. Third
p
is the Higgs boson mass divergence. At the tree level Higgs boson mass equals to mh = −2µ2 . More accurate
calculations introduce fermionic and bosonic loops with contributions to the Higgs boson mass and are of order
Λ (the cut off scale till which the SM is valid). It requires so called "fine tuning" of the tree level mass parameter
to cancel the large quantum corrections. As the most elegant extension which overcomes some of those problems,
a minimal supersymmetric extension of the SM was proposed.
∗
Figure III-2 shows also decay widths for the MSSM model which will be discussed in Section III.2.
III.1. The Higgs Mechanism in the Standard Model
15
Figure III-1: The Standard Model Higgs boson branching ratio as a function of the Higgs boson mass mhS M .
In the low Higgs boson mass region, below 200 GeV, the decays into the W + W − , ZZ and bb̄ are dominant. The
decay into ττ pair drops from ca. 10% at 100 GeV to 1% at 160 GeV [28].
Figure III-2: The Standard Model and Minimal Supersymmetric Standard MAodel Higgs bosons widths as a
function of the Higgs boson mass [28]. In the MSSM total width depends also on tan β, one of the basic theory
parameters. The drop of h(H) Higgs boson width corresponds to critical Higgs boson mass MC , as discussed in
Section III.2.
16
C III. T H B P
III.2 The Higgs Mechanism in the Minimal Supersymmetric Standard Model
The Supersymmetry (SUSY) is a theoretical model that can solve some of the problems of the SM [30, 31].
In this theory we assume that the SM particles have also SUSY partners, which are connected together via the
Supersymmetry operator Q. This operator is an anti-commuting spinor that transforms bosons and fermions into
each other:
Q|Bosoni = |Fermioni,
Q|Fermioni = |Bosoni.
Table III-1 summarizes the naming convention and the correspondence between particles and their supersymmetric partners (usually denoted by ˜ over their symbol).
Table III-1: The expected SM and MSSM particles.
Particle
Symbol
Spin
Partner
Symbol
Spin
quarks
leptons
B boson
W boson
Higgs boson
gluon
q
l
B
W
H
g
1/2
1/2
0
0
0
0
squark
sleptons
bino
wino
higgsino
gluino
q̃
l˜
B̃
W̃
H̃
g̃
0
0
1/2
1/2
1/2
1/2
From the variety of supersymmetric models, we choose the one for which a minimal number of additional
parameters is required. The Minimal Supersymmetric Standard Model (MSSM) assumes only one superpartner
for a given particle and that the Higgs sector has two complex Higgs doublets Hu and Hd which create masses
for the u-type quarks and the d-type quarks respectively. The Higgs potential is minimized for the nonzero Higgs
field vacuum expectation values which equal vu (vd ) for Hu (Hd ) field respectively. The ratio of these vacuum
expectation values is taken as a basic parameter of the MSSM, apart from the CP-odd Higgs boson mass mA :
tanβ =
vu
.
vd
The Higgs doublets interact with gauge bosons, introducing the masses of the observed W ± and Z 0 bosons, but
leaving photons and gluon massless. We obtain five scalar boson states: CP-even neutral h and H, CP-odd neutral
scalar A and two charged scalars H ± . When CP-even Higgs squared-mass matrix is diagonalized to obtain the
physical CP-even Higgs states, the mixing angle α can be introduced:
!
!
!
Hd
cos α sin α
H
=
Hu
− sin α cos α
h
and at tree level is given by the following expression [31]:
cos2 (β − α) =
m2h (m2Z − m2h )
m2A (m2H − m2h )
,
where mh(H) is the mass of lighter (heavier) CP-even Higgs boson given by [32]:
q
1 2
2
mh(H) = (mA + mZ ) ∓ (m2A + m2Z )2 − 4m2A m2Z cos2 2β
2
and mZ is the Z boson mass.
III.2. The Higgs Mechanism in the Minimal Supersymmetric Standard Model
17
The couplings of the different Higgs bosons to fermions (taken from [33]) are presented in Table III-2. We
can notice that CP-odd Higgs boson A does not interact with gauge bosons at all, its interaction with up-type
quarks is strongly suppressed when compared to the SM predictions and the coupling to down-type quarks (τ
lepton in particular) is strongly enhanced (if tan β is large). The couplings between CP-even Higgs bosons and
SM particles are more complex and are usually discussed in various approximations.
Table III-2: Neutral Higgs boson couplings to fermions and gauge bosons in the MSSM normalized to the SM
Higgs boson couplings [33].
Φ
gΦūu
h
cos α/ sin β →1
→− f1 + f2 / tan β
H
gΦd̄d
→− f tan β+ f2
− sin α/ cos β →tan1β
→ f − f2 / tan β
→tan β
1
sin α/ sin β →−1
A
cos α/ cos β →− f1 tanβ+ f2
1/ tan β
gΦVV
sin(β − α) →1
→− f1 +(1+ f2 )/ tan β
cos(β − α)
tan β
→ f1 +(1− f2 )/ tan β
→−1
0
In Table III-2, two limits are shown, which are obtained using trigonometric relation, for example:
gΦdd = ghττ = −
sin α
= sin(β − α) − tan β cos(β − α)
cos β
and two situations are considered: mA > MC and mA < MC , where the critical Higgs mass MC :
q
min =
=
m
MC = mmax
m2Z + ǫ.
H
h
The mmax
is the maximal mass value for the lighter of two CP-even Higgs bosons, mmin
H is the minimal value
h
for the heavier of two CP-even Higgs bosons and ǫ represents radiative corrections, which are positive and to
leading order in mt grow like:
MS2 3G F m4t
,
log
1
+
ǫ= √
m2t
2π2 sin2 β
where mt is the top quark mass and MS is the squark mass. In this approximation the upper arrow (in the second
and the third line) of Table III-2 represents:
mA > MC : cos α ≈ sin β ≈ 1 and sin α ≈ f1 − f2 / tan β
and the lower arrow:
mA < MC : sin α ≈ − sin β ≈ −1 and cos α ≈ − f1 + f2 / tan β .
Terms:
f1 =
m2A + m2Z
ǫ ′ /2
,
f
=
2
m2H − m2h
m2H − m2h
18
C III. T H B P
contain another radiative correction to the Higgs mass, determined by a parameter ǫ ′ related to the ratio of µ/MS :
ǫ′ =
MS2 i
m4t µ h A3t
GF
4α s
6At ih
,
1
−
log
−
√
π
m2t
2 2π2 sin2 β MS MS3 MS
where µ is the higgsino mass, At is a stop trilinear coupling and α s is a strong running constant [33].
In Figure III-3 the exemplary MSSM Higgs boson branching ratio is presented. A more detailed discussion
can be found in [28]. The branching ratio for A → ττ decays stays at the level of 8-11% in broad mA range, while
for h → ττ branching ratio shows a sudden drop at the critical mass of MC .
Figure III-3: The branching ratio of the MSSM h (left), H (middle) and A (right) Higgs bosons for non-SUSY
decay modes as a function of their mass for tan β = 30 (for the H boson also for tan β = 1.5) and vanishing
mixing. The common squark mass has been chosen as MS = 1 T eV [28].
III.3 Experimental limits
At the Large Electron and Positron (LEP) collider, the SM Higgs boson was expected to be produced mainly in
association with Z boson through the Higgsstrahlung process e+ e− → hS M Z. At the LEP experiments evidence
for the Higgs boson was not found, only the lower mass limit for this particle was set-up. The following two
scenarios were considered: the background scenario, where contribution from only background was assumed,
and the signal + background scenario, where Higgs boson test mass mH was added. Then, the confidence level for
signal + background hypothesis CL s+b and only background CLb were estimated. The ratio CL s = CL s+b /CLb
is shown in Figure III-4. The lowest hypothetic (test) mass giving CL s = 0.05 is taken as the lower bound
of the mass at the 95% confience level. The combined LEP data yield limit at 114.4 GeV, while the expected
limit is 115.3 GeV. The difference reflects a slight excess observed in the data with respect to the background
expectations at high masses [2].
The MSSM model predicts that at LEP accelerator Higgs boson can be produced in Higgsstrahlung process
+
−
e e → Zh, ZH and in associated (pair) production e+ e− → Ah, AH, if kinematically allowed.
In the decoupling regime of the MSSM (i.e. when Higgs bosons A, H and H ± are heavy and nearly degenerate
in mass), the h boson has almost identical couplings as the SM Higgs boson. Thus, for mA > 200 GeV, the Higgs
boson h discovery reach is nearly identical to that of the SM Higgs boson of the same mass.
The tree-level value for mh within MSSM is determined by the ratio of Higgs doublet expectation values
tan β, the CP-odd Higgs boson mass mA and the Z-boson mass mZ . Beyond the tree-level, the correction to
mh comes from top quark mass mt and the energy scale of SUSY breaking MS US Y , which is common mass
parameter for all sfermions at the electro-weak scale. In the searches presented below the top quark mass mt is
fixed at mt = 179.3 GeV † .
†
The value of the top quark published at the time the reported analysis was done. Present (2006) value is lower, 171.4 ± 2.1 GeV [34].
III.3. Experimental limits
19
Figure III-4: The confidence level for the signal plus background hypothesis CL s , as a function of test mass mH . A
solid line: observation; a dashed line: median background expectation. The dark and light shaded bands around
the median expectation for the background hypothesis correspond to the 68% and 95% probability bands. The
intersection of the horizontal line for CL s = 0.05 with the observed curve is used to define 95% confidence level
lower bound on the mass of the SM Higgs boson [2].
Due to a large number of free parameters a complete scan of the whole MSSM parameter space was not
possible. Therefore, the search has been published in a few, so called, benchmark scenarios. The remaining
parameters of the model, the M2 - a gaugino mass at the electro-weak scale, µ - the strength of the supersymmetric
Higgs mixing, A - a common trilinear Higgs-squark coupling (please distinguish it from CP-odd Higgs boson
A) and mg̃ - the gluino mass, are fixed. Three of these parameters define the stop and sbottom mixing parameters
Xt = A − µ cot β and Xb = A − µ tan β. Thus the values of t˜ and b̃ sector as well as the gaugino masses are fixed
(MS US Y = Mt˜ = Mb̃ and Ab = At = Xt + µ cot β), while tan β and mA will vary [3, 35]:
scenario for which the parameters are chosen so the maximum possible Higgs boson mass as a
• the mmax
h
function of tan β is obtained:
mt = 179.3 GeV, MS US Y = 1 T eV, µ = −200 GeV, M2 = 200 GeV,
mg̃ = 800 GeV, Xt = 2 MS US Y , Ab = At ;
˜
• the no mixing scenario is similar to mmax
h , but with a vanishing mixing in the t sector and a higher SUSY
mass scale to avoid the LEP Higgs bounds:
mt = 179.3 GeV, MS US Y = 1 T eV, µ = −200 GeV, M2 = 200 GeV,
mg̃ = 800 GeV, Xt = 0, Ab = At ;
• the large µ scenario is characterized by a relatively large value of |µ| compared to MS US Y . Additionally, it
is assumed that MS US Y is small and there is a moderate mixing in the scalar top sector:
mt = 179.3 GeV, MS US Y = 400 GeV, µ = 1 T eV, M2 = 400 GeV,
mg̃ = 200 GeV, Xt = −300 GeV, Ab = At .
20
C III. T H B P
scenario, which should set the most
Here, we just summarize the LEP-2 results presented in [3]. In the mmax
h
restrictive bounds, at 95% level Higgs boson mass should be greater than mh > 92.8 GeV and mA > 93.4 GeV.
For the same scenario, and mt = 174.3 GeV, a tan β region 0.7 < tan β < 2.0 was excluded. The large µ scenario
was nearly completely ruled out.
and nomixing scenarios as well.
The results obtained by Tevatron experiments are presented in terms of mmax
h
In Figure III-5 DØ and CDF limit contour with LEP-2 bounds extrapolated to tan β = 100 are presented [36].
The excluded parameter space complements LEP-2 results for high tan β and mA . However, large regions of mA
and tan β will be accessed only by experiments at the LHC accelerator.
Figure III-5: The excluded region at 95% confidence level in (mA , tan β) plane for the no-mixing (left) and mmax
h
scenario. The values of mt = 172.7 GeV and µ = +0.2 T eV or µ = −0.2 T eV are assumed. The LEP-2 limits are
extrapolated for tan β > 50 [36].
III.4 Summary
The Standard Model is considered as an effective approximation at the electro-weak scale (246 GeV) of a more
general theory. One of the theoretical models, that can be the extention of the SM is the Minimal Supersymmetric
Standard Model, in which more basic symmetry between fermions and boson exists at a scale of TeV.
In both models the Higgs mechanism is invoked to generate masses of all particles. However, the Higgs
mechanism also predicts the existence of physical Higgs boson(s) states, which has not been discovered yet.
The experimental search for this particle, which may originate either from the SM or the MSSM scenarios,
has led to the exclusion contours at the 95% level of confidence. The published results of the LEP-2 set allowed
region of mhS M > 114.4 GeV for SM Higgs boson [2] and mhMS S M > 92.8 GeV, mA > 93.4 GeV, tan β < 0.7 or
tan β > 2.0 for the MSSM [3].
C IV
T    bb̄H, H → ττ 
IV.1 Introduction
The prospects for the detection of the Higgs boson at the LHC have been evaluated using various physics processes and decay modes. Among them one is of special interest, namely the Yukawa induced associated production with bottom quarks, denoted here as bb̄H. The bb̄H will also mean bb̄h or bb̄A, depending on the context,
because we consider contributions from the lighter CP-even Higgs boson h, heavier CP-even Higgs boson H and
CP-odd Higgs boson A. In Figure IV-1 we show two lowest order Feynman diagrams contributing to the bb̄H
production process.
g
b
q
b
b
h/H/A
h/H/A
b
g
b
q
b
Figure IV-1: The Feynman diagrams for associated production of the Higgs boson with two high-pT bottom
quarks: gg → bb̄H (left) and qq̄ → bb̄H (right).
This production channel in the Standard Model is negligible, due to its small cross-section. However, in the
MSSM this mode is highly enhanced, due to proportionality of the coupling between Higgs and b-quarks to
tan β. For large values of the tan β, the production is dominated by the strongly enhanced associated bb̄H and
bb̄A production and the H/A → ττ branching ratio is about 10% in the mass range 200-500 GeV. The relative
contribution from the associated production is roughly 50% for tan β = 5 and about 90% for tan β = 20.
The studies for the detection of the Higgs boson with the ATLAS experiment [11] were focused on the
discovery potential of various decay modes: h → γγ, h → bb̄, H → ZZ → 4l important in the SM as well as
decays enhanced in the MSSM for large tan β: H/A → ττ and H/A → µµ. The MSSM parameters were chosen in
such a way that supersymmetric particles masses are large and the Higgs boson decay into them is forbidden. The
conclusions drawn from these studies showed that the complete region of parameter space mA = 50 − 500 GeV
and tan β = 1 − 50 should be accessible for Higgs-boson discovery in the ATLAS experiment. Over the large
fraction of the parameter space more than one Higgs boson and/or one decay mode would be accessible. The
most difficult region was identified as the moderate mA and tan β. For larger values of mA > 500 GeV only the
lightest Higgs boson might be observable.
In the minimal mixing scenario the predicted mh for mA > 140 GeV and tan β = 30 depends very weakly on
mA (see Figure IV-6). For larger values of tan β all Higgs bosons except h are heavy and degenerated in mass. The
investigations of Higgs boson decay into τ lepton pair with different Higgs production mechanisms and decay
22
C IV. T    bb̄H, H → ττ 
modes of τ-s based on the full simulation of the ATLAS detector were carried out for the ATLAS Physics TDR
[11]. More detailed studies within the MSSM of direct and Yukawa induced Higgs boson production mechanisms
in mass range 150 - 450 GeV were documented in publications [37, 38]. They concluded that the MSSM Higgs
boson can be discovered in ℓ had ETmiss mode over large range of (mA , tanβ) parameter space already at 30 f b−1 of
data. The contribution from ℓℓETmiss channel mode was concluded as negligible already in [38] and not discussed
afterwards. An extension of these studies to the mass range up to 800 GeV was performed for ℓ had ETmiss [39]
and had had ETmiss channel [40]. It was therefore very interesting to notice that in the analyses for VBF production
qq → qqH and H → ττ, the ℓℓETmiss channel was bringing ∼ 30% of an additional signal significance [41]. Thus
we decided to reevaluate signal and background for bb̄H process, including also ℓℓETmiss mode.
The total decay widths of the MSSM Higgs bosons differ significantly from that of the SM Higgs boson of
the same mass. For larger values of tan β, the width of the h-boson is usually larger than that of a SM Higgs.
However, it tends toward the SM value, as the h-boson mass approaches its maximal value for given value of
tan β. Consequently, in most cases, the h-boson width is much smaller than the experimental resolution expected
for the decay modes observable at the LHC. For the heavier H, A bosons the width is growing with mass and
tan β, but is not exceeding ∼ 10 GeV, for mA,H < 200 GeV.
The various theoretical aspects of modeling bb̄H process will be discussed in Chapter V. We concentrated
here on the main signal and background processes only. The backgrounds are the mixture of bb̄, Z/γ∗ , tt¯ and
W + jet, where jet is mis-identified as lepton . They can be significantly reduced by selection based on reconstructed leptons (including τ-s) and ETmiss . The studies of various Monte Carlo approaches to generate expected
background coming from Z/γ∗ , W and tt¯ processes are an important part of the analysis. The background from
associated bb̄Z and bb̄W was thus separately estimated. The different approaches to generate the tt¯ background
starting from the processes with two particles in the initial state and two in the final state (2 → 2) up to inclusive
(2 → 6) process are also discussed.
In Figure IV-2, the 5 σ discovery contour for H/h/A → ττ in (mA , tan β) plane is presented [39]. As already
mentioned earlier, the ℓ had ETmiss mode was found as primary discovery channel in bb̄H process in broad range
of the parameter space (in blue). The ℓ had ETmiss channel provides best sensitivity, due to its large rate (46%)
and more favourable kinematics of the τ-decay. The mass range above 450 GeV, where events can be triggered
efficiently by only the τ trigger, the had had ETmiss (green) should be combined with ℓ had ETmiss (red). The
ℓℓETmiss , as already mentioned, was considered negligible and has not been shown on that plot.
Figure IV-2: The MSSM parameter space with 5 σ discovery contour for the ATLAS experiment searches of
associated Higgs production [39].
The aim of the study presented in this chapter was to reevaluate, in comparative manner, the ℓℓETmiss vs
ℓ had ETmiss channels and their contributions to the total significance of the bb̄H, H → ττ process. The results
were obtained with SM cross-sections times branching ratio and could be used as a reference point for MSSM
scans, where cross-sections of the Yukawa induced bb̄H production is highly enhanced (∼ tan2 β). It will be
shown that ℓℓETmiss mode should not be neglected. For the lower mass range (below 200 GeV) it becomes important contribution and can extend signal significance.
IV.2. Events generation
23
IV.2 Events generation
In the presented analysis interactions of heavy quarks and gauge bosons lead to very promising experimental
signatures. Recently created framework AcerMC 2.0 [42] was designed for Monte Carlo simulations of such
events and it implements the massive matrix elements that describe associated production of heavy quarks, Z
and W bosons. The associated Higgs boson production is available as native Pythia process. The AcerMC
is a fortran-based framework interfaced to Pythia 6.214 [43], Tauola [44] and Photos [45] packages. It
provides framework to generate both native Pythia or native AcerMC processes. If not stated otherwise, Pythia
matrix elements were used to generate hard process events, while Tauola and Photos packages were used
for the correct simulation of τ-decays and radiative QED bremsstrahlung. Events generated with Pythia or
AcerMC native matrix elements were processed with Pythia parton shower model. The Data Challenge 2 (DC2)
recommended parameters for the underlying event (usually defined as everything except the two outgoing hard
scattered jets and consists of two components: hard - ISR + FSR and soft - beam-beam remnants) were set for
Pythia initialization [46]. All data samples used in this study are summarized in Table IV-1 for both ℓℓETmiss
and ℓ had ETmiss modes and different signal mass points.
The signal selection: We took into account two distinct Higgs boson signatures saturated by the following
production mechanisms: the gluon fusion and the associated production with bottom quarks.
The first signature veto the final state b-jet, the underlying process, primaly mediated by the virtual top-quark
loop, is a dominant Higgs boson production channel in the Standard Model. The second process is dominant at
large tan β in the MSSM. The final state b-jet is explicitly tagged. There are three approaches for modeling
this process. The direct bb̄ → H fusion with no high pT b-jet in the event (b-jet veto) has the highest crosssection. However, it is easier to reduce background for H → ττ decay channel requiring one identified b-jet
in the event. The second is associated Higgs boson and one b-quark production gb → bH that yields one high
pT b-jet. The third approach, gg → bb̄H, is characterized by at least two b-jets in the event. However, since
b-jet tagging procedure is not efficient enough, it is optimal to require tagging of only one b-jet. The analysis
presented here was guided by the default analysis scheme from the ATLAS TDR and the discussion of a possible
double counting of signal was beyond the scope of these theses.
The background selection: The background for the bb̄H process comes from bb̄, W, Z/γ∗ and tt¯ production.
We have estimated those backgrounds using different approaches or generating specifically sub-processes using
exact matrix elements in the hard process.
• The background from the single W production was estimated in different approaches for the hard-scattering
matrix elements used. The inclusive (2 → 1) single W production process with additional QCD jets from
initial state radiation has a large cross-section. It has been generated in five phard
bins∗ with 2.0 · 106 events
T
in each bin. Another approach takes a (2 → 2) W + jet hard scattering process. This background was
generated in five phard
bins as well, but since the cross-section has singularity, while pW
T
T → 0, the default
Pythia threshold on minimal pT of 1 GeV was applied. The associated bb̄W was generated with AcerMC
matrix elements. It has 3 orders of magnitude smaller cross-section times branching ratio, but has two
b-quarks in the final state and can fake signal events easier than W + jet events. We stress here that bb̄W
is part of the inclusive W + jet background.
• The irreducible Drell-Yan qq̄ → Z/γ∗ → ττ production will be the main background at the Higgs boson
mass at 120 GeV. However, for the same flavour (SF) leptons from τ decay in the final state also directly
produced Z/γ∗ → ℓℓ will be an overwhelming background at the production level. For not the same flavour
∗
(NSF) leptons in the final
√ state, †the direct Z/γ6 → ℓℓ will contribute only marginally. This background has
been generated in eight ŝ bins with 2.0·10 events in each bin. The results obtained with inclusive DrellYan process, discussed above, have been cross-checked with estimates for background from associated bb̄Z
production. Events were generated with AcerMC matrix elements.
∗ hard
p√T
†
denotes transverse momentum of the hard process.
ŝ denotes the center of mass energy of scattering partons equivalent to the mass of the out-going lepton pair.
C IV. T    bb̄H, H → ττ 
24
• The tt¯ background was generated with the AcerMC generator matrix elements. We considered (2 → 6)
resonant process gg, qq̄ → tt¯ → f f¯ f f¯bb̄ and complete gg, qq̄ → WWbb̄ → f f¯ f f¯bb̄. The off-shell (2 →
2) production process gg, qq̄ → tt¯ (as implemented in Pythia) was also taken into account.
• The bb̄ background was studied and results were published in [39]. It was concluded that the kinematical selections reduce sufficiently this type of background and that it can be safely neglected. It was not
reevaluated here.
For the analysis results presented here for the W and Z background we will use estimates from the inclusive
production and for the tt¯ background from the (2 → 6) process. Other approaches will be used only to control a
level of uncertainty of theoretical predictions.
Table IV-1: Summary on the σ × BR for the signal and background samples used in the analysis. For the Higgs
production the SM couplings are used. Effective branching ratio (BR) used for configuration with both τ → ℓνν,
BR = 0.127, for one τ → ℓνν and one τ → had ν, BR = 0.459. The τ → ℓνν and W ± → ℓν stand for the decay
to electron or muon. The decay of the top quarks was not forced.
σ × BR [pb]
τ decays
both τ → ℓνν τ → ℓνν, τ → had ν
Process
gg→ bb̄H(→ ττ)
bb̄ → H(→ ττ)
gb → bH(→ ττ)
gg→ H(→ ττ)
gg→ bb̄H(→ ττ)
bb̄ → H(→ ττ)
gb → bH(→ ττ)
gg→ H(→ ττ)
gg→ bb̄H(→ ττ)
bb̄ → H(→ ττ)
gb → bH(→ ττ)
gg→ H(→ ττ)
qq̄ → Z 0 /γ∗ (→ ττ)
mH = 120 GeV
mH = 150 GeV
mH = 200 GeV
√
ŝ > 50 GeV
gg, qq → bb̄Z(→ ττ)
qq̄ → W ± (→ ℓν)
qq̄, qg → W(→ ℓν) + jet
–
–
pW
T
> 1 GeV
Matrix element used
2.2·10−3
9.3·10−3
5.3·10−3
1.8·10−1
7.9·10−3
3.3·10−2
1.9·10−2
6.3·10−1
2.5·10−4
1.0·10−3
8.7·10−4
2.9·10−2
9.2·10−4
3.7·10−3
3.1·10−3
1.0·10−1
1.4·10−6
5.4·10−6
7.9·10−6
2.7·10−4
5.1·10−6
1.9·10−5
2.8·10−5
9.8·10−4
2.2·102
7.8·102
Pythia
3.5·100
1.3·101
AcerMC
Pythia
Pythia
Pythia
3.4·104
Pythia
7.6·104
Pythia
AcerMC
qq̄ → bb̄W(→ ℓν)
–
3.8·101
gg, qq̄ → tt¯ (off-shell)
gg, qq̄ →WWbb̄ → f f¯ f f¯bb̄
–
4.3·102
AcerMC
–
4.5·102
AcerMC
–
4.2·102
AcerMC
gg, qq̄ → tt¯ (on-shell)
IV.3. Events simulation
25
IV.3 Events simulation
The fully generated events were passed to the fast simulation package of the ATLAS detector, Atlfast 2.60
[47]. The Atlfast package reconstructs isolated leptons and photons, labels b-jets, c-jets, τ-jets and estimates
the missing transverse energy. This simulation provides parametrized response of the crucial detector performance figures, based on detailed Geant [48] calculations describing the passage of a particle through the detector [11]. Although to a large extent it represents the best performance of the detector, we believe that it is fairly
adequate for the comparative studies presented in these theses.
The labeling of τ-jets in the pseudorapidity range of |η| < 2.5 is based on the energy deposition profile in the
calorimeter and the number of tracks pointing to the calorimeter cluster. The more detailed study was already
performed on fully simulated events some time ago [49] and it was parametrized for the fast simulation. For the
analysis presented we have completed parametrization for jet energy calibration existing in [47] by the dedicated
statistical energy calibration of τ-jets. The detailed discussion can be found in the Appendix A.1. For signal
and Z/γ∗ background in the ℓ had ETmiss channel, where true τ-jets are present in the event, fixed efficiency of
50% was used. For the W and the tt¯ backgrounds the random τ-tagging procedure with efficiency of 50% and
pT -dependent rejection was applied.
The calibration of jet energies is needed to obtain realistic values for reconstructed kinematical quantities
(close to partonic ones) [50]. In the case of b-jets, Atlfast labeling algorithm relies on finding within cone
∆Rcone < 0.2 around the jet axis a b-quark after FSR with pT > 5 GeV. The calibration factor is pT -dependent
and for lower pT is of the order of 1.4. In this analysis the random b-jet tagging procedure with efficiency of
60% and rejection R = 90 against QCD jets (i.e. we accept 1 out of 90 QCD jets as a b-jet.) was applied on all
samples.
It is assumed that electrons and muons can be reconstructed in the pseudorapidity range of |η| < 2.5 with the
efficiency of 90%. The lepton‡ isolation for semi-leptonic decay inside jets is rather loose, this background can
be suppressed much more strongly in the analysis of the fully simulated samples. Fake leptons (e/jet separation)
were not included. All efficiencies§ are summarized in Table IV-2.
Table IV-2: The efficiencies ε and rejection R used in this analysis .
ℓℓETmiss
ℓ had ETmiss
Sample
Signal
Z/γ∗
background
W
background
tt¯
background
‡
Leptons
b-jet
tag
Rejection
QCD jets
Leptons
τ − jet
tag
b-jet
tag
Rejection
QCD jets
fixed
ε = 90%
random
ε = 60%
random
R = 90
fixed
ε = 90%
fixed
ε = 50%
random
ε = 60%
random
R = 90
fixed
ε = 90%
fixed
ε = 50%
random
ε = 50%
random
ε = 50%
random
ε = 60%
random
R = 90
fixed
ε = 90%
random
ε = 60%
random
R = 90
By lepton we mean electron or muon throughout this text.
The term “fixed” denotes that constant weight is applied, while “random” - random number generator was used. The specific values
were chosen in accordance with the ATLAS parametrization of the QCD jets rejection avaiable for the fast simulation.
§
C IV. T    bb̄H, H → ττ 
26
IV.4 Events selection
In our analysis the Higgs boson decay into τ-lepton pair is characterized by at least one lepton in the final state.
Thus we can start to filter interesting events on the base of a single or di-lepton trigger. In the case of ℓℓE miss
T
analysis the following selections, corresponding to the foreseen threshold values for the ATLAS experiment for
single lepton, di-lepton or τ triggers, were used:
• trigger selection - at least 1 isolated lepton in the event
– the single lepton trigger:
– peT ≥ 25 GeV in the case of 1 electron;
µ
– pT ≥ 20 GeV in the case of 1 muon;
– the di-lepton trigger:
– pe1,e2
≥ 15 GeV for 2 electrons;
T
µ1,µ2
– pT
≥ 10 GeV for 2 muons;
µ
e
– pT ≥ 15 GeV and pT ≥ 10 GeV for a pair of 1 electron and 1 muon;
• primary selection - the same nominal threshold as for Trigger selection, but exactly 2 leptons in the event
are required in order to reconstruct di-τ lepton pair mass.
In the case of ℓ had E miss analysis the selections used are the following:
T
• trigger selection - 1 isolated lepton in the event with pT ≥ 20 GeV;
τ− jet
• primary selection - Trigger selection + additional 1 τ-tagged jet with pT
≥ 30 GeV;
The possibility to trigger on hadronic τ decay + ETmiss was not included in the presented estimates. Given high
thresholds on the transverse energy of the τ trigger objects and ETmiss , which are allowed for the τ trigger stream,
it will contribute insignificantly to the recorded signal events rates and it was not discussed here.
As the next step of the selection, we chose the reconstruction of invariant mass of the τ-lepton system, for
which it is required to resolve neutrinos 4-momenta. This is made on the assumption that the τ-lepton is massless
and thus it decays collinearly. Two different formulas have been proposed and used since some time:
- the procedure prescription used in [37] or [38]: if E1 , E2 , û1 , û2 are energies and directions of measured
miss are the projections onto the x, y axes of the measured
visible τ-decay products respectively and pmiss
x , py
−−miss
−→
pT , then the energies Eν1 and Eν2 of the neutrino systems from τ-decay can be obtained by resolving the
system:
( miss
= (Eν1 · û1 ) x + (Eν2 · û2 ) x
px
.
miss
= (Eν1 · û1 )y + (Eν2 · û2 )y
py
The measurement accuracy of pmiss
and pmiss
and the assumptions used result in some cases in unphysical
x
y
negative solutions for Eν1 and Eν2 . Such events are excluded from the analysis. The reconstructed mass is
expressed as:
p
mττ = 2(E1 + Eν1 )(E2 + Eν2 )(1 − cos θ12 ) ,
(IV.1)
where θ12 is an angle between the directions of the measured τ-decay products;
- the procedure prescription used in [51] or [52]: the fractions of the two τ′ s momenta, which are carried by
the measured visible decay products, xτ1 and xτ2 , can be calculated by solving equations of conservation
of the transverse momenta in the Higgs decay. The physical solutions are those for which 0 < xτ1(2) < 1.
In these cases the invariant mass of the system of the visible decay products mvis is calculated and the
invariant mass of the τ-system is expressed as (see Appendix A.3):
mvis
,
(IV.2)
mττ = √
xτ1 · xτ2
IV.4. Events selection
27
where xτi are the fractions of momenta carried by the visible Higgs decay products. In the analysis of ℓℓETmiss
channel 2 leptons are used, while in ℓ had ETmiss channel - 1 lepton and 1 τ-jet. It has been already shown in [39]
that when only physical solution is considered both formulas are equivalent and lead to the same acceptance and
shape of the reconstructed mττ . For the analysis presented here we have chosen formula IV.2.
We also applied additional selection, following what proposed in [52]. The primary aim was to improve the
mass resolution without losing too many signal events. As it will be shown later, the additional selection indeed
improves mass resolution at rather small losses of the signal acceptance. The consecutive cuts in ℓℓE miss case
T
consisted of:
• threshold on the minimal angular separation between two leptons, |sin(∆φℓℓ )| > 0.2;
• threshold on missing transverse momentum, pmiss
> 30 GeV;
T
• threshold on the minimal angular separation between two leptons, cos(∆φℓℓ ) > −0.9;
• distance between two leptons in (η, φ) plane: ∆Rℓℓ < 2.8.
The additional selection for ℓ had E miss is similar to the ℓℓETmiss analysis, which allows for the consistent
T
comparison of performances in different final states. Also the same procedure is used for the reconstruction of the
invariant mass of the τ-pair, mττ (just the second lepton is replaced by the τ-jet). The consecutive cuts consisted
of:
• threshold on the minimal angular separation between lepton and τ-jet, |sin(∆φℓτ− jet )| > 0.2;
• threshold on
q the maximal missing transverse mass, calculated from lepton and missing transverse energy
ℓ,miss
mT
= 2pℓT pmiss
T (1 − cos(∆φℓ,pmiss )) < 50 GeV;
T
• threshold on missing transverse momentum, pmiss
> 30 GeV;
T
• threshold on the minimal angular separation between lepton and τ-jet, cos(∆φℓτ− jet ) > −0.9;
• distance between the visible τ’s decay products in (η, φ) plane ∆Rℓτ− jet < 2.8.
All consecutive selections (trigger, primary and additional) are called generic selection. After generic selection for the SF leptons in ℓℓE miss somewhat more stringent selection, directly oriented toward suppression of
T
potentially overwhelming Drell-Yan Z/γ∗ → ℓℓ background, is adopted. For the events with NSF leptons this
background can be considered as negligible:
• the interval of the invariant mass of di-lepton system, 20 GeV < mℓℓ < 80 GeV;
• increased threshold on pmiss
> 50 GeV.
T
The further analysis for each final mode, ℓℓETmiss (NSF and SF) and ℓ had ETmiss , splits into two streams: the
b-jet veto - when there is no b-jet in the event, and b-jet tag - with at least one b-jet. Details can be found in
Section IV.6.1. The complete list of selections and acceptances is given in Table IV-3 and Table IV-5 for ℓℓETmiss
and ℓ had ETmiss respectively.
Distributions of variables used for selections are presented in Figures IV-3 and IV-4. The background distributions are normalized to the total cross-section times branching ratio σ × BR for the given process, while the
signal is additionally scaled by a factor of 103 and 104 for |sin(∆φ)| > 0.2 and cos(∆φ) > −0.9 cut respectively¶ .
Please note also, that the invariant mass of the visible decay products is well localized and far from the Z-peak.
Thus the selection of events that have 20 GeV < mℓℓ < 80 GeV will reduce the Drell-Yan Z/γ∗ → ℓℓ background
for the SF leptons. In contrast to the invariant mass of the τ-system, the invariant mass of the system of visible
decay products (leptons) can be quite precisely reconstructed, but it does not show the resonant structure because
of the missing neutrinos momenta.
¶
We expect signal σ × BR to scale with parameter tan β with respect to the SM values used as a reference here.
C IV. T    bb̄H, H → ττ 
28
141
Scaled bbH
Z/γ
1
W±
Entries
Mean
RMS
161
1385584
0.0001314
0.4571
Underflow
0
Overflow 0.0008726
Integral
12.16
Skewness 0.0004813
Entries
707955
Mean
24.94
20.76
RMS
0
Underflow
Overflow 0.00766
Integral
6.708
Skewness 2.67
Scaled bbH
Z/γ
1
W±
tt
tt
10-1
10-2
10-1
10-3
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
0
20
40
60
80
sin(∆φ)
100 120 140 160 180 200
pmiss
[GeV]
T
171
Scaled bbH
Z/γ
W±
10-1
Entries
Mean
RMS
181
281912
-0.3018
0.5536
Underflow
0
Overflow 0.0003407
Integral
1.784
Skewness 0.6221
Entries
Mean
RMS
Scaled bbH
Z/γ
10-1
Underflow
0
Overflow 0.0003407
Integral
1.528
Skewness -0.3242
W±
tt
209860
2.027
0.5229
tt
10-2
10-3
10-4
-2
10
10-5
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
0
1
2
3
4
5
6
7
8
9
10
∆Rll
cos(∆φ)
191
Scaled bbH
Z/γ
10-1
W±
Entries
Mean
RMS
201
93163
40.49
12.69
Underflow 2.849e-06
Overflow 0.0005327
Integral
0.7487
Skewness
1.697
Scaled bbH
Z/γ
10-1
W±
tt
Entries
Mean
RMS
79692
52.15
24.15
Underflow
0
Overflow 0.002353
Integral
0.7275
Skewness
2.249
tt
10-2
10-2
-3
10
10-4
10-5 0
10-3
20
40
60
80
100 120 140 160 180 200
mll [GeV]
0
20
40
60
80
100 120 140 160 180 200
pmiss
T
Figure IV-3: Distributions of variables used for events selection in ℓℓE miss channel. The main backgrounds from
T
Z/γ∗ , W + jet and tt¯ are shown in different colors. Distributions are normalized to total σ × BR [pb]. The bb̄H
signal process, scaled by factor 103 for sin(∆φ) cut and 104 for cos(∆φ) cut, is shown for reference only.
IV.4. Events selection
29
141
Scaled bbH
Z/γ
1
W±
Entries
Mean
RMS
151
544836
0.003606
0.4698
Scaled bbH
Z/γ
1
Underflow
Overflow
Integral
0
0
9.016
Skewness 0.001733
Entries
Mean
RMS
17.24
14.73
Underflow
0
Overflow 0.0007921
Integral
4.649
Skewness
1.795
W±
tt
253836
tt
-1
10
10-2
10-3
10-1
10-4
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
0
20
40
60
80
100 120 140 160 180 200
sin(∆φ)
mmiss
T [GeV]
161
Scaled bbH
Z/γ
1
W±
Entries
Mean
RMS
171
221600
24.54
22.69
Entries
84018
Mean
0.01706
0.6034
RMS
0
Underflow
0
Overflow
Integral
1.099
Skewness -0.1833
Scaled bbH
Z/γ
Underflow
0
Overflow 0.009487
Integral
4.502
Skewness
2.794
W±
tt
tt
10-1
10-2
10-3
10-2
0
20
40
60
80
100 120 140 160 180 200
pmiss
[GeV]
T
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
181
Entries
59428
Mean
1.618
0.5533
RMS
0
Underflow
0
Overflow
Integral
0.9921
Skewness 0.3219
Scaled bbH
Z/γ
10-1
W±
tt
-2
10
10-3
10-4
10-5
10-6
0
1
2
3
4
1
cos(∆φ)
5
6
7
8
9
10
∆Rl,τ-jet
Figure IV-4: The same as Figure IV-3, but for ℓ had E miss channel.
T
C IV. T    bb̄H, H → ττ 
30
IV.5 Acceptance for signal and background events
The acceptance for a given cut was calculated as a ratio of a number of accepted events after the cut N acc and a
number of generated events N gen :
N acc
Acc = gen .
(IV.3)
N
In order to obtain the total acceptance for background processes generated in a phard
or mass bins, we summed
T
gen
acceptances in given bins Niacc /Ni weighed with corresponding cross-section σi and normalized to the total
P
cross-section for this process σtot = i σi .
Acc =
X N acc σi
i
gen tot ,
σ
N
i
i
√
where i enumerates pT or ŝ bins. The error of acceptance was estimated according to the binomial distribution
with p = N acc /N gen and n = N gen · σtot /σi :
∆Acc =
X Acc · (1 − Acc)
gen
i
Ni
·
σtot
σi
.
In Table IV-3 and Table IV-5 signal acceptance for ℓℓETmiss and ℓ had ETmiss channels is presented. It should
be noticed that there is little difference in acceptance after primary selection for various Higgs boson production
mechanism and the same final signatures (ca. 22% for ℓℓETmiss and ca. 11% for ℓ had ETmiss channels). Although
acceptance after resolving neutrino’s four-momenta is similar for all production processes (ca. 13% and 5%),
after optimization selection, which leads to improvement of mass resolution, the acceptance is 2.97/1.25 = 2.4
(0.944/0.272 = 3.5) times larger in gb → bH than bb̄ → H in ℓℓETmiss (ℓ had ETmiss ) channel.
The acceptance for various backgrounds is shown in Table IV-4 and Table IV-6 for ℓℓETmiss and ℓ had ETmiss
channel respectively.
The consecutive cuts reject specific backgrounds. In ℓℓETmiss channel, although a cut on |sin∆φ| > 0.2 eliminates 1-(1.44/2.39) = 40% of the signal, it reduces about 1-(5.44·104 /9.85·104 ) = 65% of Z/γ∗ ,
1-(503/706) = 34% of W background in ℓℓETmiss and ca. 1-(2.09·104 /4.06·104 ) = 50% of both in ℓ had ETmiss
channel.
The cut on missing transverse mass (mℓ,miss
) is efficient for W and tt¯ backgrounds reduction
T
3
4
(ca. 1-(7.06·10 /1.47·10 ) = 50%) and it is imposed only in ℓ had ETmiss channel. The signal is not degraded (94%
of events survives).
The threshold of 30 GeV set on pmiss
cuts off both Z and W backgrounds at a high rate
T
3
4
(1-(4.95·10 /2.03·10 ) = 75%) in ℓ had ETmiss channel. The W background has insufficient statistic in ℓℓETmiss
channel.
The additional cut on cos(∆φ) restricts the angular distance between visible τ decay products by extra 28
degrees in respect to |sin(∆φ)| cut. It yields in ca. 1-(1.24·104 /1.45·104 )= 18% reduction of all backgrounds in
both ℓℓETmiss and ℓ had ETmiss channels, while signal is reduced only 1-(2.23/2.83) = 21%.
The separation in the (η, φ) plane ∆Rℓℓ (∆Rℓτ− jet ) reduces the W background the most
(1-(241/330) = 30-40%).
The acceptance of b-jet tag/veto analysis is discussed in more details in Section IV.6.1.
The Z/γ background has the acceptance at the level of few percent, but after pmiss
cut it is reduced to less
T
than 1%. The bb̄Z background after primary selection has the highest acceptance from all backgrounds in both
ℓℓETmiss (13.5%) and ℓ had ETmiss channels (3.44%), since it has a topology the most similar to signal.
In the case of the W background an acceptance for the bb̄W process, after primary selection, is at the level
of 0.16% and is 2 orders of magnitude higher than for inclusive W or W + jet background in ℓℓETmiss channel. In
ℓ had ETmiss channel bb̄W acceptance after primary selection is two times higher than other W background (ca.
0.2%). The reason for it is that a semi-leptonic decay of b-quark is more frequent than a light or gluon jet. A
misidentification of jets as electrons is not taken into account.
IV.5. Acceptance for signal and background events
31
Table IV-3: The cumulative acceptance after consecutive selections for signal mH = 120 GeV events in ℓℓE miss
T
channel∗∗ . After applying common set of selections the analysis splits into two streams. One selects only NSF
leptons and performs b-tagging procedure directly, while the other takes SF leptons and introduces additional
selections against Z → ℓℓ events and applies b-jet tagging procedure. Statistical errors at the level of the generic
selection are typically less than 1%; they increase to 1-3% for b-jet veto and b-jet tagged analyses.
Analysis
type
NSF+SF
only NSF
only SF
Selection
gg → bb̄H
%
bb̄ → H
%
gb → bH
%
gg → H
%
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
37.8
22.5
13.5
8.09
2.83
2.23
2.07
36.9
21.9
13.0
7.32
2.0
1.4
1.25
37.6
21.8
13.9
8.79
3.84
3.16
2.97
39.1
22.3
14.9
9.83
5.13
4.48
4.29
after generic selection
1.02
0.614
1.47
2.14
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.426
0.265
0.261
0.311
0.216
0.214
0.706
0.423
0.413
2.01
1.08
1.05
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.594
0.449
0.44
0.303
0.254
0.251
0.767
0.564
0.547
0.135
0.0752
0.0728
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
1.05
1.03
0.454
0.632
0.623
0.158
1.5
1.45
0.792
2.15
2.07
1.27
b-jet veto
3rd jet veto
0.172
0.0896
0.0755
0.0469
0.339
0.183
1.18
0.586
b-jet tagged
3rd jet veto
0.282
0.195
0.0821
0.066
0.452
0.318
0.087
0.045
∗∗
Please note, that we present numbers for the gluon fusion and three approaches for the Higgs boson production associated with
b-quarks. Only the gluon fusion and the bb̄H are used in further analysis and calculation of the expected number of events.
C IV. T    bb̄H, H → ττ 
32
Table IV-4: The cumulative acceptance after consecutive cuts for background events in ℓℓE miss channel. StatisT
tical errors at the level of primary selection are around 0.1% and after generic selection they increase to 1%.
The b-jet tagged and b-jet veto numbers have a few percent uncertainty except background from W (qq̄ → W
and W + jet) where it reaches even 30% due to the lack of statistics.
Analysis
type
NSF+SF
only NSF
only SF
Selection
bb̄Z
%
Z/γ∗
%
qq̄ → W
%
W + jet
%
bb̄W
%
tt¯
%
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
26.3
13.5
8.69
6.86
3.02
2.77
2.69
18.2
9.55
5.59
3.09
0.82
0.703
0.674
44.8
0.0016
0.000273
0.000181
0.000139
0.000119
8.65·10−5
44.6
0.00169
0.000251
0.000205
0.000116
0.000106
7.21·10−5
51.0
0.159
0.0221
0.0161
0.00954
0.0072
0.00649
27.6
3.64
0.867
0.723
0.617
0.485
0.39
after generic selection
1.32
0.33
1.69·10−5
6.32·10−6
0.00168
0.182
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.577
0.245
0.241
0.304
0.194
0.191
1.59·10−5
4.79·10−6
4.79·10−6
5.66·10−6
1.39·10−6
7.37·10−7
0.00156
0.000914
0.000772
0.0471
0.00637
0.00336
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.746
0.414
0.404
0.0254
0.0184
0.0182
1.01·10−6
2.95·10−7
2.95·10−7
6.62·10−7
2.61·10−7
2·10−7
0.000114
6.02·10−5
4.7·10−5
0.135
0.0513
0.0261
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
1.37
1.33
0.675
0.345
0.336
0.128
6.96·10−5
6.73·10−5
2.04·10−5
6.57·10−5
6.16·10−5
1.38·10−5
0.00481
0.00106
0.000287
0.208
0.116
0.0874
b-jet veto
3rd jet veto
0.279
0.101
0.117
0.0714
1.76·10−5
1.75·10−5
1.3·10−5
7.72·10−6
0.000268
0.000189
0.0264
0.00385
b-jet tagged
3rd jet veto
0.396
0.193
0.0103
0.00683
2.88·10−6
2.88·10−6
7.74·10−7
3.5·10−7
1.93·10−5
1.47·10−5
0.061
0.0197
IV.5. Acceptance for signal and background events
33
Table IV-5: The same as Table IV-3, but for ℓ had E miss channel. Statistical errors at the level of the generic
T
selection are typically less than 1%, they increase to 1-3% for b-jet veto and b-jet tagged analyses.
Selection
gg → bb̄H
%
bb̄ → H
%
gb → bH
%
gg→ H
%
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
25.3
11.0
5.25
2.88
2.72
0.726
0.564
0.551
24.6
10.7
5.05
2.53
2.4
0.452
0.286
0.272
25.3
10.8
5.69
3.38
3.17
1.14
0.96
0.944
26.3
11.1
6.18
3.94
3.68
1.63
1.47
1.46
b-jet veto
3rd jet veto
0.22
0.127
0.137
0.093
0.422
0.239
1.35
0.691
b-jet tagged
3rd jet veto
0.331
0.241
0.136
0.111
0.522
0.369
0.105
0.0566
Table IV-6: The same as Table IV-4, but for ℓ had E miss channel. Statistical errors at the level of primary
T
selection are around 0.1% and after generic selection‡‡ they increase to 1%. The b-jet tagged and b-jet veto
numbers have a few percent uncertainty.
Selection
bb̄Z
%
Z/γ∗
%
qq̄ → W
%
W + jet
%
bb̄W
%
tt¯
%
trigger selection
16.3
10.8
44.8
44.6
50.8
24.0
primary selection
3.44
2.31
0.192
0.121
0.387
1.59
resolved neutrinos
1.85
1.15
0.0193
0.0103
0.0485
0.435
|sin(∆φℓτ− jet )| > 0.2
1.47
0.594
0.00998
0.00494
0.0291
0.364
1.42
0.577
0.00544
0.00254
0.0135
0.175
0.612
0.141
0.00142
0.000593
0.00503
0.126
cos(∆φℓτ− jet ) > −0.9
0.588
0.127
0.000967
0.000396
0.00353
0.108
∆Rℓτ− jet < 2.8
0.586
0.125
0.000577
0.000223
0.00234
0.0866
b-jet veto
0.239
0.115
0.000531
0.000209
0.00119
0.0269
3rd jet veto
0.0877
0.0706
0.000265
0.000107
0.000548
0.00226
b-jet tagged
0.347
0.01
4.56·10−5
1.44·10−5
0.00115
0.0597
0.0069
2.77·10−5
7.57·10−6
0.000688
0.0125
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
3rd
‡‡
jet veto
0.175
generic selection = selection as specified in the first block of Table IV-6, up to ∆Rℓτ− jet < 2.8 cut.
C IV. T    bb̄H, H → ττ 
34
We have used three approaches for generation of t t̄ background as specified in Section IV.2. The acceptance
in both final states is presented in Table IV-7 and Table IV-8. It turned out that the relative difference between
the maximal and the minimal acceptance at the primary selection, for example in ℓ had ETmiss , is (1.59-1.5)/1.59
= 3%, while after generic selection is around 8%. This discrepancy is larger than the uncertainty corresponding
to statistical errors at the given selection 0.1% and 2% respectively. Thus we also investigated the number of
expected events for 10 f b−1 for all types of Monte Carlo approaches, which is not shown here, and observed
similar results on all levels of cuts. So we decided not to overestimate this background and we used the full
(2 → 6) process gg, qḡ →WWbb̄ → f f¯ f f¯bb̄, as generated with AcerMC 2.0 MC generator, for further analysis.
In the tt¯ background an acceptance after primary selection in ℓℓETmiss is 3.6%/1.5% = 2.3 times higher than
in ℓ had ETmiss channel. After generic selection this discrepancy increases to 4.5. The acceptance after primary
selection (so choosing 2 leptons or 1 lepton and 1 τ-jet with pT over threshold) is in good agreement with W
boson decay branching ratios: W → hadrons: 68% and W → ℓν: 11% yielding 24·0.68·0.11 = 1.8 for ℓ had ETmiss
and 27.6 · (1 − 0.68) · 3 · 0.11 = 2.9 for ℓℓETmiss .
A veto against the third jet with |η| < 3.2 and pT > 15 GeV is set to cut out tt¯ background on average
1-(91.4/1.09·103 ) = 80-90% (tt¯ background in b-jet tag analysis stream of the ℓℓETmiss channel is reduced only in
1-(1.87·103 /4.9·103 ) = 60%).
Table IV-7: The cumulative acceptance after consecutive cuts for tt¯ background events in ℓ had E miss channel.
T
Statistical errors at the level of primary selection are typically around 0.1% and after generic selection they
increase to 2%. The b-jet tagged and b-jet veto numbers have a few percent uncertainty.
Selection
gg, qq̄ → WWbb̄ →
→ f f¯ f f¯bb̄
%
gg, qq̄ → tt¯
(off-shell)
%
gg, qq̄ → tt¯
(on-shell)
%
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
pmiss
>
30 GeV
T
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
24.0
1.59
0.435
0.364
0.175
0.126
0.108
0.0866
24.2
1.54
0.425
0.356
0.175
0.125
0.106
0.0832
23.7
1.5
0.415
0.345
0.167
0.119
0.1
0.0792
b-jet veto
3rd jet veto
0.0269
0.00226
0.0259
0.00288
0.0249
0.00261
b-jet tagged
3rd jet veto
0.0597
0.0125
0.0572
0.0163
0.0542
0.0152
IV.5. Acceptance for signal and background events
35
Table IV-8: The same as Table IV-7, but for ℓℓE miss channel. After applying generic selection, analysis splits into
T
two streams. One selects only NSF leptons and performs b-tagging procedure directly, while the other takes SF
leptons and introduces additional selections against Z → ℓℓ. Statistical errors at the level of primary selection
are around 0.1% and after generic selection they increase to 1%. The b-jet tagged and b-jet veto numbers have
a few percent uncertainty.
Analysis
type
NSF+SF
only NSF
only SF
Selection
gg, qq̄ → WWbb̄ →
→ f f¯ f f¯bb̄
%
gg, qq̄ → tt¯
(on-shell)
%
gg, qq̄ → tt¯
(off-shell)
%
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
27.6
3.64
0.867
0.723
0.617
0.485
0.39
27.9
3.68
0.87
0.717
0.599
0.467
0.371
27.2
3.49
0.89
0.724
0.607
0.465
0.372
after generic selection
0.182
0.168
0.172
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.0471
0.00637
0.00336
0.0419
0.0075
0.00395
0.0427
0.00775
0.00413
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.135
0.0513
0.0261
0.126
0.058
0.0297
0.129
0.0553
0.0286
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
0.208
0.116
0.0874
0.203
0.115
0.0838
0.2
0.113
0.0846
b-jet veto
3rd jet veto
0.0264
0.00385
0.0238
0.00455
0.0259
0.00374
b-jet tagged
3rd jet veto
0.061
0.0197
0.06
0.025
0.0587
0.0247
36
C IV. T    bb̄H, H → ττ 
IV.6 Expected number of events and the mass resolution
The expected number of events N expec is calculated as:
N expec = const × σ × Acc ,
(IV.4)
where const contains electron or τ-jet identification efficiency and coefficient 104 coming from units conversion
(1 pb−1 to 10 f b−1 ), σ stands for cross-section times branching ratio and Acc - the acceptance calculated according to Equation IV.3 for a given cut. The error is estimated according to the total derivative. We assumed 10%
uncertainty on σ, following what was estimated in [17]. The expected number of events is shown in Table IV-9
and Table IV-10 for ℓℓETmiss and ℓ had ETmiss mode respectively. The efficiency and rejection factors used are
described in Section IV.3.
Despite three orders of magnitude difference in the expected number of events after trigger selection, the
sin(∆φll ) cut brings all main backgrounds at the same level of 2 · 104 events.
After generic selection in ℓℓETmiss channel the Z/γ∗ and the tt¯ backgrounds are comparable (1.19·104 /(1.19 ·
104 + 241 + 1.42 · 104 ) = 45% and 54%). The optimization procedure accepts 1.19·104 /9.85 · 104 = 12% of
expected Z/γ∗ events in respect to the primary selection plus resolved neutrino cut.
The W background is marginal (less than 1% of total) through all cuts. In ℓ had ETmiss channel it becomes
more important. After generic selection it contributes (1.78·103 /(4.41 · 103 + 1.78 · 103 + 3.5 · 103 )) = 18% of the
total background. The optimization selection accepts 4.41·103 /4.06·104 = 11% of Z/γ∗ , 1.78·103 /5.98·104 = 3%
of the W and 3.5·103 /1.76 · 104 = 20% of the tt¯ background. Actually, every cut imposed on tt¯ reduces it ca. 20%
on each level (except the missing transverse mass: 52%).
In Table IV-11 and Table IV-12 the mass resolution, fitted within mass window of mH = 120 GeV ± 20 GeV,
after consecutive cuts is presented. It can be noticed that the mass resolution of Yukawa induced processes improves after optimization selection on average (25.8 GeV-16.6 GeV)/25.8 GeV = 35% in ℓℓETmiss and (22.2 GeV15.2 GeV)/22.2 GeV = 30% in ℓ had ETmiss case. The best resolution is obtained for the gb → bH in both ℓℓETmiss
(14.6 GeV) and ℓ had ETmiss (12.3 GeV) channels.
It should be also pointed out that in the case of the ℓ had ETmiss channel we obtain
(16.6 GeV-13.5 GeV)/16.6 GeV = 18% better mass resolution than in ℓℓETmiss one. It is reasonable and consistent
with reported results from full simulation [53], since in ℓ had ETmiss case there are three neutrinos (instead of
four) that escape detection and the assumption of the collinearity of the τ decay products with respect to τ itself
works better in this case. The reconstructed mass of τ lepton pair with Gaussian fit in range mH = 120 GeV ±
20 GeV is shown on Figure IV-5. The interesting observation is that Gaussian fits to ℓℓETmiss distributions usually
underestimate nominal Higgs boson mass while fits to ℓ had ETmiss overestimate it. This may be due to long tails
in the invariant mass of di-τ system.
We can notice that in ℓℓETmiss channel after generic selection there is a similar number of expected events in
all types of signal and background samples apart from W-background. Inclusive W + jet is classified in 191/241
= 80-91% as SF, while bb̄W only in 14.7/19.8= 74%. Interesting is that misidentified jet is SF in W + jet. If
we misidentify b-jet as lepton we lack one b-jet, and b-jet tag analysis should result in a lower number of the
expected events than in ℓ had ETmiss for other processes.
After generic selection signal in ℓ had ETmiss is smaller by 0.196/0.368= 53% as compared to ℓℓETmiss , while
background from Z is 4.41 · 103 /1.19 · 104 = 37%. The W background is 1.54 · 103 /446 = 3.5 times higher and
tt¯ is 3.5 · 103 /1.42 · 104 = 25%. However more important is the evaluation of the expected number of events in a
mass window around Higgs boson mass in the further analysis.
IV.6. Expected number of events and the mass resolution
IV.6.1
37
Analysis streams with b-jet tag and b-jet veto
In the final state of signal events in addition to τ leptons bottom quarks are also present, so the b-jet tagging is
an important ingredient of the analysis. For the ATLAS detector b-tagging performance was studied with full
simulation. Here, we use only parametrized version, a pT -dependent b-jet tagging procedure, from Atlfast-b
package with the nominal b-jet tagging efficiency of 60% ( See Section IV.3 for more details). The case in which
the “b-tagging procedure” has identified at least one b-jet is called “b-jet tagged” event; the opposite case, when
no b-jet has been found, is called “b-jet vetoed” event.
The b-jet tagged analysis is efficient to suppress by factor 5.81·103 /448 = 13 the Z/γ∗ background in ℓℓETmiss
and ℓ had ETmiss analyses. The inclusive W ± is suppressed by factor 47/2.82 = 17 in NSF, 24 times in SF and 13
times in ℓ had ETmiss mode. An interesting observation is that the background which comes from associated Z and
W production with b-quark behaves differently, due to different kinematics of the hard process [54]. We expect
that the b-jet tagging procedure should accept more events than the b-jet veto one for processes with topology
containing at least one b-quark. This is true for all signal and background events except bb̄W where pT spectrum
of b-quarks is very soft.
On the other hand, a signal containing at least one b-jet in the final state is reduced ca. 0.106/0.181 = 60%
in both ℓℓETmiss and ℓ had ETmiss channels with “b-jet tagged” selection. Similar numbers are obtained for the
expected number of events within a mass window mH = 120 GeV ± 20 GeV.
The mass resolution slightly improves ca. (13.5-13.3)/13.5 = 1% when applying b-jet tagged analysis in
ℓ had ETmiss and ca. (18.0-17.6)/18.0 = 3.6% in ℓℓETmiss channel.
The application of the b-jet veto reduces 0.196/0.0781 = 2-3 times the associated Higgs boson production, while the tt¯ background is reduced 3.5 · 103 /1.09 · 103 = 3-4 times. For the gluon fusion we lose only
1-(28.6/30.5) = 7% of the signal events.
In order to suppress the tt¯ background even more efficiently, an additional selection, as used in [11], was
introduced (called 3rd jet veto). It requires no more than two non b-jets with pT > 15 GeV and |η| < 3.2 in
the event. We noticed that the mass resolution gets worse after the application of 3rd jet veto cut; however we
gained better signal to background ratio after this selection. The reason for worsening resolution is that we
Higgs
increase fraction of events with low pT , for which τ-system kinematics is more back-to-back and collinear
approximation is less precise.
In ℓℓETmiss channel the Z/γ∗ background becomes dominant for the b-jet veto analysis (96% for NSF and 87%
for SF of total), while the tt¯ background becomes dominant in the b-jet tag analysis ( 949/(321+0.82+949) = 75%
for NSF and 85% for SF). The W background is marginal (less than 1% of total).
In ℓ had ETmiss channel the W background becomes important. It contributes 818/(2.49·103 +818+91.4) = 24%
(b-jet veto) and 11% (b-jet tag) of the total. The Z background is dominant again in b-jet veto analysis stream,
while tt¯ background is leading in b-jet tag analysis (60% of total).
C IV. T    bb̄H, H → ττ 
38
0.5
×10
3213
SF After b-jet veto
-6
Entries
3448
Mean
123.1
RMS
21.7
χ2 / ndf
4.568 / 5
Prob
0.4
0.4708
Constant 4.436e-07 ± 1.261e-08
Mean
119.3 ± 0.4
Sigma
14.84 ± 0.64
0.3
×10
3223
SF After b-jet tag
-6
0.8
Entries
5633
Mean
122.5
RMS
21.3
χ2 / ndf
0.7
7.115 / 5
Prob
0.2122
Constant 7.584e-07 ± 1.632e-08
0.6
0.5
Mean
118.4 ± 0.3
Sigma
14.2 ± 0.4
0.4
0.2
0.3
0.2
0.1
0.1
00
50
100
150
200
250
00
300
50
100
150
200
250
mττ(GeV)
×10
4213
NSF After b-jet veto
-6
1
Entries
8524
Mean
122.2
RMS
23.94
χ2
/ ndf
1.477 / 5
Prob
0.8
300
mττ(GeV)
1.6
×10
4223
NSF After b-jet tag
-6
Mean
117.1 ± 0.5
Sigma
17.86 ± 0.72
0.6
11886
Mean
121.3
RMS
1.4
χ2
0.9158
Constant 9.437e-07 ± 1.801e-08
Entries
22.72
/ ndf
9.633 / 5
Prob
0.08632
Constant 1.433e-06 ± 2.241e-08
1.2
1
Mean
117.4 ± 0.3
Sigma
15.87 ± 0.43
0.8
0.4
0.6
0.4
0.2
0.2
00
50
100
150
200
250
00
300
50
100
150
200
250
mττ(GeV)
×10
213
After b-jet veto
-6
2.4
Entries
4402
Mean
127.7
RMS
2.2
19.82
χ2 / ndf
2
0.0166
Constant 2.148e-06 ± 5.255e-08
1.6
×10
223
After b-jet tag
-6
Mean
122.3 ± 0.4
Sigma
13.8 ± 0.5
Entries
6628
Mean
126.3
RMS
3.5
13.85 / 5
Prob
1.8
300
mττ(GeV)
3
19.34
χ2 / ndf
16.39 / 5
Prob
0.005817
Constant 3.371e-06 ± 6.671e-08
2.5
Mean
121.7 ± 0.3
Sigma
13.29 ± 0.34
1.4
2
1.2
1
1.5
0.8
1
0.6
0.4
0.5
0.2
00
20
40
60
80
100
120
140
160
180
200
mττ(GeV)
00
20
40
60
80
100
120
140
160
180
200
mττ(GeV)
Figure IV-5: The Gaussian fit to reconstructed mττ distribution in mass window 120 GeV ± 20 GeV for bb̄H
process. The top four present fit for ℓℓE miss : SF b-jet veto (top left), SF b-jet tag (top right), NSF b-jet veto
T
(middle left), NSF b-jet tag (middle right) and the bottom two for ℓ had E miss b-jet veto (bottom left) and b-jet
T
tag (bottom right).
Analysis
type
NSF+SF
only NSF
only SF
gg → bb̄H
gg → H
bb̄Z
Z/γ∗
qq̄ → W
W + jet
bb̄W
tt¯
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
6.71
3.99
2.39
1.44
0.502
0.396
0.368
558
318
212
140
73
63.9
61.2
7.44·103
3.84·103
2.46·103
1.94·103
854
783
762
3.2·105
1.68·105
9.85·104
5.44·104
1.45·104
1.24·104
1.19·104
1.25·108
4.44·103
760
503
386
330
241
2.77·108
1.05·104
1.56·103
1.27·103
722
654
446
1.56·105
485
67.5
49.4
29.2
22
19.8
1.01·106
1.32·105
3.15·104
2.63·104
2.24·104
1.76·104
1.42·104
after generic selection
0.181
30.5
375
5.81·103
47
39.1
5.12
6.61·103
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.0757
0.047
0.0463
28.6
15.4
15
163
69.5
68.3
5.36·103
3.42·103
3.36·103
44.2
13.3
13.3
35
8.63
4.57
4.77
2.8
2.36
1.71·103
232
122
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.106
0.0798
0.0781
1.92
1.07
1.04
211
117
114.0
448
324
321.0
2.82
0.82
0.82
4.1
1.62
1.24
0.35
0.184
0.144
4.9·103
1.87·103
949.0
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
0.186
0.182
0.0806
30.6
29.5
18.1
388
376
191
6.07·103
5.91·103
2.25·103
194
187
56.9
407
381
85.3
14.7
3.25
0.88
7.57·103
4.21·103
3.18·103
b-jet veto
3rd jet veto
0.0306
0.0159
16.8
8.34
78.9
28.5
2.07·103
1.26·103
48.9
48.6
80.5
47.8
0.821
0.578
961
140
b-jet tagged
3rd jet veto
0.05
0.0346
1.24
0.642
112
54.8
182
120.0
8.02
8.0
4.8
2.17
0.0589
0.0451
2.22·103
717.0
39
Selection
IV.6. Expected number of events and the mass resolution
Table IV-9: The expected number of signal mH = 120 GeV and background events for an integrated luminosity 10 f b−1 after consecutive cuts in ℓℓE miss
T
channel. Efficiencies for leptons and b-jet identification are included (90% and 60% respectively). Statistical errors are typically at the level of 10%. Only
the background from W (qq̄ → W and W + jet) suffers a lack of statistics and at the level of generic selection the statistical errors are around 13% and they
increase to 32% throughout the rest of the analysis.
40
Table IV-10: The same as Table IV-9, but for ℓ had E miss . Statistical errors are typically at the level of 10%.
T
gg → bb̄H
gg→ H
bb̄Z
Z/γ∗
qq̄ → W
W + jet
bb̄W
tt¯
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
8.98
3.9
1.86
1.02
0.966
0.258
0.2
0.196
745
315
175
112
104
46.1
41.7
41.4
9.24·103
1.95·103
1.05·103
831
804
346
333
331
3.79·105
8.14·104
4.06·104
2.09·104
2.03·104
4.95·103
4.46·103
4.41·103
1.38·108
5.94·105
5.98·104
3.09·104
1.68·104
4.39·103
2.99·103
1.78·103
3.07·108
8.35·105
7.12·104
3.4·104
1.75·104
4.09·103
2.72·103
1.54·103
1.73·105
1.31·103
165
99.1
45.9
17.1
12
7.97
9.71·105
6.44·104
1.76·104
1.47·104
7.06·103
5.11·103
4.37·103
3.5·103
b-jet veto
3rd jet veto
0.0781
0.0451
38.4
19.6
135
49.7
4.06·103
2.49·103
1.64·103
818
1.44·103
737
4.06
1.86
1.09·103
91.4
b-jet tagged
3rd jet veto
0.118
0.0854
2.97
1.61
196
99.0
353
243.0
141
85.7
99.2
52.1
3.91
2.34
2.42·103
505.0
C IV. T    bb̄H, H → ττ 
Selection
IV.6. Expected number of events and the mass resolution
41
Table IV-11: The resolution of the reconstructed invariant mass of the τ system for signal events in ℓℓE miss
T
channel. Results from gaussian fit in mass window mH = 120 GeV ± 20 GeV.
Analysis
type
NSF+SF
Selection
gg→ bb̄H
[GeV]
bb̄ → H
[GeV]
gb → bH
[GeV]
gg → H
[GeV]
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
25.8 ± 0.5
23.6 ± 0.4
17.7 ± 0.3
16.8 ± 0.3
16.6 ± 0.2
30.9 ± 0.9
28.0 ± 0.8
20.7 ± 0.6
19.4 ± 0.5
19.0 ± 0.5
21.3 ± 0.3
19.7 ± 0.2
15.4 ± 0.2
14.8 ± 0.2
14.6 ± 0.1
17.2 ± 0.1
16.2 ± 0.1
13.4 ± 0.1
13.1 ± 0.1
12.9 ± 0.1
15.9 ± 0.4
16.4 ± 0.6
16.4 ± 0.5
18.8 ± 1.0
18.0 ± 0.9
18.0 ± 0.9
13.8 ± 0.3
14.0 ± 0.3
14.0 ± 0.3
12.5 ± 0.4
12.5 ± 0.6
12.6 ± 0.6
b-jet veto
3rd jet veto
14.8 ± 0.6
15.7 ± 1.0
18.7 ± 2.1
18.2 ± 2.3
13.6 ± 0.4
13.4 ± 0.5
11.7 ± 0.1
11.4 ± 0.2
b-jet tagged
3rd jet veto
14.2 ± 0.4
14.2 ± 0.5
17.6 ± 1.5
19.6 ± 2.3
12.7 ± 0.3
12.7 ± 0.3
12.2 ± 0.5
12.5 ± 0.7
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
only NSF
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
only SF
17.9 ± 0.7
17.7 ± 0.9
17.7 ± 0.9
16.6 ± 0.4
14.4 ± 0.4
18.2 ± 0.9
17.9 ± 0.8
17.9 ± 1.0
15.2 ± 0.3
15.3 ± 0.4
15.3 ± 0.5
19.5 ± 0.8
18.2 ± 1.3
14.8 ± 0.2
13.0 ± 0.2
12.9 ± 0.1
13.0 ± 0.2
13.1 ± 0.2
13.1 ± 0.1
11.7 ± 0.1
Table IV-12: The same as Table IV-11, but for ℓ had E miss channel.
T
Selection
gg→ bb̄H
[GeV]
bb̄ → H
[GeV]
gb → bH
[GeV]
gg→ H
[GeV]
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
20.0 ± 0.4
18.4 ± 0.3
18.5 ± 0.3
13.9 ± 0.3
13.5 ± 0.3
13.5 ± 0.3
22.2 ± 0.5
20.9 ± 0.6
20.8 ± 0.5
15.5 ± 0.5
15.2 ± 0.6
15.2 ± 0.6
16.7 ± 0.2
15.8 ± 0.2
15.9 ± 0.2
12.6 ± 0.1
12.3 ± 0.2
12.3 ± 0.2
14.4 ± 0.1
13.7 ± 0.1
13.7 ± 0.1
11.1 ± 0.1
10.9 ± 0.1
10.9 ± 0.1
13.3 ± 0.3
13.6 ± 0.4
15.2 ± 0.8
15.7 ± 0.8
12.1 ± 0.2
12.2 ± 0.2
11.4 ± 0.4
11.5 ± 0.5
b-jet veto
3rd jet veto
b-jet tagged
3rd jet veto
13.8 ± 0.5
14.6 ± 0.4
15.2 ± 0.8
15.1 ± 0.9
12.4 ± 0.2
12.7 ± 0.3
10.9 ± 0.1
10.7 ± 0.1
C IV. T    bb̄H, H → ττ 
42
IV.6.2
Events in the mass window
Once the mass of di-τ system is reconstructed, the number of expected events within mass window mH =
120 GeV ± 20 GeV for an integrated luminosity 10 f b−1 can be calculated and is presented in Table IV-13 and
Table IV-14 for ℓℓETmiss and ℓ had ETmiss modes respectively.
The main background in ℓℓETmiss channel in b-jet veto analysis stream arises from resonant Z/γ∗ and after all
cuts constitutes 1130/(1130+13.3+29.9) = 95% of the total background for NSF events. The bb̄Z process has a
similar topology to the signal and after all cuts contributes only 23.2/1130 = 2% to possible Z/γ∗ background
events in b-jet veto analysis and 35.4/110 = 30-40% in b-jet tagged. The background from W was found marginal
through the whole selection in ℓℓETmiss channel. The tt¯ process contributes 70-80% of the total background in
b-jet tag analysis.
In ℓ had ETmiss channel the W background comprises 434/(1.46·103 +434+646) = 17% of the total background
after generic selection. In the b-jet veto analysis the Z/γ∗ is dominant 796/(796+205+21.3) = 68%, while in bjet tagged analysis stream the tt¯ background grows to 48% of total and is comparable with the Z/γ∗ background
(79/(79+16.6+88.3) = 43%).
At the generator level ratio of cross-sections σ(bb̄Z)/σ(Z/γ∗ ) = 3.5 · 100 pb/2.2 · 102 pb = 1.6% is similar for
miss
ℓℓET and ℓ had ETmiss channels. The corresponding ratio for σ(bb̄W)/σ(W + jet) = 3.8 · 101 pb/7.6 · 104 pb =
0.05%. After generic selection the contribution of the bb̄W to W + jet is 1.53/308 = 0.5% and respective ratio
of bb̄Z to the Z/γ∗ 112/1.46 · 103 = 7.7%. In b-jet tag analysis, which is appropriate for processes with bquarks in the final state, this ratio increases to 0.439/9.7 = 4.5% and 29.7/79.0 = 37.6% for the bb̄W and the
bb̄Z respectively. As the final estimates for signal significance and the level of background we take the numbers
obtained with inclusive W, Z production. The bb̄W and bb̄Z estimates are used in discussion as a reference level
of irreducible background only.
After generic selection ratio of the expected number of signal bb̄H events is 0.25/0.145 = 1.7 (for the gg → H
it is 1.4) times higher in ℓℓETmiss than ℓ had ETmiss , while the Z background is 3.96 · 103 /1.46 · 103 = 2.7 higher
than Z background in ℓ had ETmiss . The W + jet background is 13/308 = 4% of W background in ℓ had ETmiss and
tt¯ is 1.85 · 103 /646 = 2.86 times higher than ℓ had ETmiss . In general, the total background in ℓℓETmiss is 5823/2414
= 2.41 times higher than the total background in ℓ had ETmiss mode. This is opposite to the observation for higher
masses of 150 GeV and 200 GeV, where the expected number of total background events in the mass window in
both ℓℓETmiss and ℓ had ETmiss is similar after generic selection.
We observed that in ℓℓETmiss and ℓ had ETmiss the W + jet process gives a smaller estimate for a number of
expected events in mass window than the inclusive W process. However, after application of all selections in
b-jet veto analysis, the values are similar and the estimate from the W + jet is a more conservative one.
The peak position of the gaussian fit tends to be underestimated in the ℓℓETmiss mode and overestimated in
the ℓ had ETmiss mode, see Figure IV-5. Please note also that the NSF versus SF selection includes selection
pmiss
> 50 GeV, which also causes a slight bias in the position of the gaussian fit (by 2 GeV). Already with the
T
fast simulation even with gaussian parametrization of the detector resolutions, we observe asymmetric tail in the
reconstruction of the invariant mass. The asymmetric tail is present both in ℓℓETmiss and ℓ had ETmiss mode and
can be attributed to the effect of the collinear approximation.
Analysis
type
NSF+SF
only NSF
only SF
Selection
gg → bb̄H
gg → H
bb̄Z
Z/γ∗
qq̄ → W
W + jet
bb̄W
tt¯
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
0.839
0.682
0.295
0.26
0.25
94
82.3
51.3
48.3
47.2
627
547
278
259
252
2.21·104
1.55·104
4.75·103
4.15·103
3.96·103
124
110
83.1
33.4
19.8
68.2
62.9
18.2
17.5
13
7.15
6.39
3.06
2.56
2.52
2.71·103
2.67·103
1.91·103
1.87·103
1.85·103
after generic selection
0.123
23.6
124
1.96·103
19.8
11.5
1.15
976
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.0502
0.0312
0.0308
22.1
12
11.6
56.1
23.4
23.2
1.8·103
1.14·103
1.13·103
19.1
13.3
13.3
9.34
0
0
1.06
0.59
0.59
272
32.5
29.9
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.0729
0.055
0.054
1.45
0.818
0.795
67.9
35.7
35.4
159.0
111.0
110.0
0.643
0.272
0.272
2.18
0.607
0.607
0.0841
0.0367
0.0367
704.0
304.0
258.0
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
0.127
0.124
0.0589
23.6
22.8
14.7
128
126
65.3
2.01·103
1.99·103
710.0
0
0
0.0
1.43
0.716
0.0
1.38
0.841
0.153
876
748
529.0
b-jet veto
3rd jet veto
0.0221
0.0116
13.8
6.89
27.6
9.33
652.0
390.0
0.0
0.0
0.0
0.0
0.133
0.0727
116.0
20.8
b-jet tagged
3rd jet veto
0.0368
0.0254
0.979
0.508
37.7
17.2
57.1
36.3
0.0
0.0
0.0
0.0
0.0199
0.0122
413.0
150.0
IV.6. Expected number of events and the mass resolution
Table IV-13: The expected number of signal and background events within mass window mH = 120 GeV ± 20 GeV for an integrated luminosity 10 f b−1 after
consecutive cuts in ℓℓE miss channel. Efficiencies for lepton and b-jet identification are included (90% and 50% respectively). Statistical errors are typically
T
at the level of 10%. Throughout the b-jet veto and b-jet tag analysis statistical errors for all backgrounds increase to 15%, while signal uncertainty stays
at the level of 10%. The background from W (qq̄ → W and W + jet) suffers a lack of statistics and at the level of generic selection the statistical errors are
around 14% and they increase to 44% and more throughout the rest of the analysis. For tt¯ background in b-jet veto analysis numbers have 30% uncertainty.
43
44
Table IV-14: The same as Table IV-13, but for ℓ had E miss channel. Statistical errors are typically at the level of 10%. Throughout the b-jet veto and b-jet
T
tag analysis statistical errors for all backgrounds increase to 15%, while signal uncertainty stays at the level of 10%. For tt¯ background in b-jet veto analysis
numbers have 30% uncertainty.
gg → bb̄H
gg→ H
bb̄Z
Z/γ∗
qq̄ → W
W + jet
bb̄W
tt¯
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
pmiss
>
30 GeV
T
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
0.73
0.592
0.56
0.163
0.146
0.145
87
76.4
71.3
36.1
34.8
34.7
309
271
260
115
112
112
1.06·104
7.37·103
7.14·103
1.59·103
1.46·103
1.46·103
6.83·103
5.43·103
3.77·103
502
446
434
7.49·103
5.72·103
3.77·103
348
314
308
15.9
13.9
9.01
1.64
1.54
1.53
1.59·103
1.58·103
1.17·103
654
648
646
b-jet veto
3rd jet veto
0.057
0.0324
32.3
16.6
48.1
17.5
1.34·103
796.0
408
205.0
290
163.0
0.828
0.404
212
21.3
b-jet tagged
3rd jet veto
0.0879
0.0633
2.43
1.32
63.4
29.7
118.0
79.0
25.9
16.6
18.1
9.7
0.705
0.439
433.0
88.3
C IV. T    bb̄H, H → ττ 
Selection
IV.7. Sensitivity in ℓℓETmiss versus ℓ had ETmiss channel
45
IV.7 Sensitivity in ℓℓETmiss versus ℓ had ETmiss channel
Finally, we compared ℓℓETmiss vs ℓ had ETmiss channel in terms of signal (S) over square root of background (B)
√
ratio, S / B, see Table IV-15. The errors were estimated according to the total derivative. The signal significance
was computed by adding in quadrature significances of NSF and SF for ℓℓETmiss channel. Then we combined
ℓℓETmiss and ℓ had ETmiss modes. For comparison, we also present the combined significance of b-jet veto and
b-jet tag analysis denoted in this table as “b-jet veto + b-jet tag”. These results were obtained for the SM Higgs
boson and do not take into account the MSSM enhancement of signal cross-section dependent on tan2 β.
The similar calculations were also performed for mass points mH = 150 GeV and mH = 200 GeV, and gaussian fits were performed within a mass window of mH = 150 GeV ± 30 GeV and mH = 200 GeV ± 40 GeV
respectively. The corresponding tables for signal acceptance (Tables B-1, B-3, B-9, B-11), the number of expected events for 10 f b−1 (Tables B-2, B-4, B-10, B-12), the number of expected events in the corresponding
mass window (Tables B-7, B-8, B-15, B-16) and the mass resolution (Tables B-5, B-6, B-13, B-14), as well as
a short discussion can be found in the Appendix B.1 (for mH = 150 GeV) and B.2 (for mH = 200 GeV).
For the gg → H process at each mass point b-jet veto or b-jet tag analysis (or both combined) does not
improve the significance in either of final modes (within errors). Since this uncertainty of the significance is
large, it is impossible to draw the final conclusion whether for this process the analysis should finish at the
generic selection. We should also remember that the presented selection was optimized for the bb̄H process.
Perhaps the development of the dedicated strategy for the gg → H process event selection, as proposed in [39],
will be mandatory. For this process, our estimations show for each mass point that both final states have a similar
significance in combined b-jet veto + b-jet tag analysis .
For the bb̄H process, in b-jet tag analysis for the ℓ had ETmiss mode, the significance improves for all mass
points with respect to generic selection, while for ℓℓ ETmiss the significance does not change significantly. We
found that the significance for b-jet veto is at the same level for all mass points for both ℓ ℓ ETmiss and ℓ had ETmiss
modes. It is the b-jet tag analysis that dominates the final combined significance from both final states.
The b-jet veto analysis stream decreases the signal significance of the bb̄H production channel, as compared
to generic selection. This decrease was expected, as there are at least one b-jet in the final state of this process.
The improvement J of signal significance for these mass points is presented in Table IV-16. It was calculated
as:
S comb
J = ( ll+lhad − 1) · 100% ,
(IV.5)
S lhad
comb is the combined significance of ℓℓE miss and ℓ had E miss modes for the given mass point and S
where S ll+lhad
lhad
T
T
- significance of ℓ had ETmiss final state alone.
The b-jet veto analysis stream for the gg → H process improves combined significance by 35-40% in the
whole analyzed mass range and it dominates the final (b-jet veto + b-jet tag) result for this production mode.
At the same time, b-jet tag analysis stream for the bb̄H process improves combined significance by 11-23%
(raising for lower masses) and it dominates the final result in associated production channel. When estimating
significance, we should remember that for a given Higgs boson mass point and corresponding mass window
the results indicate that after generic selection the number of expected signal events is similar in ℓℓETmiss and
ℓ had ETmiss modes, but the ratio of the total background in ℓ had ETmiss in respect to the total background in
ℓℓETmiss mode increases with mass from 41% to 48%. After b-jet tag analysis, this ratio increases from 32% at
120 GeV, 34% at 150 GeV to 52% at 200 GeV, while the signal in both final states is comparable at 120 GeV and
150 GeV. However, at mass point of 200 GeV the signal from ℓ had ETmiss is 1.8 times larger than from ℓℓETmiss
mode. In the b-jet veto analysis the total background in ℓ had ETmiss is 62% of the total background ℓℓETmiss at
120 GeV, 93% at 150 GeV and becomes even 2.6 times larger for 200 GeV. The ratio of the number of expected
events for the signal in ℓ had ETmiss and ℓ had ETmiss modes behaves similarly as in the b-jet tag analysis. Let
us stress that the discussed signal can not be observed in the SM and the numbers obtained here should be now
interpreted in the MSSM scenario.
46
√
Table IV-15: The signal significance in terms of the signal (S) to square root background (B), S / B for 10 f b−1 in different mass points. Values for crosssection of bb̄H and gg → H processes are shown for SM predictions and do not include the MSSM signal enhancement.
Decay
mode
Analysis
type
gg → bb̄H
gg → H
gg → bb̄H
gg → H
gg → bb̄H
gg → H
√
S/ B
·10−4
√
S/ B
·10−2
√
S/ B
·10−4
√
S/ B
·10−2
√
S/ B
·10−4
√
S/ B
·10−2
32.7 ± 4.9
10.7 ± 1.7
33.7 ± 5.8
35.4 ± 6.0
61.8 ± 9.3
48.0 ± 7.6
5.6 ± 1.0
48.3 ± 7.7
6.7 ± 1.0
2.9 ± 0.5
5.9 ± 1.0
6.6 ± 1.1
17.1 ± 2.6
17.3 ± 2.9
1.3 ± 0.3
17.3 ± 2.9
0.051 ± 0.008
0.031 ± 0.006
0.038 ± 0.006
0.049 ± 0.008
0.24 ± 0.04
0.30 ± 0.06
0.014 ± 0.002
0.30 ± 0.06
10.0 ± 1.5
4.3 ± 0.7
12.3 ± 2.3
13.0 ± 2.4
27.4 ± 4.3
25.7 ± 4.3
3.0 ± 0.6
25.9 ± 4.3
0.09 ± 0.01
0.046 ± 0.008
0.10 ± 0.02
0.11 ± 0.02
mH = 120 GeV
T
ℓ had
E miss
T
Combined
generic selection
b-jet veto
b-jet tag
b-jet tag + b-jet veto
generic selection
b-jet veto
b-jet tag
b-jet tag + b-jet veto
generic selection
b-jet veto
b-jet tag
b-jet tag + b-jet veto
28.8 ± 4.5
10.1 ± 1.5
46.7 ± 9.2
47.8 ± 9.3
43.6 ± 6.7
14.7 ± 2.3
57.6 ± 10.8
59.4 ± 11.0
68.9 ± 10.7
51.9 ± 8.4
9.7 ± 2.0
52.8 ± 8.6
92.5 ± 14.2
70.7 ± 11.3
11.2 ± 2.2
71.6 ± 11.5
7.4 ± 1.1
3.2 ± 0.5
10.8 ± 2.0
11.3 ± 2.1
21.5 ± 3.3
19.0 ± 3.1
2.7 ± 0.5
19.2 ± 3.1
mH = 200 GeV
0.07 ± 0.01
0.033 ± 0.006
0.090 ± 0.002
0.096 ± 0.004
0.32 ± 0.05
0.32 ± 0.05
0.035 ± 0.006
0.32 ± 0.05
0.40 ± 0.06
0.45 ± 0.08
0.038 ± 0.007
0.45 ± 0.08
C IV. T    bb̄H, H → ττ 
ℓℓE miss
mH = 150 GeV
IV.8. Interpretation in the MSSM model
47
Table IV-16: The improvement of combined significance from both ℓℓE miss and ℓ had E miss channels relative to
T
T
significance of ℓ had E miss channel.
T
Analysis
type
gg → bb̄H
%
gg → H
%
gg → bb̄H
%
mH = 120 GeV
generic selection
b-jet veto
b-jet tag
b-jet veto + b-jet tag
51
45
23
24
34
36
15
36
gg → H
%
mH = 150 GeV
35
34
14
15
27
35
11
35
gg → bb̄H
%
gg → H
%
mH = 200 GeV
28
39
11
15
25
40
9
41
IV.8 Interpretation in the MSSM model
The improvement of signal significance described in the previous section was based on the SM couplings. Thus,
as a next step, we interpreted this significance with the use of the MSSM cross-sections and branching ratios. The
overview of benchmark scenario, as well as results of the searches at LEP, Tevatron and planned strategies for
the LHC experiments are described in [55] and briefly reviewed in Section III.3 of these theses. In our analysis
scenario. It will give us the possibility to compare with the ATLAS former results and with
we have chosen mmax
h
the on-going Tevatron experiments limits.
The corresponding cross-sections and branching ratios were obtained from the Suspect [56] and HDECAY [57]
packages. The reference numbers from the official ATLAS Higgs Working Group initializations were used here.
In Figure IV-6 we plotted h and H boson masses as a function of A boson mass for tan β = 10 (black points) and
tan β = 30 (red points). In the bottom line of this figure, we also plotted the total width of different Higgs bosons
in the MSSM model for the same two tan β values. The mass of h and H bosons depends very weakly on tan β,
for tan β > 10. On the contrary, the width of the h and H boson depends very strongly on tan β, but for tan β = 10
the width does not exceed 0.5 GeV in the low mass region. For the mA = 120 GeV the width ∼ 0.3 GeV is below
the experimental resolution (typically 16 GeV). The 5σ significance will not be affected since even if natural
width of the Higgs boson is growing fast with tan β, its effective contribution to the experimental width of the
reconstructed ττ invariant mass is rising much slower than the cross-section. Thus, we do not have to include
this effect in the experimental mass resolution for the analysis presented here.
We also evaluated significance for 30 f b−1 of data, according to Equation IV.4. We assumed that the results
from the full simulation would confirm our estimates. This assumption is valid, as will be shown in Chapter VII
(Table VII-5).
The full procedure of combining results consisted of:
• combination of not the same flavour (NSF) and the same flavour (SF) leptons contributions in the ℓℓ ETmiss
final state;
• estimation of the mass overlap effect, as described below;
• combination of contribution from the gg → H and the bb̄H processes;
• combination of b-jet veto and b-jet tag analysis streams, since they consisted of independent events;
• combination of ℓℓ ETmiss and ℓ had ETmiss modes.
C IV. T    bb̄H, H → ττ 
48
In order to evaluate correctly (and not underestimate) the effect of degenerated in mass A/H (above ca.
150 GeV) bosons, in [32] the following prescription was proposed:
q
overlap
S H,A = S 2H + S 2A − 2 · ǫ · S H · S A ,
(IV.6)
overlap
250
mH [GeV]
mh [GeV]
where S H,A is the combined significance from the two Higgs boson degenerated in mass, S H(A) is the significance from H(A) boson, ǫ is variable proportional to |mH − mA |/σm , where σm is the expected mass resolution
of H or A Higgs bosons for a given mass and ǫ = −0.33 for |mH − mA |/σm ∼ 1.4, ǫ = −1 for |mH − mA |/σm ∼ 0
and ǫ = 0 for |mH − mA |/σm >> 2 as obtained with the full simulation studies [32].
200
150
250
200
150
tanβ = 10
100
tanβ = 10
100
tanβ = 30
tanβ = 30
50
50
0
100
120
140
160
180
200
0
100
220
120
140
160
180
4.5
4
3.5
200
220
mA [GeV]
5
Γ A [GeV]
5
Γ H [GeV]
Γ h [GeV]
mA [GeV]
4.5
4
3.5
5
4.5
4
3.5
3
3
3
2.5
2.5
2.5
2
tanβ = 10
2
tanβ = 10
2
tanβ = 10
1.5
tanβ = 30
1.5
tanβ = 30
1.5
tanβ = 30
1
1
1
0.5
0.5
0.5
100
120
140
160
180
200
220
mA [GeV]
100
120
140
160
180
200
220
mA [GeV]
100
120
140
160
180
200
220
mA [GeV]
Figure IV-6: The mass of h (top left) and H (top right) bosons versus mass of A boson for tan β = 10 (black
points) and tan β = 30 (red points). The total width of different Higgs bosons in the MSSM model for the h boson
(bottom left), H boson (bottom middle) and A boson (bottom right) is shown for the same two tan β values.
We extended this approach to cover also the cases in which A/h are degenerate (below ca. 150 GeV) and H/h
bosons partially overlap and all three bosons have the similar mass (for example for tan β = 10, mA = 120 GeV:
mh ∼ 115 GeV, mH ∼ 135 GeV and σm ∼ 16 GeV. We estimate the combined significance according to the
formula:
q
overlap
S A,H,h = S 2A + S 2H + S h2 − 2 · ǫAH · S A · S H − 2 · ǫAh · S A · S h − 2 · ǫHh · S H · S h ,
(IV.7)
where ǫi j is variable describing overlap of i and j Higgs boson (i, j = h, H, A) reconstructed mass distributions.
We performed calculation of significance for bb̄A/H/h only, separately for ℓℓ ETmiss and ℓ had ETmiss . Finally,
we combined the results from both final states. In Figure IV-7 the limit for tan β in (mA , tan β) plane, where 5 σ
significance is reached for 30 f b−1 , is shown.
10
1
100
Tan β
49
Tan β
Tan β
IV.8. Interpretation in the MSSM model
10
120
140
160
180
200
220
10
1
100
120
140
160
mA [GeV]
180
200
220
1
100
mA [GeV]
120
140
160
180
200
220
mA [GeV]
Figure IV-7: The discovery limit for three mass points 120 GeV, 150 GeV and 200 GeV for ℓℓE miss (left),
T
ℓ had E miss (middle) and both final states combined (right) for 30 f b−1 integrated luminosity. The end of the
T
black line indicates sensitivity equal 5σ.
In Table IV-17 we present details on the minimal tan β above which the significance is larger than 5σ. Our
results are in agreement with the previous analyzes of the ATLAS collaboration [39], where minimal tan β at the
level of 7.5-8.0 for the ℓ had ETmiss final state alone was reported. Only for the mass point 200 GeV we obtained
a worse estimate for minimal tan β = 11.59, while the previous results indicate the value of 8.0. We expect that
this is due to specific selection of the gg → H events in the analysis presented in that publication and not used
here. The improvement I in terms of minimal tan β for which 5σ significance is obtained was calculated as:
I = (1 −
comb
S ll+lhad
S lhad
) · 100% ,
(IV.8)
where S comb is the combined significance for the given mass point and S lhad - significance of ℓ had ETmiss final
state alone. This improvement was found to be at the level of 8-11%.
Table IV-17: The tan β reach for 30 f b−1 and discovery sensitivity of 5σ for the bb̄A/H/h and gg → H processes
combined. Given is also the improvement of combined significance with respect to ℓ had ETmiss mode alone. For
more details see the text.
Selection
120 GeV
Mass points
150 GeV 200 GeV
ℓ ℓ ETmiss
ℓ had ETmiss
combined
8.79
7.81
6.93
11.14
8.79
8.12
15.28
11.59
10.71
improvement I
11.3%
7.6%
7.6%
C IV. T    bb̄H, H → ττ 
50
In Table IV-18 the individual signal significances are presented for ℓℓ ETmiss , ℓ had ETmiss and both channels
combined for mass points: 120 GeV, 150 GeV, 200 GeV and tan β for which "5σ" combined significance limit is
obtained. The improvement J was calculated according to Equation IV.5.
The presented improvement is consistent with the results from the previous section. One should compare
b-jet tag + b-jet veto results from Table IV-16, since in Table IV-18 we already combined the two analyzes. The
25.8% improvement for the mass point 120 GeV is also fully consistent with the reported for the VBF process
30% improvement obtained in the SM analysis.
Table IV-18: The signal significance at given tan β. For more details see the text.
Selection
Mass points
150 GeV
200 GeV
tan β = 8.1 tan β = 10.7
120 GeV
tan β = 6.9
ℓ ℓ ETmiss
ℓ had ETmiss
combined
3.22
4.22
5.31
2.73
4.47
5.23
2.42
4.40
5.02
improvement J
25.8%
17.0%
14.1%
Tan b
In Figure IV-8 we show the final 5σ discovery contour in (mA , tan β) plane for 30 f b−1 of combined gg →
H → ττ and bb̄H, H → ττ processes. The upper line (black) shows the limit for ℓℓ ETmiss , the middle line (blue)
represents the limit for ℓ had ETmiss and the bottom line (red) corresponds to the significance limit when both
final states are combined.
50
40
30
20
10
9
8
7
6
5
4
3
2
1
100
110
120
130
140
150
160
170
180
analyzed range
190
200
210
220
mA [GeV]
Figure IV-8: The MSSM parameter space with new 5 σ discovery contour evaluated in these theses. The upper
line (black) shows the limit for ℓℓ ETmiss , the middle line (blue) represents the limit for ℓ had ETmiss , while the
bottom line (red) corresponds to the significance limit when both final states are combined.
IV.9. Summary
51
IV.9 Summary
In this Chapter the analysis of the signal and background processes for the associated Higgs boson production
with bottom quarks using as reference the Higgs boson mass of mH = 120 GeV, 150 GeV and 200 GeV and the
fast simulation of the ATLAS detector was presented.
As a discovery decay mode discussed was H → ττ decay, with ℓℓ ETmiss or ℓ had ETmiss final state. Establishing
the increase of the discovery potential, with the addition of ℓℓ ETmiss final state, was the main goal of these
studies. In the first step the analysis was carried for the reference SM predictions for the σ × BR. In addition to
the associated production with bottom quarks also the production in gluon fusion was analyzed as adding non
negligible contribution to the final sensitivity. In the second step the obtained estimates for the expected signal
and background have been interpreted in the MSSM model, while taking into account the contributions from all
neutral Higgs bosons: h, H, A.
The studies have been completed with the extended discussion of backgrounds. We have discussed several
approaches for events generations, using either the lowest order Born matrix element and the parton shower or
including higher order matrix element calculations when available. In particular:
• tt¯ background was estimated using (2 → 2), (2 → 4) and (2 → 6) matrix element, and for the final results
the most complete (2 → 6) implementation was chosen;
• W + jet background was estimated with (2 → 1) and (2 → 2) matrix element; the irreducible bb̄W final
state was also discussed explicitly;
• a similar procedure as above was applied to the Z + jet background.
With these very extensive studies, we have chosen for the final results the most conservative predictions
(highest background), but let us stress that the difference did not exceed 20-30% level. It indicates good stability
of the presented analysis. The more insight can come only when we estimate the background from the real data
and tune MC predictions with control channels. The more extended discussion on the signal production processes
is the subject of Chapter V.
The conclusion is that the final state ℓℓETmiss is found to be very important for low mass region, where it
contributes additional 20-40% to the total significance, especially in b-jet tag analysis. This result based on
the fast simulation studies was interpreted in the MSSM model. The scan of the MSSM parameter space was
performed and the improvement of the combined (b-jet veto + b-jet tag) significance dependent on the Higgs
boson mass was found to be between 26% at 120 GeV and 14% at 200 GeV. The presented analysis confirms that
the contribution from ℓℓETmiss channel is small for higher masses of the Higgs boson, above 200 GeV [38].
It has been also confirmed that the background originating from the W boson is marginal in ℓℓETmiss channel.
The dominant background for b-jet veto analysis stream comes from Z/γ∗ , while for b-jet tag analysis comes
from tt¯ process.
The observed effect of smaller acceptance for bb̄W after b-jet tagging procedure in both ℓℓETmiss and ℓ had ETmiss
channels remains to be investigated further in more details. However, it is not crucial for the presented analysis,
since bb̄W contributes 0.3-6.5% of the total expected W background (13.5% for NSF ℓℓETmiss channel) depending
on the analysis stream and the decay mode.
In the full simulation studies it should be possible to control better the background, that has the same sign
(SS) and the opposite sign (OS) of reconstructed visible τ decay products in ℓ had ETmiss . In the Atlfast package
this was not implemented. The reduction of W + jets background by factor 2 is expected. We did not investigate
it in these theses, but it should improve our estimation of signal significance, especially in ℓ had ETmiss mode, by
2-5%, depending on the mass point.
52
C IV. T    bb̄H, H → ττ 
C V
T    
V.1 Introduction
It should be emphasized that the complete calculations embedded in the Monte Carlo generator for the Yukawa
induced Higgs boson production in the bb̄H coupling are not available so far. The inclusive cross-section is
dominated by the bottom-quark fusion hard process bb̄ → H [58]. Recently, a remarkable progress has been
achieved in the theoretical description of the total integrated cross-section. The total inclusive cross-section for
the Yukawa induced Higgs boson production in the bb̄H coupling, the bb̄ → H, has been evaluated to the
next-to-next-to-leading order (NNLO) [59]. The NNLO calculations show almost no scale dependence. The
inclusive cross-section was obtained at the next-to-leading order via fixed order calculations for the hard process
gg, qq̄ → bb̄H [60]. In Figure V-1 we present three Feynman diagrams contributing to the bb̄H production
process.
b
b
h
b
h
g
b
g
b
h
b
Figure V-1: The alternative to bb̄H process Feynman diagrams for bottom quark fusion: bb̄ → H (left) and
gb → bH processes (middle and right).
The obtained results are compatible with the bb̄ → H at the NNLO, and show that there is actually no
large discrepancy between the NLO fixed order calculations and the use of the b-quark structure functions.
This turned out to be contrary to what discussed since long time. The results of the fixed order calculation
have a substantial scale dependence and a better control of the residual large uncertainties was mandatory for
a complete understanding of the comparison between the two approaches. In the discussion about what is the
relevant subprocess for the analyses, as designed in [11], one can argue that if the identified final state had one
high pT bottom quark, the relevant hard process should be gb → bH [61]. The cross-section for gb → bH hard
process has been also computed at the NLO [62] and due to higher order corrections the residual uncertainties
are small. Recently, these results have been improved by the first calculations of the complete O(α) electroweak
corrections to associated bottom quark Higgs production bb̄φ (φ = A, H, h) in the MSSM [63]. The description of
the associated Higgs boson production with bottom quark is still under development and new improvements are
proposed [64]. They concern consistent treatment of the top-quark loop diagrams, the NNLO parton distributions
and the resummation.
54
C V. T    
Although several new NLO and even NNLO calculations have become available for the integrated crosssections, only the LO matrix element + parton shower approach is available for events generation. Three different
hard processes: the (2 → 1) process bb̄ → H, the (2 → 2) process gb → bH and the (2 → 3) process
gg, qq̄ → bb̄H can be used alternatively for evaluating Yukawa induced Higgs boson production in the bb̄H
coupling. As we will argue in this chapter, the proposed reconstruction steps are very sensitive to the topology of
the signal production process. The good theoretical modeling and understanding of the possible control channels
will be therefore mandatory for the convincing experimental evidence. Those problems still need to be addressed
from the perspective of the experimental analyses.
For the comparative study presented in this chapter and published in [4, 5] we decided to discuss SM-like
Higgs boson of the mass 120 GeV. We compare quantitatively reconstruction efficiencies and final resolution
figures for different production mechanisms and for both, ℓℓETmiss and ℓ had ETmiss , final states.
V.2 Different production mechanisms: sensitivity to the kinematics
For the signal we consider three production mechanisms which in the discussed mass range could contribute to
the discovery potential for the SM and/or the MSSM:
• the production mechanism via gluon fusion gg → H, dominant in the SM. This is so called direct Higgs
production process;
• the production mechanism in association with the b-quarks, gg, qq̄ → bb̄H. This is so called associated
Higgs production process. This production is almost negligible in the SM scenarios, but could be strongly
enhanced in the MSSM scenarios. The characteristic topology comes with the presence of the pair of rather
soft b-quarks in the final state. In fact we will later discuss three different approaches for generation of
physics events which explore a Yukawa b-quark coupling to the Higgs boson (so b-quark fusion);
• the production mechanism in the vector boson fusion, the VBF production qq → qqH. This production
contributes on the level of 20% of the direct production at the mass of 120 GeV of the Higgs boson. The
characteristic topology comes with the presence of the pair of forward/backward quarks with large rapidity
gaps∗ .
Only the third production mechanism is shown to provide perspectives for signal observability in the SM,
while all three processes contribute to the discovery potential in MSSM model. The purpose of the discussion
presented here is to quantify the impact of the different production topologies on the quality of signal reconstruction and not to embark on the discussion on the theoretical precision of the Monte Carlo predictions for different
production mechanisms.
∗
This production process was not discussed in the analysis presented in previous chapter, since we concentrated on the associated
Higgs boson production with bottom quarks production process, thus the analysis of the VBF process was beyond the scope of these
theses.
V.2. Different production mechanisms: sensitivity to the kinematics
55
Table V-1 gives the cross-section times branching ratio of a decay into one or two leptons (single flavour) for
ℓℓETmiss and ℓ had ETmiss final states.
Table V-1: Cross-sections for signal processes and single flavour lepton. Branching ratio of H → ττ and both
τ → ℓνν (in ℓℓETmiss mode) as well as branching ratio of one τ → ℓνν and another τ → had ν (in ℓ had ETmiss
mode) are included. The SM Higgs boson of the mass of 120 GeV was generated.
Process
σ × BR
[fb]
gg → H → ττ
gg, qq̄ → bb̄H → ττ
qq → qqH → ττ
41.5
0.5
10.0
both τ → ℓνν
315
3.9
78
τ → ℓνν, τ → had ν
gg → H → ττ
gg, qq̄ → bb̄H → ττ
qq → qqH → ττ
τ decay
The first line in Figure V-2 shows the transverse momenta distribution of the Higgs boson generated with
different production mechanisms in ℓℓETmiss final state.
101
Entries 400000
Mean
34.63
RMS
36.6
0.016
×10
101
Entries 100000
Mean
27.53
RMS
26.3
-3
0.25
101
Entries 300000
Mean
81.3
RMS
47.08
0.0014
0.014
0.0012
0.2
0.012
0.001
0.01
0.15
0.0008
0.008
0.1
0.006
0.004
0.0006
0.0004
0.05
0.002
00
0.0002
20
40
60
80
00
100 120 140 160 180 200
pHiggs(GeV)
T
20
40
60
80
100 120 140 160 180 200
pHiggs(GeV)
T
104
Entries 150200
Mean
18.51
RMS
16.65
0.1
0
20
40
60
80
100 120 140 160 180 200
pHiggs(GeV)
T
105
Entries 59457
Mean
31.43
RMS
20.29
0.024
0.022
0.02
0.08
0.018
0.06
0.014
0.016
0.012
0.01
0.04
0.008
0.006
0.02
0.004
0.002
00
20
40
60
80
100
120
140
160
180
200
pl (GeV)
T
Higgs
00
20
40
60
80
100
120
140
160 180 200
phad(GeV)
T
Figure V-2: The pT
distribution for three production mechanisms: gg → H (upper left), gg → bb̄H (upper
middle) and qq → qqH (upper right) in ℓℓE miss . The transverse momenta distribution of the lepton from the
T
leptonic τ decay (bottom left) and of the ρ hadron (bottom right) from the hadronic τ decay in ℓ had E miss for
T
the gg → H production. Distribution normalized to total σ × BR [pb].
56
C V. T    
Higgs
The average pT
value for the gg → H is 35 GeV, the gg → bb̄H is 28 GeV and the qqH is 82 GeV. The
observed higher average transverse momenta in the gg → H production than in the gg → bb̄H production is
a direct consequence of modeling for the QCD ISR radiation, as implemented in the Monte Carlo generator.
For the gg → H production implemented is the, so called, improved parton shower model [65], in contrast to
the case of the gg → bb̄H process, for which the simple parton shower model is only available. As has been
Higgs
already widely discussed in [11, 53], the pT
distribution has a direct impact on the efficiency of the signal
reconstruction. It will be therefore very important to have a precise theoretical understanding and predictions for
its shape. This would require the availability of the NLO or even the NNLO predictions in the form of the Monte
Carlo generators.
In the ℓ had ETmiss channel there is on average more visible energy from the τ-lepton decays. In the case of
hadronic decay only the ντ is emitted, while ντ and νℓ are emitted in the case of the leptonic one. This fact is
illustrated in the bottom line of plots in Figure V-2 for the gg → H production process. The average transverse
momenta of the lepton component of the τ decay is 18.5 GeV, while the average transverse momenta of the
hadron component of the decay of another τ is 31.4 GeV.
V.3 Selection criteria
For studies of different theoretical approaches for modeling bb̄H process, we simplified selection procedure
as defined in Chapter IV, and applied it to Higgs production mechanisms expected at the LHC. We decided
to first apply kinematic cuts on | sin ∆φ1,2 | > 0.2, where 1 and 2 correspond to a visible decay product of τ
decay, pmiss
> 15 GeV and only then we resolved neutrino four-momenta. We have not performed b-jet tag/veto
T
selection. The detailed selection can be found in Table V-2 and Table V-3 for ℓℓETmiss and ℓ had ETmiss respectively.
The pmiss
> 15 GeV selection is definitely too low for studies done with the fast simulation, since the
T
estimates might be too optimistic. This threshold should be raised to at least 30 GeV; however for the consistency
with the analyzes done previously, we keep nevertheless a low threshold for the basic selection. An additional
requirement (xτ21 + xτ22 ) < 1 has been used in publication [52]. We found that this requirement is not improving
mass resolution, but it only leads to an unnecessary loss of signal acceptances, so we decided not to apply it here.
V.4 Signal reconstruction
Table V-2 and Table V-3 present cumulated acceptances for the selection described in the previous section in
ℓℓETmiss and ℓ had ETmiss respectively. After the basic selection, acceptance for the VBF production (qqH) of the
Higgs boson is more than two times higher than for the direct production. It is the kinematics of those events (two
associated quarks with pseudorapidity gap and high transverse momenta of the Higgs boson) that leads to higher
acceptance in this case. The less favourable for the reconstruction is the kinematics of the associated production,
thus resulting in the lowest acceptance of all production mechanisms. The similar behaviour is observed after
adding an additional selection and in the case of the SF events. The acceptance for qqH processes is by factor
10 larger than for the bb̄H in both final states.
V.4. Signal reconstruction
57
Table V-2: The cumulative acceptances of the selection criteria in ℓℓE miss for three different production mechaT
nisms.
gg → H
%
bb̄H
%
qqH
%
2 isolated ℓ, pT > 15 GeV
|sin(∆φℓℓ )| > 0.2
pmiss
> 15 GeV
T
resolved neutrinos
18.6
10.5
7.8
6.5
19.1
10.0
6.1
4.4
21.4
19.0
17.5
15.9
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
4.0
3.6
3.5
1.9
1.6
1.5
13.0
12.4
12.3
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
3.4
2.0
1.5
0.7
11.7
8.3
Selection
basic selection
additional selection
only SF
Table V-3: The same as Table V-2, but for ℓ had E miss channel.
T
gg → H
%
bb̄H
%
qqH
%
basic selection
1 isolated ℓ, pT > 20 GeV
1 τ-jet, pT > 30 GeV
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
resolved neutrinos
14.2
8.0
7.5
4.8
14.6
7.5
7.2
3.5
16.5
14.8
13.7
10.7
additional selection
pmiss
> 30 GeV
T
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
2.0
1.8
1.8
0.9
0.7
0.7
7.1
6.9
6.9
Selection
In Figure V-3 we show distributions for some of the kinematical variables used during the events selection: sin(∆φℓℓ ), pmiss
and mℓℓ . The distributions of corresponding variables for ℓ had ETmiss look similar. One
T
can clearly observe different angular correlations between visible decay products, which are related to the average transverse momenta of the Higgs system for a given production mechanism. This is the most outstanding
favourable effect for the higher acceptance in the VBF production. The second noticeable effect is the higher
acceptance for the ETmiss selection and efficiency for resolving neutrino system for the gg → H production with
respect to the associated gg → bb̄H production.
58
C V. T    
×10
121
Entries 37269
Mean 0.00365
RMS
0.4778
-3
0.45
×10
121
Entries
9591
Mean 0.001346
RMS
0.4049
-6
6
0.4
×10
121
Entries 32061
Mean -0.001932
RMS
0.7351
-3
0.22
0.2
5
0.18
0.35
0.16
4
0.3
0.14
0.25
0.12
3
0.1
0.2
0.08
2
0.15
0.06
0.1
0.04
1
0.05
-1
-0.8 -0.6
-0.4 -0.2
0
0.2
0.4
0.6
0.8
1
-1
-0.8 -0.6
-0.4 -0.2
0
0.2
0.4
sin(∆φ(l,l))
×10
141
Entries 20928
Mean
35.91
RMS
32.73
-3
0.5
0.6
0.8
1
-0.8 -0.6
-0.4 -0.2
0
0.2
0.4
sin(∆φ(l,l))
9
×10
-6
0.6
0.8
1
sin(∆φ(l,l))
141
Entries
5013
Mean
24.12
RMS
20.49
×10
141
Entries 28535
Mean
58.36
RMS
39.61
-3
0.12
8
7
0.4
0.02
-1
0.1
6
0.08
5
0.3
0.06
4
0.2
3
0.04
2
0.1
0.02
1
00
×10
20
40
60
80
100
120
140
160 180 200
pmiss(GeV)
T
191
Entries
6996
Mean
51.75
RMS
14.01
-3
00
1.2
×10
20
40
60
80
100
120
140
160 180 200
pmiss(GeV)
T
191
Entries
809
Mean
51.46
RMS
12.09
-6
0.16
×10
20
40
60
80
100
120
140
160 180 200
pmiss(GeV)
T
191
Entries 18391
Mean
52.02
RMS
14.9
-3
0.12
1
0.14
00
0.1
0.12
0.8
0.08
0.1
0.6
0.08
0.06
0.06
0.4
0.04
0.04
0.2
0.02
0.02
00
20
40
60
80
100
120
140
160
180
200
mll(GeV)
00
20
40
60
80
100
120
140
160
180
200
mll(GeV)
00
20
40
60
80
100
120
140
160
180
200
mll(GeV)
Figure V-3: The characteristic kinematical distributions before respective selection in ℓℓE miss for different proT
duction processes: gg → H (left column), gg, qq̄ → bb̄H (middle column) and qq → qqH (right column). The
shaded (yellow) area will be accepted by the respective selection. Distributions normalised to total σ × BR [pb].
V.5. Mass reconstruction for signal events
59
V.5 Mass reconstruction for signal events
The expected mass resolution of the ττ system is the second important ingredient of the total cumulative acceptance. Basing on the several previous studies [11, 38], it is rather obvious that the resolution of the reconstructed
mττ distribution and the level of tails outside the fixed mass window depend on the average transverse momenta
of the Higgs boson at production (so the assumption that τ-decay products are parallel is correct) and on the quality of the reconstruction of ETmiss . A quantitative discussion on the impact of ETmiss reconstruction can be found in
Appendix A.3. It has been shown that the resolution of the reconstructed mττ is proportional to σE miss /sin(∆φℓℓ ),
T
where ∆φℓℓ is the angular separation in the transverse plane between visible products of τ decays [53]. The
Higgs
average sin(∆φℓℓ ) is closer to zero for lower average pT
(see first line of plots in Figure V-3).
Table V-4 and Table V-5 give the gaussian resolution and the acceptance in the fixed mass window of
mH = 120 GeV ± 20 GeV after consecutive selection in ℓℓETmiss and ℓ had ETmiss modes respectively. After
generic selection almost (15.9 GeV-10.1 GeV)/10.1 GeV = 57% (40%) worse resolution could be expected for
the topology of the gg → bb̄H production and 10% (6%) for the topology of the gg → H production with respect
to the topology of the VBF production in ℓℓETmiss (ℓ had ETmiss ). One should therefore be careful when discussing
theoretical uncertainties of the expected signal observability. The systematic error of the theoretical predictions
on the topology of production process might be the dominant source of the theoretical error.
From Table V-4 is also obvious that ∆Rℓℓ < 2.8 selection is not improving resolution any further, while the
pmiss
> 30 GeV and cos(∆φℓℓ ) > −0.9 are both helpful in improving mass resolution. The resolution can be still
T
reduced by further increasing threshold on the pmiss
and by rejecting upper tails in the mℓℓ distributions. But
T
the improvement from increasing threshold on pmiss
comes
with the price of reducing signal acceptance rather
T
strongly. The kinematics of the gg → bb̄H production remains less favourable for the expected mass resolution.
One can also notice that the resolution in the ℓ had ETmiss final state is on average 10% better than in the
miss
ℓℓET final state for the chosen selection. This is due to the fact that the mean value of the transverse momenta
of hadronic decay product of the τ-lepton is factor two higher than the mean value of the leptonic decay product
(see Figure V-2).
Table V-4: The resolution of the reconstructed invariant mass of the ττ system in ℓℓE miss channel for different
T
Higgs boson production mechanisms. Results from gaussian fit in mass window mH = 120 GeV ± 20 GeV.
Acceptance within the same mass window is shown in brackets.
Selection
gg → H
bb̄H
qqH
basic selection
12.8 ± 0.3 GeV
(72.0%)
19.8 ± 2.6 GeV
(60.3%)
10.9 ± 0.1 GeV
(82.6%)
pmiss
> 30 GeV
T
11.3 ± 0.2 GeV
(80.0%)
11.1 ± 0.2 GeV
(83.9%)
11.1 ± 0.2 GeV
(84.8%)
17.5 ± 2.5 GeV
(68.6%)
16.8 ± 2.4 GeV
(74.1%)
15.9 ± 2.1 GeV
(75.3%)
10.3 ± 0.1 GeV
(86.0%)
10.2 ± 0.1 GeV
(88.0%)
10.1 ± 0.1 GeV
(88.4%)
11.1 ± 0.3 GeV
(84.8%)
9.9 ± 0.2 GeV
(89.0%)
15.5 ± 1.9 GeV
(75.2%)
13.4 ± 1.8 GeV
(80.7%)
10.1 ± 0.1 GeV
(88.4%)
9.4 ± 0.1 GeV
(90.8%)
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
60
C V. T    
Table V-5: The same as Table V-4, but for ℓ had E miss channel.
T
Selection
gg → H
bb̄H
qqH
basic selection
13.4 ± 0.4 GeV
(73.3 %)
22.9 ± 2.9 GeV
(63.1%)
10.8 ± 0.1 GeV
(85.1 %)
pmiss
> 30 GeV
T
10.5 ± 0.3 GeV
(84.7 %)
10.3 ± 0.3 GeV
(88.8 %)
10.2 ± 0.3 GeV
(89.1 %)
14.4 ± 1.5 GeV
(73.3%)
13.4 ± 1.3 GeV
(81.0%)
13.4 ± 1.3 GeV
(81.5%)
9.7 ± 0.1 GeV
(90.1 %)
9.6 ± 0.1 GeV
(91.5%)
9.6 ± 0.1 GeV
(91.6 %)
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
V.6 Different Monte Carlo approaches for Yukawa induced bb̄ → H production
process
As has been already discussed in Section V.1, there are very interesting theoretical issues related to predicting
total cross-section and modeling events topologies for generating Yukawa induced bb̄ → H production process.
We will concentrate just on event topologies only and present the status of the Monte Carlo generators. At the
hard scattering we may consider only (2 → 1) process of the bb̄ → H annihilation convoluted with the structure
functions for the b-quarks. The second approach would be to consider (2 → 2) process, gb → bH scattering, also
relying on the structure functions for b-quarks. The third one is to consider (2 → 3) processes, the gg, qq̄ → bb̄H,
with no b-quarks structure functions involved. If the bb̄ → H is considered as the lowest order matrix element,
the second and third hard process contribute to NLO and NNLO terms respectively. With neither of the existing
Monte Carlo generators we can predict correctly the mixture of all the above topologies, generated according
to the complete NNLO predictions. It will be mandatory to have available such a Monte Carlo sample, because
the complete experimental analysis, which is foreseen for signal observation in the MSSM scenario, requires
identification of one relatively soft b-jet, or vetoing the b-jet. The detailed discussion on theoretical issues related
to different approaches was published in [58–62].
V.6. Different Monte Carlo approaches for Yukawa induced bb̄ → H production process
61
In Table V-6 we list the cross-section (for single flavour leptons) as obtained from Pythia 6.2 simulation
according to default initialization. We used default CTEQ5L structure function and no attempt was made to
change the definition of the renormalization scale, the Q2 scale of the hard process or the definition of the bquark mass. Thus the normalization of the cross-section could be used for illustrative purpose only. We will
not pursue further the subject of cross-section normalization but we will concentrate on the issues related to the
kinematics and acceptances for the signal reconstruction only.
Table V-6: Cross-section for signal production with bb̄H Yukawa coupling (single flavour leptons) in ℓℓE miss
T
and ℓ had E miss mode. Three different approaches are discussed. Branching ratio of H → ττ as well as of both
T
τ → ℓν are included. The SM Higgs boson of the mass of 120 GeV was generated.
σ × BR [fb]
τ decay
both τ → ℓνν τ → ℓνν, τ → had ν
Process
bb̄ → H → ττ
gb → bH → ττ
gg, qq̄ → bb̄H → ττ
2.2
1.2
0.5
16.7
9.5
3.9
Figure V-4 shows the transverse momenta distribution of the Higgs boson as generated with different hard
Higgs
processes. The average pT
for: the bb̄ → H is 23 GeV, the gb → bH is 31 GeV and the gg → bb̄H is 28 GeV.
101
Entries 400000
Mean
23.15
RMS
18.32
×10
101
Entries 400000
Mean
30.87
RMS
31.97
-3
×10
101
Entries 100000
Mean
27.53
RMS
26.3
-3
0.25
0.5
0.001
0.2
0.4
0.0008
0.15
0.0006
0.3
0.0004
0.2
0.0002
0.1
00
20
40
60
80
100 120 140 160 180 200
pHiggs(GeV)
T
Higgs
00
0.1
0.05
20
40
60
80
100 120 140 160 180 200
pHiggs(GeV)
T
00
20
40
60
80
100 120 140 160 180 200
pHiggs(GeV)
T
Figure V-4: The pT
distribution in ℓℓE miss for the three production mechanisms: bb̄ → H (left), gb → bH
T
(middle) and gg → bb̄H (right). Distribution normalised to total σ × BR [pb].
62
C V. T    
In Table V-7 and V-8 we compare acceptances for the signal events generated with different processes in
ℓℓETmiss and ℓ had ETmiss modes. We follow the same pattern of the selection criteria as discussed in Section V.4.
Higgs
Although the differences in the average pT
may look not too sizable, the cumulative effect on the acceptances
after ∆Rℓℓ selection is of factor two between the events generated with bb̄ → H and bb̄H hard processes.
These tables indicate that, with analyses as designed presently, the large systematic theoretical uncertainty
should be assumed for the efficiency of the selection and reconstruction. This is the consequence of a lack of
definitive theoretical predictions for modeling the topology of the complete production process. This effect is
even stronger for the SF case and additional selection.
Table V-7: The cumulative acceptance of the selection criteria in ℓℓE miss for different approaches of modelling
T
production process.
bb̄ → H
%
gb → bH
%
bb̄H
%
2 isolated ℓ, pT > 15 GeV
|sin(∆φℓℓ )| > 0.2
pmiss
> 15 GeV
T
resolved neutrinos
18.6
9.1
5.3
3.7
18.6
10.2
7.1
5.5
19.1
10.0
6.1
4.4
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
1.3
0.9
0.9
2.9
2.5
2.4
1.9
1.6
1.5
mℓℓ < 80 GeV
pmiss
> 50 GeV
T
0.9
0.2
2.3
1.3
1.5
0.7
Selection
basic selection
additional selection
only SF
Table V-8: The same as Table V-7, but for ℓ had E miss channel.
T
bb̄ → H
%
gb → bH
%
bb̄H
%
basic selection
1 isolated ℓ, pT > 20 GeV
1 τ-jet, pT > 30 GeV
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
resolved neutrinos
14.2
6.9
6.6
3.2
14.2
7.8
7.4
4.2
14.6
7.5
7.2
3.5
additional selection
pmiss
> 30 GeV
T
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
0.6
0.4
0.3
1.4
1.2
1.1
0.9
0.7
0.7
Selection
V.6. Different Monte Carlo approaches for Yukawa induced bb̄ → H production process
63
In Table V-9 we compare gaussian resolutions and acceptances inside mass window of mH = 120 GeV ±
20 GeV for different production processes. The obtained resolutions are moderately different, eg. by 20% between bb̄ → H and gb → bH topologies, but they will still enhance the differences in total acceptances already
introduced by the selection efficiencies.
Table V-9: The resolution of the reconstructed invariant mass of the ττ system in ℓℓE miss channel for different
T
approaches of modeling production process. The results from gaussian fit in mass window mH = 120 GeV ±
20 GeV. Acceptance within the same mass window is shown in brackets.
Selection
bb̄ → H
gb → bH
bb̄H
basic selection
23.2 ± 2.3 GeV
(57.2 %)
16.5 ± 0.5 GeV
(62.7 %)
19.8 ± 2.6 GeV
(60.3%)
pmiss
> 30 GeV
T
17.8 ± 1.3 GeV
(63.1 %)
17.7 ± 1.9 GeV
(70.5 %)
18.0 ± 2.0 GeV
(72.0 %)
14.4 ± 0.6 GeV
( 71.5.0 %)
13.7 ± 0.5 GeV
(76.9 %)
13.6 ± 0.5 GeV
(77.7 %)
17.5 ± 2.5 GeV
(68.6%)
16.8 ± 2.4 GeV
(74.1%)
15.9 ± 2.1 GeV
(75.3%)
17.7 ± 1.9 GeV
(72.0 %)
17.1 ± 3.4 GeV
(74.9 %)
13.6 ± 0.5 GeV
(77.6 %)
11.6 ± 0.5 GeV
(83.8 %)
15.5 ± 1.9 GeV
(75.2%)
13.4 ± 1.8 GeV
(80.7%)
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
mℓℓ < 80 GeV
pmiss
> 50 GeV
T
The gaussian resolution for the reconstructed invariant mass of the ττ system in ℓ had ETmiss channel is
specified in Table V-10. Similarly, as in the ℓℓETmiss channel, the best resolution is obtained for the gb → bH hard
process, the bb̄ → H, gives almost 20% worse resolution. The sensitivity to the topology is weaker than in the
ℓℓETmiss channel and the resolution is on average better (for chosen selection criteria). The differences in the mass
resolution will enhance the differences already observed for the cumulative acceptances of the selection criteria.
Table V-10: The same as Table V-9, but for ℓ had E miss channel.
T
Selection
bb̄ → H
gb → bH
bb̄H
basic selection
21.0 ± 1.8 GeV
(58.5 %)
15.7 ± 0.6 GeV
(64.2%)
22.9 ± 2.9 GeV
(63.1%)
pmiss
> 30 GeV
T
17.0 ± 2.1 GeV
(63.5%)
14.2 ± 1.5 GeV
(72.8%)
14.4 ± 1.6 GeV
(74.0%)
12.6 ± 0.5 GeV
(75.1%)
12.4 ± 0.5 GeV
(82.3 %)
12.3 ± 0.5 GeV
(83.2 %)
14.4 ± 1.5 GeV
(73.3%)
13.4 ± 1.3 GeV
(81.0%)
13.4 ± 1.3 GeV
(81.5%)
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
64
C V. T    
The different estimates for the total cumulative acceptance inside mass window, including selection efficiencies, are presented in Table V-11 and Table V-12. The less favourable is bb̄ → H topology. These tables are
a clear indication of the size of the systematic uncertainty which should be assigned to the predictions of the
expected number of signal events. One should consider it an indication of the size of the theoretical uncertainties
related to the lack of definitive prescription for the modeling of the production process.
Table V-11: The cumulative acceptance in the mass window mH = 120 GeV ± 20 GeV in ℓℓE miss for different
T
approaches of modeling production process.
Selection
bb̄ → H
%
gb → bH
%
bb̄H
%
basic selection
2.1
3.5
3.0
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
0.8
0.7
0.6
2.1
1.9
1.8
1.5
1.4
1.3
mℓℓ < 80 GeV
pmiss
> 50 GeV
T
0.6
0.1
1.8
1.1
1.3
0.6
Table V-12: The same as Table V-11, but for ℓ had E miss channel.
T
Selection
bb̄ → H
%
gb → bH
%
bb̄H
%
basic selection
1.9
2.7
2.2
1.0
9.6 · 10−1
9.5 · 10−1
6.4 · 10−1
5.7 · 10−1
5.6 · 10−1
pmiss
T
> 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
10−1
3.5 ·
2.6 · 10−1
2.5 · 10−1
V.7 Summary
In this chapter we have discussed a theoretical uncertainty of modeling Yukawa induced Higgs boson production
associated with b-quarks. We have concentrated on the presentation of the impact on the experimental efficiencies
and mass resolution from different modeling of the production process, hence different event topologies.
• We have shown that for the signal reconstruction only (depending on the production process) the cumulative acceptance in the mass window may differ by factor few (even up to factor 10). The main effect is a
result of the different average transverse momenta of the Higgs boson, predicted by different approximations.
• The strong sensitivity to the production topology indicates that for the more complicated production
processes like bb̄H Yukawa coupling induced mechanism the possible large theoretical systematic error
should be carefully discussed for the predictions. Even if the overall normalization can be calculated nowadays with the NNLO approximation and the effects related to the QCD regularization and renormalization
scale are well understood, the Monte Carlo implementation will be mandatory for the final experimental
analysis before the limits or discovery can be firmly established.
V.7. Summary
65
Let us just recall that for the MSSM Higgs scenarios in the parameter space corresponding to the A/H/h
masses in the range 100-150 GeV one would have to combine statistically different production modes (gg → H,
qqH and bb̄ → H), different final states (ℓℓETmiss and ℓ had ETmiss ) and the overlapping mass values (degeneracy
for the h/H/A masses). The key challenge for the theoretical systematic error will be normalization and modeling
of the production mechanism. The key challenge for the experimental analysis will be controlling the contribution
from the resonant Z/γ∗ → ττ process. A more detailed discussion of the latter can be found in Appendix A.4. A
further discussion of theoretical uncertainty corresponding to different approaches for modeling the bb̄H process
is beyond the scope of these theses.
66
C V. T    
C VI
T 1P3P A
VI.1 Introduction
The τ leptons play an important role in electroweak measurements, in the studies of the top quark properties and
in the search for new physics. They interact electroweakly but still decay hadronically in ca. 64% cases. The τ-s
coming from W or H ± decay are 100% polarized. The spin correlations between τ-s in H → ττ or Z → ττ might
be explored to enhance the signal or measure CP of the decaying resonance.
In the regions of the MSSM parameter space with high tan β, τ̃ - the supersymmetric τ - becomes the lightest
supersymmetric lepton and it decays predominantly into τ-s.
The τ lepton decays either into lighter leptons (∼ 36%) or into hadronic jet (∼ 64%). At the moment, the
leptonic decays can not be distinguished experimentally from prompt electrons or muons emerging in the event,
so in the analyzes, for triggering leptonic decays of τ, generic electron or muon trigger are usually used. The
reconstruction of hadronic τ-decay at hadron colliders is faced with overwhelming cross-section of the expected
background dominated by multi-jet production. The exclusive feature of τ decay is that τ decay products are
well collimated in space (opening angle is limited by ratio mτ /Eτ ), thus leading to narrow jets with typically 1
charged track (originating from one π± ∼ 78%) or 3 charged tracks (∼ 22%). In general, both excellent tracking
and calorimetry are essential for the hadronic τ decay reconstruction.
We will begin this chapter with an overview of the on-going experiments at Tevatron and their techniques for
reconstruction and identification of hadronic τ (Section VI.2). In the next Section VI.3 the CMS collaboration
methods are summarized. Then, in Section VI.4 the generic ATLAS algorithm for τ reconstruction is described.
In the following section the tau1P3P algorithm is introduced. In Section VI.5 we recall the main features of
the hadronic τ decays, basing on the truth∗ information from the generation level. In Section VI.6 we give a
detailed description of the algorithm for reconstruction and identification of one-prong and three-prong decays.
In Section VI.7 we present the results on the performance for reconstructing true and fake hadronic τ′ s from
large samples of qq̄ → Z → ττ, qq̄ → W → τν and QCD di-jet events. Separately discussed are one-prong and
three-prong modes, together with the estimates for the rejection performance for fake tau’s originating from hardprocess quarks or gluons. In Section VI.8 the optimization of discussed algorithm with multivariate methods is
presented.
VI.2 Identification of τ leptons at Tevatron
At present, the hadron collider that has the highest energy available in the center of mass is Tevatron, placed at
Fermi National Accelerator Laboratory, Batavia, Illinois, USA. During the first data taking period (Run I: 19921996) the two experiments, the Collider Detector at Fermilab (CDF) and the DØ , have accumulated around
125pb−1 of data at 1.8 TeV. The new data taking period with improved detectors started in March 2001 and
should allow to collect 4 − 9 f b−1 before the year 2009. The Tevatron accelerator was improved as well, and
now it collides protons with anti-protons at the center of mass energy of 1.96 TeV with initial luminosity of
8.6 · 1031 cm−2 s−1 .
∗
By truth we mean the information about kinetic and flavours of generated particles obtained from MC generators.
68
C VI. T 1P3P A
VI.2.1
Detectors overview
Both Tevatron detectors, the DØ and the CDF, have been built according to the same scheme as the ATLAS
detector described in Chapter II: the closest to the interaction point is a tracker (placed in the magnetic field),
then a calorimeter (divided into an electromagnetic and a hadronic part), and the most distant are muons chambers
(the most outer part of the detector).
In the DØ experiment the central tracking consists of a silicon microstrip tracker and a central fiber tracker,
both located in 2 T magnetic field generated by a superconducting solenoidal magnet. Both systems trackers
were optimized to provide a precise tracking and vertexing capabilities over pseudorapidity rage |η| < 2.5. The
calorimeter is divided, similarly as in the ATLAS detector, into central section (barrel) covering |η| < 1.1 and two
end-cap calorimeters that complete coverage to |η| < 4.2, each housed in a separate cryostat. A muon system, at
|η| < 2, consists of a layer of tracking and scintillation trigger counters in front of 1.8 T toroids, followed by two
similar layers behind them [66].
The tracking system of the the CDF-II detector comprises of silicon micro-strip detectors and a cylindrical wire drift chamber and is placed in 1.4 T magnetic field of a superconducting solenoid magnet. Outside the
solenoid there are electromagnetic and hadronic calorimeters covering |η| < 3.6. The essential advantage of the
CDF experiment is a central electromagnetic shower maximum detector placed in the electromagnetic calorimeter at a depth of 6 X0 . It consists of proportional chambers with anode wires parallel to the beam axis and
orthogonal cathode strips that allow to determine the electromagnetic shower with spatial resolution of ∼ 0.5 cm
[67, 68].
VI.2.2
Reconstruction of hadronic τ decays at Tevatron
The Tau Trigger
The first step in finding τ leptons is to trigger an interesting event. Both experiments have single τh † , and di-τ
triggers (e + τh and µ + τh .).
The CDF experiment as τh takes a single track at LVL2 plus isolation around it at LVL3. The DØ has a
similar τh trigger adding calorimetric tower at LVL1 and loose Neural Network (NN) [69] cut at LVL3.
For triggering basic physics processes like W → τν both experiments use τh + ETmiss trigger. In the case of
Z(H) → τe,µ τh , also a single electron or single muon trigger is used.
Building Tau Candidates
Both the DØ and the CDF collaborations worked out the methods for τ lepton reconstruction and identification,
taking advantage of a very good resolution of specific detectors [70, 71]. The τ candidate in both experiments
is reconstructed by matching calorimeter clusters with tracks. However, a seed around which the cone is built is
different for each experiment.
The DØ Collaboration starts the reconstruction of a τ-candidate with building a calorimeter cluster from cells
inside cone ∆R < 0.5 around the seed tower and keeps clusters for which the collected energy in cone ∆R < 0.3
is ET > 5 GeV. The τ candidate must have at least one track associated inside ∆R < 0.3. The three tracks are
associated to the τ if the invariant mass of two tracks with highest pT is less then 1.1 GeV and the invariant mass
of three tracks is less than the mass of the τ.
The CDF collaboration starts with a seed track with pT > 6 GeV in |η| < 1.0. In order to exploit the fact that
τ-jet is very well collimated the signal cone is not constant, but is defined as:
αtrk = min (0.17, max (5 GeV/Evis , 0.05)) ,
where Evis is visible energy measured in the calorimeter. This method is called a tau shrinking cone method.
The cluster energy is collected in towers that have granularity in (η, φ) equal 0.1 × 2π/24. The seed tower should
have at least 6 GeV. The adjacent towers (up to six) with at least 1 GeV are also included into the cluster. The
†
by τh we mean hadronic decay of a τ-lepton, τe - decay into electron and τµ - decay into muon
VI.3. Identification of Tau Leptons with CMS
69
additional tracks (prongs) are associated with the τ candidate if they have pT > 1 GeV and have z0 (z-position of
the track point, closest to the interaction point) compatible with a seed track:
seed
|ztrk
0 − z0 | < 5 cm.
The identification of π0 is an important aspect of building a τ-candidate. In order to identify clusters that can
be assigned to π0 , the CDF experiment takes advantage of the multi-wire proportional chamber placed in the electromagnetic calorimeter at the shower maximum (6X0 ) with spatial resolution of 2-3 mm. In the DØ experiment
the sub-clusters in the electromagnetic calorimeter with a minimum energy of 0.8 GeV indicate π0 .
VI.2.3
Identification of hadronic τ decays at Tevatron
After reconstruction, the next step is the identification of a candidate for hadronic τ-decay. The CDF Collaboration uses the following set of variables:
• the visible mass of tau candidate, mτtrk+π0 ;
• the track mass of tau candidate, mτtrk ;
• the charge of all prongs, Qtrk =
• the ratio of E T /
P
τ−tracks
P
τ−tracks
Qtrk ;
ptrk
T for e/τ separation;
• isolation I of tracks and π0 candidates, calculated by summing pT within 300 cone around track.
The DØ Collaboration uses Neural Networks in the identification of hadronic τ decays. The NN are trained
on isolation, calorimeter shape and calorimeter-track correlations variables.
The above presented procedure yields for the CDF experiment in ca. 48% τ-jet reconstruction + identification
efficiency for visible transverse momenta of the τ candidate with pT > 30 GeV and less than 0.5% fake rate
in the same pT region [72]. In the search for the new phenomena (MSSM Higgs boson decay into τ-s) the
exemplary CDF analysis starts with a trigger selection: electron or muon with pT > 10 GeV and a tau candidate
with pT > 15 GeV in the event. Then a lepton and a τ identification cuts are applied. The events tagged as
Z → ee, Z → µµ events, triggered as coming from cosmic rays or γ conversions are rejected. Additionally, to
suppress W + jets and Z → ττ they require HT = pτT1 + pτT2 + ETmiss > 50 GeV. Also a cut on the direction and
magnitude of ETmiss with respect to the two tau candidates is applied. However, the observed number of events is
in agreement with the SM expectations (excluding Higgs). With no excess of new physics, they set a limit on the
MSSM Higgs production, as reported in Section III.3.
VI.3 Identification of Tau Leptons with CMS
In the publications presented recently by the CMS Collaboration [73–75], concerning τ-jet reconstruction and
searches for the Higgs boson, in its decays into τ lepton pair, with consecutive decay into τe τh or τµ τh the
following procedure (with details dependent on the final state) is described.
The τ-jet candidates are reconstructed from the calorimeter cells in a cone of 0.4 in (η, φ) plane. The observed
jet
jet with ET > 40 GeV is considered a τ candidate if there are 1 - 3 tracks in the τ signal cone of 0.04. The tracks
are constructed inside the jet reconstruction cone and the leading track is searched for in a cone of ∆R = 0.1
around τ-jet direction. There are separate thresholds on transverse momentum for 1-prong leading track pT >
10 GeV and 3-prong leading track pT > 20 GeV. The CMS analyzes require also an opposite charge of the e(µ)
leadingtrack
and τ jet signal tracks. The identified electrons (on the basis of ETHAD /pT
ratio) are removed from the
sample of τ-jet candidates.
The tracker isolation provides rejection factor more than 10 against QCD jets for τ-jet efficiency of 70%.
The tagging by a flight path method for τ-jet efficiency of 80% an additional rejection factor 5 can be obtained.
70
C VI. T 1P3P A
VI.4 Identification of Tau Leptons with ATLAS
Hadronic τ identification in ATLAS has been studied for several years as a key benchmark signature for optimization of a detector design and presently, to optimize the performance of the final reconstruction algorithms. The
results have been reported on several occasions and the most recent references are [11, 37, 38, 49, 76]. Presently
(Spring 2007), there are two well-established reconstruction algorithms: calorimeter-based and track-based. The
second one was developed as a part of these theses.
VI.4.1
The tauRec package
Until 2005, the ATLAS Collaboration base-line algorithm for reconstruction of hadronic τ-decays in the Athena
framework was based on the calorimeter, implemented as, so called, tauRec package [77].
This algorithm starts with calorimetric cluster as a seed for a τ-candidate. It sums up the energy deposition
in calorimetric towers ∆η × ∆φ = 0.1 × 2π/64 in cone ∆R < 0.4. Since calorimetric clusters have a default
threshold on minimal energy (15 GeV), every calorimeter cluster becomes a τ-candidate. For each candidate
tauRec collects all the tracks with ∆R < 0.3 with pT > 2 GeV around the cluster center. In the next step
the clusters are calibrated using a H1-style method. This method was used in the H1 experiment at the HERA
accelerator at the Deutsches Elektronen-Synchrotron (DESY) in Hamburg. It is based on parametrisation of
weigths for each calorimeter cell. The weights depend on the transverse energy deposited in given cell (ET ) and
the position in (η, φ) plane. They are obtained in process of minimization jets energy resolution from jets samples
with known ET , φ and η.
For all candidates, the identification variables are evaluated around the seed center. The most important
variables are: a number of cells with energy deposition above 0.2 GeV in the first layer of electromagnetic
calorimeter (for its fine granularity), the fraction of energy in a ring between cone 0.1 and 0.2 in respect to
the energy deposited in cone 0.4 (isolation parameter) in all layers, and energy deposition and electromagnetic
radius: the sum of cells ET weighed by distance in (η, φ) between a cell and the seed (shower shape).
The last step is the calculation of the likelihood (default LLH2004), on which then an identification cut is
applied (see left plot in Figure VI-1) [78].
The above described procedure is obviously also applied to fake candidates originating from QCD jets. As
a result, the rejection versus τ-jet efficiency can be plotted (right plot in Figure VI-1). For efficiency of 50%
rejection of ca. 100 can be obtained for low pT τ candidates.
Figure VI-1: The tauRec likelihood discriminant, LLH2004, distribution (left): τ-jet candidates are in black and
QCD fakes are in red. The rejection against QCD jets versus τ-jet efficiency in different pT windows (right). The
dotted lines represent results with noise, while solid - without noise [78].
VI.5. Hadronic τ decays
VI.4.2
71
The tau1P3P algorithm
As an important part of these theses, the new algorithm for reconstruction and identification of hadronic τ-decays
called tau1P3P [7,79] was developed. Its main concept is to start building a τ-candidate from good quality tracks,
which are used as a seed. The algorithm is intended for studies of a low mass Higgs, around 120 GeV, with visible
energy from hadronic τ decays in the range 20 - 70 GeV. The algorithm is designed to explore exclusive features
of hadronic τ decays: one-prong or three-prong signature; the presence of only charged hadronic energy (π± or
3π± ) and of only neutral pure electromagnetic energy (nπ0 ), both components being collimated in space. We
have accommodated the energy flow algorithm [80, 81] to define energy scale of reconstructed candidates, as
will be described in more details later. The tau1P3P algorithm was introduced to the official ATLAS software
in summer 2006. It is used for simulated data processing since October 2006.
VI.5 Hadronic τ decays
For the partonic level studies the events were generated using interface of Pythia and Tauola packages provided
by the AcerMC 2.0 framework [42]. The generation correctly included full spin correlations in the τ production
and decays.
Table VI-1 shows branching ratios as presently implemented in the Tauola package [44], with form factors
tuned by the CLEO collaboration [82].
Table VI-1: The τ decay branching ratios, based on 108 simulated τ decays from Z → ττ events. Numbers were
taken from Demo runs of MC-Tester [83] - the package for automatic validation of the Monte Carlo generators.
Decay modes
Tauola-CLEO
τ → eνe ντ
τ → µνµ ντ
17.8 %
17.4 %
τ → π± ντ
τ → π0 π± ντ
τ → π0 π0 π± ντ
τ → π0 π0 π0 π± ντ
τ → π± π± π± ντ
τ → π0 π± π± π± ντ
τ → π0 π0 π± π± π± ντ
τ → π0 π0 π0 π± π± π± ντ
τ → K ± Xντ
τ → (π0 )π± π± π± π± π± ντ
others
11.1 %
25.4 %
9.19 %
1.08 %
8.98 %
4.30 %
0.50 %
0.11 %
3.74 %
0.10 %
0.03 %
For one-prong hadronic decays, the τ → π± ν mode contributes 23.4% and τ → nπ0 π± ν mode the remaining
76.6%. For three-prong hadronic decays, the τ → 3π± ν decay contributes 64.6%, and τ → nπ0 3π± ν mode only
25.6 %.
We have studied an expected fraction of charged and neutral energy in the hadronic tau decays and a cone
separation between decay products using dedicated partonic level sample of 105 events. Figure VI-2 shows a
P
P
fraction of π± and π0 energies with respect to the visible energy of the hadronic decay products of τ, ETtruth ,
for a one-prong (left) and three-prong (right) decay modes, selected by requiring ETtruth > 20 GeV and
±
±
pπT max > 10 GeV. The requirement for pπT max > 10 GeV is clearly enhancing a fraction of charged energy in the
selected hadronic τ. For one-prong this fraction is on average 70% at ETtruth = 20 GeV, decreasing to around 50%
for larger values of ETtruth . For three-prong this fraction is on average around 80%-70%, and remains stable in the
energy range ETtruth = 20 − 100 GeV.
72
C VI. T 1P3P A
Z → τ τ: 3 prongs
hist100005
1
ET3π / ETvis
0.9
±
±
1π
ET
/ ETvis
Z → τ τ: 1 prong
0.8
0.7
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
10
20
30
40
50
60
70
80
0
0
90 100
Evis
T (GeV)
Z → τ τ: 1 prong
0
0.9
0.8
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
30
40
50
60
70
80
40
50
60
70
80
90 100
Evis
T (GeV)
0
0
90 100
Evis
T (GeV)
hist100106
0.8
0.7
20
30
0.9
0.6
10
20
1
0.7
0
0
10
Z → τ τ: 3 prongs
hist100006
1
ETn π / ETvis
0
0.8
0.6
0
0
ETn π / ETvis
0.9
0.7
0.1
hist100105
1
10
20
30
40
50
60
70
80
90 100
Evis
T (GeV)
P
P
Figure VI-2: The fraction of energy carried by the π± (top), π0 (bottom) with respect to the visible transverse
energy for hadronic one-prong (left) and three-prong (right) decay modes. Preselection of ETtruth > 20 GeV and
±
pπT max > 10 GeV was applied. Results shown for qq̄ → Z → ττ events.
P
Figure VI-3 shows cone separation ∆R between π± and ETtruth directions (calculated as energy weighted
barycenter) for a one-prong and three-prong decays. In the case of the three-prong decays cone separation of the
most energetic π±lead and ETtruth direction is also shown. It is easy to notice that the visible decay products of the τ
are close to each other. In the case of one-prong decays the mean distance between direction of the π± and ETtruth
P
direction (< ∆R >) is less than 0.02. In case of three-prong decays, the mean distance of the barycenter of π± ’s
and ETtruth direction < ∆R > is less than 0.01, and is much smaller than the distance of the direction of leading
π± and ETtruth direction.
Z → τ τ: 3 prongs
vis
0.09
±
±
vis
∆ R (πlead, ET )
0.09
0.08
0.07
Z → τ τ: 3 prongs
hist100109
0.1
∆ R (3π , ET )
hist100008
0.1
±
vis
∆ R (πlead, ET )
Z → τ τ: 1 prong
0.08
0.09
0.08
0.07
0.07
0.06
0.06
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0
0
0
0
10
20
30
40
50
60
70
80
90 100
Evis
T (GeV)
10
20
30
40
50
60
70
80
90 100
Evis
T (GeV)
hist100108
0.1
0
0
10
20
30
40
50
60
70
80
90 100
Evis
T (GeV)
Figure VI-3: The cone separation between the most energetic π±lead and ETtruth directions for a one-prong (left)
and three-prong (middle), and between ETtruth direction and energy weighted barycenter for three-prong (right).
±
Preselection of ETtruth > 20 GeV and pπT max > 10 GeV was applied.
VI.6. Reconstruction of the hadronic τ’s
73
VI.6 Reconstruction of the hadronic τ’s
After studying the topology of the hadronic τ decays at the LHC, we constructed the algorithm which explores
the features of the object. We applied it to the fully simulated data. The definition of the one-prong and threeprong hadronic τ-candidates is based on the presence of the good quality hadronic track(s) which will seed τ
reconstruction. The reconstruction and the identification of the τ-candidates is based on the following steps:
• reconstruction
– identify and qualify a leading hadronic tracks;
– create one-prong (τ1P ) and three-prong (τ3P ) candidates, define (η, φ) position of a seed and the
energy scale of the candidate, check charge consistency for three-prong candidates;
• identification
– calculate calorimetric and energy-flow identification variables;
– accept a candidate as a hadronic τ (one-prong or three-prong) according to the sequential cuts on the
variables mentioned above or with use of multivariate techniques.
The cone ∆R = 0.2 around the seed is used as a core of the reconstructed visible decay products of the τ, while
region outside 0.2 < ∆R < 0.4 is used to define isolation criteria. For a one-prong mode we require exactly
one good quality hadronic track with no nearby tracks. For a three-prong mode exactly three nearby tracks are
required, as the leading chosen is the most energetic one. The nearby tracks are searched for in a cone of ∆R = 0.2
around the seed, which is defined as track position at vertex (for a one-prong mode) or barycenter of the three
tracks weighted with ptrack
(for three-prong mode). We are interested in one-prong and three-prong candidates
T
only. For more inclusive analyses, e.g. W → τν, the number of tracks associated with candidate Ntrk spectrum is
of primary interest and the algorithm presented here has been extended to discussion of two-prong and multiple
track candidates as well. This further development is not a part of these theses.
VI.6.1
The leading hadronic track
The track is considered as a good quality one if it has passed some minimal criteria for a good quality reconstruction:
S i > 8 and N S traw > 10;
• the minimal number of hits in the silicon and straw detectors, NHits
Hits
• the threshold on the value of the impact parameter, |d0 | < 1.0 mm;
• the upper limit on the value of the χ2 of the fit for the trajectory reconstruction, χ2 < 1.7.
Figure VI-4 shows efficiency, as a function of the track transverse momenta, for acceptance of a given track as a
good quality one. This efficiency is 80% at pT > 2 GeV and 90% for pT > 10 GeV in the |η| < 1.5 range.
efficiency
Z → τ τ: qualified tracks
hist1001321
1.2
1.1
1
0.9
0.8
0.7
0.6
0
5
10
15
20
25
30
35
40
45 50
ptrack
(GeV)
T
Figure VI-4: The efficiency, as a function of track transverse momenta, for accepting a given track as a good
quality one. Plot is shown for non-leptonic tracks only and |η| < 1.5. Performance based on ATLAS Software of
September 2005.
74
C VI. T 1P3P A
We require also that the good quality track is not identified as an electron or a muon track. For the time
being, this veto is based on the truth information only, because of the lack of the availability of the dedicated
algorithms.
We have only roughly checked the expected electron-track veto efficiency with use of TR hits. Figure VI-5
shows the efficiency for labeling a track as an electron track by the requirement that the minimal number of TR
hits is equal to 5. With this criterion alone, around 60-70% of true electron tracks will be labeled as such, with
around 2-3% loss of the true hadronic tracks. The results are shown for qq̄ → Z → ττ sample with electrons
coming mostly from leptonic decays of a second τ. This efficiency for electron track veto is certainly not sufficient
and for this purpose the dedicated algorithm needs to be prepared. This was beyond the scope of the presented
theses.
Z → τ τ: ele-veto on non-lep tracks
hist1001325
1
efficiency
efficiency
Z → τ τ: ele-veto on ele tracks
0.9
0.8
0.09
0.08
0.7
0.07
0.6
0.06
0.5
0.05
0.4
0.04
0.3
0.03
0.2
0.02
0.1
0.01
0
0
5
10
15
20
25
30
35
40
45 50
ptrack
(GeV)
T
hist1001326
0.1
0
0
5
10
15
20
25
30
35
40
45 50
ptrack
(GeV)
T
Figure VI-5: The efficiency for labeling a given track as electron-track for true electron tracks (left) and nonelectron tracks (right). Only good quality tracks are included in the plot. Performance based on the ATLAS
software of September 2005.
The good quality track is considered as a leading track if its transverse momentum is above a given threshold
pT > 10 GeV‡ , and if the number of nearby good quality tracks (in the cone ∆R < 0.2 and with pT > 2 GeV) is
not greater than 2. Finally, we checked that the asymmetry in the charge of the good quality tracks distribution
measured from assignments of the charge by the reconstruction algorithm is around 0.5% for ptrack
> 10 GeV
T
(in this sample we expect no asymmetry from physics). Wrong assignment of the charge of the track would lead
to some loss in the acceptance for three-prong τ decays.
VI.6.2
The τ1P and τ3P hadronic τ’s
vspace-1mm The one-prong hadronic τ candidate, called τ1P -candidate, is seeded by the leading hadronic track
which has no nearby tracks (see the previous section). No threshold is initially required on the accompanying
calorimetric energy deposition in the cone around the track.
In Figure VI-6 we show the separation ∆R at the vertex between the visible τ decay products direction (truth
information) and the reconstructed track direction. The results are presented for the qq̄ → Z → ττ sample and
for τ1P candidates with ETcalo > 20 GeV. One can conclude that the true direction of the visible τ decay products
is fairly well represented by the track η and φ at the vertex. The track η and φ at the vertex will therefore be used
as the τ1P direction, as has been already discussed in [7].
The three-prong hadronic τ candidate, called τ3P -candidate, is seeded by the leading hadronic track which
has exactly two associated good quality nearby tracks (with pT > 2 GeV). No threshold is initially required
on the accompanying calorimetric energy deposition in the cone around the track. In Figure VI-6 the middle
plot shows the separation ∆R at the vertex between the visible τ decay products direction (truth information)
and the reconstructed direction of the leading track. The right plot shows the separation between the visible τ
decay products and direction of the barycenter (weighted with ptrack
) of the three tracks at vertex. The barycenter
T
reproduces much better the original direction of the visible decay products of the τ and therefore it will be used
as the τ3P direction.
‡
This threshold is higher than the one used by the CDF experiment and certainly can be optimized further.
VI.6. Reconstruction of the hadronic τ’s
Z → τ τ: 3 prong
0.09
0.08
0.07
Z → τ τ: 3 prong
hist1031
0.1
∆ R(τvis,τ3P)
hist1021
0.1
∆ R(τvis,tracklead)
∆ R(τvis,τ1P)
Z → τ τ: 1 prong
75
0.09
0.08
0.09
0.08
0.07
0.07
0.06
0.06
0.06
0.05
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0
0
10
20
30
40
50
60
70
80
90 100
Evis
T (GeV)
0
0
hist1032
0.1
0.01
10
20
30
40
50
60
70
80
90 100
Evis
T (GeV)
0
0
10
20
30
40
50
60
70
80
90 100
Evis
T (GeV)
Figure VI-6: The separation ∆R between the true direction of the barycenter of the visible decay products of the
τ and the reconstructed direction of the hadronic τ, defined as position at vertex of a leading hadronic track in
one-prong (left), in three-prong (middle) and the barycenter of tracks at vertex in three-prong (right) hadronic
τ’s. ∆R is shown as a function of the true visible transverse energy of the τ. Error-bars denote RMS of the
distributions. Results for qq̄ → Z → ττ sample.
Table VI-2 summarizes the quality of the position reconstruction in (η, φ) coordinates for one-prong and
three-prong decays. In the ∆R(τreco , τtruth ) < 0.025 (the size of a cell in the middle layer of the electromagnetic
calorimeter) is contained around 84% and 98.1 % of reconstructed τ1P and τ3P respectively.
Table VI-2: The reconstruction quality of the visible decay products of the hadronic τ-candidates from the qq̄ →
Z → ττ sample, (η, φ) coordinates.
τreco
η
φτ
reco
−η
τtruth
− φτ
truth
∆R(τreco , τtruth ) < 0.025
τ1P
τ3P
< m >= −0.7 · 10−6
σ = 1.8 · 10−4
RMS = 1.2 · 10−2
< m >= 3.5 · 10−5
σ = 6.7 · 10−4
RMS = 1.2 · 10−2
< m >= 2.2 · 10−5
σ = 3.1 · 10−4
RMS = 4.5 · 10−3
< m >= −5.5 · 10−5
σ = 6.0 · 10−4
RMS = 5.0 · 10−3
83.9%
98.1 %
For τ1P , reconstruction is unique, namely the same track cannot be used for reconstructing two different τ1P
objects. For the τ3P , the same track can be matched together with other two to form different groups of three
nearby tracks. However, for the analyzed sample of qq̄ → Z → ττ events and true τ3P objects the probability for
not unique grouping turned out to be very small. In less than 1% of the cases the same track was classified as
nearby track to two different leading tracks.
The requirements of the total charge measured from the individual charge of the tracks to be ±1 gives 97.4 %
acceptance for the true τ3P for the sample of Z → ττ events.
76
C VI. T 1P3P A
VI.6.3
The energy scale of τ1P and τ3P
The energy scale of the hadronic τ candidate is defined with use of an energy flow algorithm, as has been
discussed in [80] and [81]. The algorithm is executed only on the cells belonging to the core of the hadronic τ,
that is within a distance ∆R = 0.2 from a seed.
Energy deposition in cells is classified into several categories:
• the pure electromagnetic energy ETemcl . Energy collection is seeded by the good quality electromagnetic
cluster, namely only those electromagnetic clusters that have no substantial hadronic leakage behind and
that are isolated from the good quality tracks are used as seeds. Only presampler, strip and middle layers
are used. The cell closest to the electromagnetic cluster position is searched for at each layer and the
distance is calculated from that cell. Energy is collected in two steps. First, narrow window in ∆η × ∆φ =
chrgEM
0.0375 × 0.0375 is used. In a second iteration, after collection of ET
(see below), a wider window,
2 · 0.0375 × 3 · 0.0375 is used,
chrgEM
• the charged electromagnetic energy ET
. Energy collection is seeded by the impact point of the
track(s) at each layer. Presampler, strip, middle and back layers are used. The cell closest to the track
impact point (η, φ) at each layer is searched for and the distance is calculated from that cell. Only narrow
window 0.0375 × 0.0375 is used,
chrgHAD
• the charged hadronic energy ET
. Energy collection is seeded by the (η, φ) impact point of the track(s)
at the last layer of the electromagnetic calorimeter. All layers of the hadronic calorimeter are used and
energy is collected in a cone ∆R = 0.2,
• the neutral electromagnetic energy ETneuEM . Energy collection is seeded by the track (η, φ) at vertex and
the closest cell is searched for at each layer. Energy is collected from remaining cells in a cone ∆R = 0.2,
only presampler, strip and middle layers are used.
chrgEM
The algorithm for the energy collection starts from collecting ETemcl in the narrow window. Then the ET
chrgHAD
and ET
are collected, followed by the second iteration for the ETemcl performed in the wide window. As
chrgEM
chrgHAD
the last one, the ETneuEM is collected. For the τ3P , the collection of ET
, ET
is done iteratively for each
track.
As a reference, the total calorimetric energy associated with the τ1P or τ3P objects, ETcalo , is calculated using
a cone ∆R = 0.4 around the seed. The distance is always calculated with respect to the closest cell at a given
layer to the nominal (η, φ) of reconstructed τ1P or τ3P objects. By definition:
chrgEM
ETcalo = ETemcl + ETneuEM + ET
chrgHAD
+ ET
+ ETotherHAD + ETotherEM ,
(VI.1)
where ETotherEM and ETotherHAD is calculated from the remaining energy deposition in a distance 0.2 < ∆R < 0.4
from the nominal (η, φ) of the reconstructed hadronic τ.
In the energy-flow approach for defining energy scale of the τ1P and τ3P :
chrgEM
chrgHAD
• we replace charged energy deposition, ET
+ET
by the track(s) momenta (no hadronic neutrals),
P
• we assume that π0 contribution is included in ETemcl and ETneuEM ,
chrgEM
• we correct for residual effects with resET
and resETneuEM ,
• we omit ETotherHAD and ETotherEM .
e f low
The definition of the energy scale ET
e f low
ET
reads as follows:
= ETemcl + ETneuEM +
X
ptrack
+
T
X
chrgEMtrk
resET
+ resETneuEM .
(VI.2)
VI.6. Reconstruction of the hadronic τ’s
77
chrgEM
The more detailed discussion on how the resET
and resETneuEM terms are built is presented in publication [81]; here we just briefly recall only final formulas.
The tracks in the τ1P object are classified into three categories, based on the indication whether the early
interaction of the hadronic track, or the π0 /π± overlap took place. It is shown in [81] that an early interaction is
correlated with the low hadronic energy deposition around the track impact point. The π± /π0 overlap is correlated
with the energy deposition in the narrow window around the track in the presampler and strips layer.
chrgEM01
• Category (A): ET
/ptrack
< 0.05;
T
chrgEM01
/ptrack
> 0.05 and ET
T
chrgEM01
/ptrack
> 0.05 and ET
T
• Category (B): ET
• Category (C): ET
chrgHAD
/ptrack
> 0.40;
T
chrgHAD
< 0.40,
/ptrack
T
chrgEM01
where ET
is a ET calculated for the cells in the first two layers of the electromagnetic calorimeter.
Depending on the category of a track, different formula is used for calculating residual terms, as specified in
Table VI-3.
chrgEMtrk
Table VI-3: Formulas used for calculating resET
type
and resETneuEM for τ1P and τ3P energy scale.
chrgEMtrk
cathegory
resETneuEM
resET
chrgEM
(A)
ET
− 0.7 · ptrack
T
0
or 0 if negative
τ1P
(B)
(C)
chrgEM01
min(2.5 · ET
chrgEM
ET
chrgEM
, ET
− 0.65 ·
)
chrgEMtrk
resET
τ3P
chrgEMtrk
= ET
−0.1 · ptrack
T
or 0 if (ETneuEM + resETneuEM ) < 0
or 0 if negative
(A)
0
ptrack
T
− 0.7 · ptrack
T
max(−0.1
P
ptrack
, −ETneuEM )
T
max(−0.1
P
ptrack
, −ETneuEM )
T
or 0 if negative
other
0
P
In the case of τ3P we simplify the procedure, as we expect much smaller contribution from π0 . Each track
chrgEMtrk
is treated separately and the resET
is non zero only for tracks belonging to category (A). The contribution
to the resETneuEM is defined independently on the track category. Table VI-4 quantifies the quality of the energy
scale determination. The fraction of events accepted in the mass window of ±10% and ±20% around nominal
value of the visible τ energy is presented. In the wider window this fraction is equal 88.3% and 93.8% for τ1P
and τ3P respectively.
e f low
Table VI-4: Acceptance inside specified windows for the ET
reco τ
mean <>
τ1P
τ3P
1.0
1.0
fraction inside window
<> ± 10% <> ± 20%
65.2 %
73.4 %
88.3 %
93.8 %
/ETtruth .
78
C VI. T 1P3P A
e f low
Figure VI-7 shows ETcalo /ETtruth and ET /ETtruth distributions for reconstructed τ1P and τ3P . Much better resolution is obtained for τ3P than for τ1P , as dominant part of the energy comes from charged pions, reconstructed
with tracking.
Z → τ τ: 1 prong
Z → τ τ: 3 prongs
hist200
Entries
9949
Mean
0.8989
0.1266
RMS
0
Underflow
0
Overflow
χ2 / ndf
49.13 / 17
783.4 ± 10.89
Constant
Mean
0.8951 ± 0.001137
0.09599 ± 0.001091
Sigma
800
700
600
500
hist300
Entries
2672
Mean
0.8403
0.117
RMS
0
Underflow
4
Overflow
χ2 / ndf
28 / 17
226.8 ± 5.925
Constant
Mean
0.8268 ± 0.001987
0.08899 ± 0.00177
Sigma
250
200
150
400
100
300
200
50
100
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Z → τ τ: 1 prong
1.6
0
0
1.8 2
truth
Ecalo
T /ET
800
600
0.4
0.6
0.8
1
1.2
1.4
1.6
Z → τ τ: 3 prongs
hist205
Entries
9817
Mean
1.016
RMS
0.1297
Underflow
0
2
Overflow
41.78 / 7
χ2 / ndf
Constant
886.5 ± 15.52
Mean
1.014 ± 0.001201
0.0663 ± 0.00151
Sigma
1000
0.2
1.8 2
truth
Ecalo
T /ET
hist305
Entries
Mean
RMS
Underflow
Overflow
χ2 / ndf
Constant
Mean
450
400
350
300
Sigma
2636
1.022
0.1004
0
4
43.67 / 3
413.4 ± 14.9
1.011 ± 0.00106
0.0303 ± 0.001059
250
200
400
150
100
200
50
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
0
1.8 2
truth
Eeflow
T /ET
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8 2
truth
Eeflow
T /ET
Figure VI-7: The energy scale of all τ1P and τ3P compared to the τ visible decay products. The ETcalo /ETtruth ratio
e f low
(left plot) and ET /ETtruth ratio (right plot) distributions are shown. Results are presented for the qq̄ → Z → ττ
sample.
e f low
Figure VI-8 shows a profile plot of the ET /ETtruth ratio as a function of ETtruth for reconstructed τ1P and
τ3P . For both cases, the mean position of the energy scale is stable within a few percent over large range of the
nominal energy of the visible τ.
Entries
9815
2
Z → τ τ: 3 prongs
ETeflow/ETtruth
ETeflow/ETtruth
Z → τ τ: 1 prong
1.8
1.6
1.6
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0
0
2632
1.8
1.4
0.2
Entries
2
0.2
10
20
30
40
50
60
70
80
90 100
Etruth
T (GeV)
0
0
10
20
30
40
50
60
70
80
90 100
Etruth
T (GeV)
Figure VI-8: The energy scale of all τ1P and τ3P compared to the τ visible decay products. The profile plots of
the ratio, as a function of ETtruth are shown. Results are presented for the qq̄ → Z → ττ sample.
VI.6. Reconstruction of the hadronic τ’s
VI.6.4
79
The calorimetric observables
Several calorimetric observables should be used to discriminate a narrow τ-cluster from the hadronic cluster
originating from quarks or gluons. As has been already discussed in the previous sections, for a one-prong
hadronic τ decays the cone separation between neutral electromagnetic and charged hadronic decay products is
very small. For three-prong decays, in most of the cases, cone ∆R = 0.2 around the barycenter of charged energy
is sufficient to contain all three tracks. The cone ∆R = 0.2 is used to define core of the hadronic τ cluster, while
a larger cone, ∆R = 0.4, is used for the isolation criteria.
The discriminating observables which we recall below have been used previously in several analyzes [49,77,
79], although the exact definitions might be slightly different.
If not stated otherwise, the calorimetric observables are calculated from cells in the distance of ∆R = 0.2
from a seed. The τ1P is seeded by the leading hadronic track at vertex (track η and φ at the vertex). The τ3P is
seeded by the barycenter of three nearby tracks. Some minimal threshold on the energy deposition in cells is also
required.
• The electromagnetic radius of the τ-candidate, Rτem , calculated from cells around the seed and weighted by
the transverse energy deposition of a given cell. Only those cells which belong to the first three samplings
of the electromagnetic calorimeter (presampler, strips and middle) are used for the calculation
Rτem
=
P
∆R seed,cell · ETcell
.
P cell
ET
(VI.3)
τ
• The number of strips, N strips
, with energy deposition above a certain threshold.
τ
• The width of the energy deposition in strips, W strips
, calculated as the variance in the η coordinate,
weighted by the transverse energy deposition in a given strip
τ
W strips
=
P
strip
(∆η seed,strip )2 · ET
P strip
ET
P
strip
( ∆η seed,strip · ET )2
−
.
P strip
( E T )2
(VI.4)
• The fraction of the transverse energy deposited, f racETR12 , in the 0.1 < ∆R < 0.2 radius with respect to
the total energy in the cone ∆R = 0.2. The cells belonging to all layers of the calorimeter are used
f racETR12
=
P
P
ETcell (∆R seed,cell < 0.2) − ETcell (∆R seed,cell < 0.1)
.
P cell
ET (∆R seed,cell < 0.2)
(VI.5)
Figures VI-9 and VI-10 present the distributions of the above variables for the reconstructed τ1P and τ3P
(with slightly larger statistics than the previous plots). The distributions for both categories are a bit different and
clearly the final optimization of the selection procedure should be done separately for τ1P and τ3P .
We also require a minimal consistency between track transverse momenta, ptrack
, and the energy deposited
T
chrgHAD
in the hadronic calorimeter, ET
. In addition, we impose the isolation criteria, i.e. some requirements on
the energy deposited in a ring 0.2 < ∆R < 0.4, namely the (ETotherEM + ETotherHAD )/ETcalo ratio.
τ
τ
It is worth mentioning, that the shapes of normalized signal and background distribution of N strips
or W strips
look very similar. This is due to the fact, that the reconstruction procedure of the tau1P3P algorithm already
filters QCD jets and passes only the candidates similar to signal.
80
C VI. T 1P3P A
001_tau1P
Entries 18060
Mean
4.222
RMS
3.822
0.3
0.25
002_tau1P
Entries
0.7
18060
Mean 0.0005287
RMS
0.6
0.001038
0.5
0.2
0.4
0.15
0.3
0.1
0.2
0.05
0
0
0.1
10
20
30
40
50
60
70
0.1
80
90
100
NτStrips
0
0
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
WτStrips
003_tau1P
004_tau1P
Entries 18060
Mean
0.183
RMS 0.1505
Entries 18060
Mean 0.05629
RMS 0.02471
0.08
0.2
0.18
0.16
0.14
0.06
0.12
0.04
0.08
0.1
0.06
0.02
0.04
0.02
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0
0.05
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
R12
Rem
fracET
005_tau1P
Entries 18060
Mean 0.3213
RMS 0.3064
0.18
0.16
006_tau1P
Entries 18060
Mean 0.1167
RMS 0.08206
0.3
0.25
0.14
0.2
0.12
0.1
0.15
0.08
0.1
0.06
0.04
0.05
0.02
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0
0
0.2
0.4
0.6
ChrgHAD track
ET
/p
T
0.8
1
1.2
1.4
(E
OtherEM
T
1.6
1.8
OtherHAD
+ET
)/E
2
calo
T
τ
Figure VI-9: Distributions of discriminating variables for τ1P candidates: number of strips N strips
with energy
τ
deposition above a threshold (upper left), width of the energy deposition in strips W strips (upper right), fraction
of the transverse energy deposited in the radius 0.1 < ∆R < 0.2 with respect to the total energy in the cone
∆R = 0.2 (middle left), electromagnetic radius, Rτem , weighted by the transverse energy deposition for given
cell (middle right), fraction of track transverse momenta and energy deposited in the hadronic calorimeter in
chrgHAD
the vicinity of the track
ET
ptrack
T
(bottom left) and ratio
ETotherEM +ETotherHAD
ETcalo
(bottom right). In the plots the solid line
denotes the distributions for signal samples while the dotted one the distributions for background. Histograms
are normalized to give integral equal to 1.
VI.6. Reconstruction of the hadronic τ’s
81
001_tau3P
Entries 4536
Mean 2.534
RMS 2.964
0.5
0.4
002_tau3P
Entries
0.6
4536
Mean 0.0006972
RMS
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10
20
30
40
50
60
70
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0.08
80
90
100
NτStrips
0
0
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
WτStrips
003_tau3P
004_tau3P
Entries 4536
Mean 0.2846
RMS 0.1653
Entries 4536
Mean 0.07132
RMS 0.02488
0.22
0.2
0.07
0.18
0.06
0.16
0.14
0.05
0.12
0.04
0.1
0.03
0.08
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0
0
0.02
0.1
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0.3
0.4
0.5
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0.7
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0.9
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0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
R12
Rem
fracET
0.12
0.1
005_tau3P
006_tau3P
Entries 4536
Mean 0.2602
RMS 0.2007
Entries 4536
Mean 0.1692
RMS 0.09672
0.25
0.2
0.08
0.15
0.06
0.1
0.04
0.05
0.02
0
0
0.2
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1
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1.4
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1.8
2
ChrgHAD track
ET
/p
T
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
(E
OtherEM
T
1.6
1.8
OtherHAD
+ET
Figure VI-10: The same as Figure VI-9, but for τ3P candidates.
)/E
2
calo
T
82
C VI. T 1P3P A
VI.7 Performance for signal and background samples
The performance of the algorithm for the τ1P and τ3P reconstruction and identification is evaluated below for the
fully simulated true and fake hadronic τ’s from qq̄ → Z → ττ, qq̄ → W → τν events and fake hadronic τ’s from
qq̄ → W → eν and gg, gq, qq̄ → gg, gq, qq̄ events. The qq̄ → Z → ττ and qq̄ → W → τν samples provide true
τ candidates from decays of gauge bosons. Those samples provide also fake τ candidates from QCD ISR and
underlying event, which are representative for background to the Higgs search from qq̄ → W → eν, µν events.
To increase available statistics of QCD ISR fake τ candidates we have used also directly the qq̄ → W → eν
sample. The gg, gq, qq̄ → gg, gq, qq̄ events with hard-process partons which initiate hadronic cascade provide a
sample of fake τ candidates that can be attributed to gluon or quark splittings. The hard-process partons can be
used as a reference for evaluating efficiencies and energy scale reconstruction.
VI.7.1
True hadronic τ′ s from qq̄ → Z → ττ and qq̄ → W → τν events
The content of the true hadronic τ samples has been studied on the basis of the Monte Carlo truth information.
Table VI-5 gives the fraction of hadronic τ events passing the different selection cuts on the particle level. The
numbers are given for τ → had ν decays within a pseudorapidity acceptance of |η| < 1.5. Approximately 4.0 · 104
true hadronic τ’s decays from qq̄ → Z → ττ and 2.0 · 104 from qq̄ → W → τν events have been found and
analyzed within kinematic acceptance.
±
The hadronically decaying τ’s will form true τ1P candidates with ETtruth > 20 GeV and pπT > 10 GeV in ca.
±
±
76.6 % and true τ3P candidates with ETtruth > 20 GeV and max(pπT ) > 10 GeV and min(pπT ) < 2 GeV in ca.
22.8%.
At the particle level, the definition of the τ hadronic decay core as ∆R = 0.2 is adequate. For three-prong
decays, 98.9% of τ′ s accepted by other selection have the visible decay products contained within a cone ∆R =
0.2. For one-prong decays this fraction is higher than 99.5%.
Table VI-5: Acceptances for different selections at the particle level, extracted from the fully simulated qq̄ → Z →
ττ events. Numbers are based on approximately 4.0 · 104 hadronic τ decays within |η| < 1.5 from qq̄ → Z → ττ
sample.
Selection/Acceptance
τ’s
one-prong τ
%
three-prongs τ
%
τ → had ντ
+max(pπ±
T ) > 10 GeV
+ETtruth > 20 GeV
+min(pπ±
T ) > 2 GeV
100.0
52.9
42.1
39.0
76.7
32.7
27.8
27.8
22.7
15.3
13.9
10.8
VI.7. Performance for signal and background samples
83
Figure VI-11 shows the transverse momenta of the visible products of analysed hadronic τ decays for τ1P
and τ3P candidates.
true τ : 1 prong
true τ : 3 prongs
hist701
1600
1400
Entries
45297
Mean
21.35
RMS
12.91
Underflow
Overflow
1200
hist702
Entries
500
0
233
400
13535
Mean
25.99
RMS
12.07
Underflow
0
Overflow
76
1000
300
800
200
600
400
100
200
0
0
10
20
30
40
50
60
70
80
90 100
Etruth
T (GeV)
0
0
10
20
30
40
50
60
70
80
90 100
Etruth
T (GeV)
Figure VI-11: The ETtruth distribution of the visible products of analyzed hadronic τ decays.
Table VI-6 gives the fraction of hadronic τ events passing selection cuts, but analyzed after full simulation
and reconstruction with the discussed algorithm. The reconstruction efficiency is 82.6%. For single prong decays
this efficiency is 90.3% and is dominated by the inefficiency for a track to be classified as good quality track.
For three-prong decays reconstruction efficiency is 62.0% and it is also dominated by the inefficiency for all
three tracks to be classified as good quality tracks. Let us recall that for low track transverse momenta this
efficiency is only around 80% per track, see Figure VI-4. A small loss is also due to the requirement of the
charge consistency. We can conclude that the performance and purity of the τ1P reconstruction are very good.
For τ3P the reconstruction efficiency is much lower but still reasonable. Some inefficiency could certainly be
recovered by relaxing the requirement on the quality of the nearby tracks. For the analysis presented here we
have not investigated this further, although it has been already included in the newer version of the algorithm.
Table VI-6: The reconstruction efficiencies with respect to all analyzed hadronic τ decays. The same sample as
used for results of Table VI-5.
Selection/Acceptance
τ’s
%
one-prong τ
%
three-prongs τ
%
τ → had ντ
100.0
76.7
22.7
33.5
6.42
39.9
32.1
0.03
32.4
1.22
6.14
7.36
τ1P , ET
> 20 GeV
e f low
τ3P , ET
> 20 GeV
26.0
6.12
25.1
0.03
0.71
5.83
total
32.0
25.1
6.54
τ1P
τ3P
total
e f low
The total efficiency for reconstructing hadronic τ’s as τ1P or τ3P is 32.0%, out of which around 78.4% will
be reconstructed as τ1P and 21.6% as τ3P . When compared to the branching ratios, with proposed algorithm the
total efficiency for reconstructing one-prong is 33.2% and three-prong is 28.8%. These numbers include around
15% of contamination of the three-prong candidates by true one-prong decays (the nearby tracks come from
underlying event or QCD ISR/FSR).
84
C VI. T 1P3P A
In the following sections a simple cut-based identification selection is proposed, with use of calorimetric
variables as discussed in Section VI.6.4. Table VI-7 shows cumulative acceptances for identification selection.
Only two of those variables have different thresholds depending on τ1P or τ3P identification. The cumulative acceptance is 58.8% and 57.3% respectively. The profile plot as a function of ETtruth for the reconstruction efficiency
and reconstruction + identification efficiency with respect to hadronic τ’s, which pass the kinematical selection
at the truth level is shown in Figure VI-12. The same efficiency, but with respect to all hadronic τ’s, is shown in
Figure VI-13.
Table VI-7: The cumulative acceptance of identification selection for true τ1P and τ3P candidates in the |η| < 1.5
range. Based on about 1.5 · 104 τ1P and 3.9 · 103 τ3P candidates.
Selection/Acceptance
true τ1P
%
true τ3P
%
τ
N strips
< 15
τ
W strips < 0.004
f racETR12
< 0.2(τ1P ), < 0.4(τ3P )
Rτem < 0.08
chrgHAD track
ET
/pT < 1.0
98.9
97.5
99.7
97.4
89.0
80.6
79.4
92.6
65.2
65.2
< 0.15(τ1P ), < 0.25(τ3P )
58.8
57.3
ETotherEM +ETotherHAD
ETcalo
true τ : 3 prongs
hist10721
1
efficiency
efficiency
true τ : 1 prong
0.9
0.8
1
0.9
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
20
25
30
35
40
45
50
55
60
65
70
Etruth
(GeV)
T
hist10722
0
20
25
30
35
40
45
50
55
60
65
70
Etruth
(GeV)
T
Figure VI-12: The reconstruction efficiency, as a function of ETtruth , for true one-prong (left) and three-prong
(right) is shown by open circles. The reconstruction+identification efficiency is shown by full circles. Normalized
respectively to one-prong or three-prong hadronic τ decays with ETtruth > 20 GeV, max(pπ±
T ) > 10 GeV and
π±
min(pT ) > 2 GeV (last line of Table VI-6).
VI.7. Performance for signal and background samples
true τ : 3 prongs
hist10711
1
efficiency
efficiency
true τ : 1 prong
85
0.9
0.8
0.9
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
20
25
30
35
40
45
50
55
60
65
70
Etruth
(GeV)
T
hist10712
1
0
20
25
30
35
40
45
50
55
60
65
70
Etruth
(GeV)
T
Figure VI-13: The same as Figure VI-12, but normalized to all hadronic τ decays.
The final numbers are summarized in Table VI-8. With respect to all hadronic decays, the total efficiency of
proposed algorithm is 18.6% with one-prong mode contributing 14.7% and three-prong contributing 3.75%.
Table VI-8: The total efficiency with respect to all hadronic τ decays, based on the democratic mixture of qq̄ →
Z → ττ and qq̄ → W → τν samples, about 1 · 105 events of each.
VI.7.2
Selection/Acceptance
τ’s
%
one-prong τ
%
three-prongs τ
%
τ → had ν
100.0
76.7
22.7
+ reconstruction
32.0
25.1
6.54
+ identification
18.6
14.7
3.75
Fake hadronic τ′ s from di-jet events
To evaluate rejection power of the proposed algorithm against fake τ′ s, we studied with the full simulation background sample of QCD di-jet events from gg, gq, qq̄ → gg, gq, qq̄ process, called later in the text the dijet35
sample. This sample is clearly biased because it was generated with minimal threshold on the transverse momenta of hard scattering, phard
> 35 GeV. Figure VI-14 shows transverse momenta distribution of the hard
T
process partons in this sample. It nevertheless provides large statistics of jets in the relevant kinematic region and
allows for straightforward control on the reconstruction and identification efficiency (hard-process parton can be
used as a reference).
We have analyzed 2 · 105 events from dijet35 sample in total. The kinematical selection of phard
and
T
|η| < 1.5 has been passed by 1.4 · 105 partons from hard scattering: 82% of them gluons and 18% quarks.
86
C VI. T 1P3P A
Entries 158684
QCD jets: hard process gluon
16000
Entries
QCD jets: hard process quark
34515
3500
14000
3000
12000
2500
10000
2000
8000
1500
6000
1000
4000
500
2000
0
20
25
30
35
40
45
50
55
60
0
20
65 70
Etruth
T (GeV)
25
30
35
40
45
50
55
60
65 70
Etruth
T (GeV)
Figure VI-14: The ETtruth distribution of the analyzed hard-process partons from the QCD jets sample.
The requirement on the charge consistency accepts 93% of reconstructed τ3P candidates. Only 75% of all
τ1P and τ3P candidates matched hard-process partons - the matching was checked within the distance ∆R < 0.2
between hard-process parton and τ1P or τ3P candidates. Around 25% of the candidates did not match, they were
just reconstructed from QCD ISR/FSR radiation.
Tables VI-9 and VI-10 summarize efficiencies for reconstructing τ1P or τ3P matching hard-process parton.
The probability for quarks fragmenting to fake τ is almost three times higher than for gluons, fragmentation of
gluons gives on average higher track multiplicities. For the same reason we should expect higher background in
τ3P than in τ1P sub-samples. In the studied di-jet sample, the total efficiency for reconstructing fake τ1P and τ3P
matching hard-process partons are 2.0% and 4.2% respectively.
Table VI-9: The reconstruction efficiency for fake hadronic τ candidates matched to the hard-process partons.
Normalised to hard-process partons accepted by kinematical selection.
Selection/Acceptance
fraction of total
%
fake τ1P
%
fake τ3P
%
gluons
quarks
82
18
1.1
0.9
2.7
1.5
total
100
2.0
4.2
Table VI-10: The probability for reconstructing τ1P or τ3P from hard-process parton.
Probability
fake τ1P
%
fake τ3P
%
gluon →
quark →
1.3
4.8
3.3
8.5
e f low
It is important to realize that ET
calculation optimized for the true hadronic τ′ s significantly underesti′
mates energy scale for the fake τ s with respect to truth energy. It helps to reject background from QCD jets,
because it requires a much harder hard-process parton than the nominal threshold on the energy scale of the τ1P
and τ3P .
VI.7. Performance for signal and background samples
87
To study the identification selection we collected statistics of 3120 τ1P and 6600 τ3P fake candidates from
dijet35 sample. Efficiencies for simple cut-based selection are summarized in Table VI-11. The rejection power
of the identification selection itself is rather moderate. After the reconstruction algorithm, that provides sample
of τ1P and τ3P calorimetric lateral profile the fake candidates are very similar to those from true τ′ s. One should
also notice more than factor three spread between rejection against fake τ1P from gluons and fake τ3P from
quarks.
Table VI-11: The cumulative acceptances of the fake τ1P and τ3P in the |η| < 1.5 pseudorapidity range¶ based
on about 3.2 · 103 τ1P and 6.6 · 103 τ3P candidates.
Selection/Acceptance
gluon → τ1P
%
gluon → τ3P
%
quark → τ1P
%
quark → τ3P
%
τ
N strips
< 15
τ
W strips < 0.004
f racETR12
< 0.2(τ1P ), < 0.4(τ3P )
Rem < 0.08
chrgHAD track
ET
/pT < 1.0
98.6
71.2
97.6
82.1
97.7
90.5
96.7
88.1
59.0
45.2
42.6
72.3
35.9
35.6
72.9
59.7
55.8
81.7
49.8
49.3
< 0.15(τ1P ), < 0.25(τ3P )
11.2
19.2
20.2
36.7
ETotherEM +ETotherHAD
ETcalo
Table VI-12 summarizes the total efficiency for fake hadronic τ′ s from hard-process partons in dijet35
sample. The most of the hard-process partons have transverse momenta in range 35-50 GeV (see Figure VI-14).
The rejection power against fake hadronic τ′ s, normalized to the hard-process gluons (quarks) amounts to 700
(150) for the τ1P and 100 (30) for τ3P categories respectively. It is clearly noticeable that the three-prong category will have 7-5 times higher background than one-prong category. This statement should not be however
generalized because the relative fraction of reconstructed τ1P and τ3P candidates is correlated with the relative
fraction of quarks and gluons seeding fake τ candidates and will depend also on the shower shape of cascading
partons.
Table VI-12: The cumulative acceptances of the τ1P and τ3P in the |η| < 1.5 pseudorapidity range for the
dijet35 samples based on reconstructed sample of about 2 · 105 events.
Selection/Acceptance
gluon → τ1P
%
gluon → τ3P
%
quark → τ1P
%
quark → τ3P
%
reconstruction
1.3
3.3
4.8
8.5
+ identification
0.14
0.63
0.97
3.12
¶
The algorithm has been already extended to the full rapidity range of the ATLAS detector, |η| < 2.5. However, for the consistency
with the originally published results [7], here we quote numbers for |η| < 1.5.
88
C VI. T 1P3P A
The profile plot as a function of ETtruth for the reconstruction efficiency and the reconstruction+identification
efficiency, with respect to hard process partons which pass the kinematical selection at the truth level, is shown
in Figure VI-15.
hist10611
fake from gluon : 1 prong
0.02
hist10612
fake from quark : 1 prong
efficiency
efficiency
0.025
0.1
0.09
0.08
0.07
0.015
0.06
0.05
0.01
0.04
0.03
0.005
0.02
0.01
0
20
25
30
35
40
45
50
55
60
hist10621
fake from gluon : 3 prong
0.1
0.09
0.08
0.12
0.05
0.1
0.04
0.08
0.03
0.06
0.02
0.04
0.01
0.02
35
40
45
50
55
60
65 70
Etruth
T (GeV)
40
45
50
55
60
65 70
Etruth
T (GeV)
hist10622
0.18
0.14
30
35
0.16
0.07
25
30
0.2
0.06
0
20
25
fake from quark : 3 prong
efficiency
efficiency
0
20
65 70
Etruth
T (GeV)
0
20
25
30
35
40
45
50
55
60
65 70
Etruth
T (GeV)
Figure VI-15: The reconstruction efficiency for τ1P (top) and τ3P (bottom) candidates is shown by open circles
in a function of ETtruth . The reconstruction+identification efficiency is shown by full circles. The results are given
separately for hard process gluons (left) and quarks (right).
VI.7. Performance for signal and background samples
VI.7.3
89
Fake hadronic τ′ s from qq̄ → Z → ττ and qq̄ → W → τν events
The fake τ′ s from the qq̄ → Z → ττ and qq̄ → W → τν events will represent physics background to the
Higgs searches in H → ττ channel. Since the seeding partons come from QCD ISR (initial state radiation), the
transverse momentum spectrum and the shape of the shower of cascading partons depend on the model of the
QCD shower used.
We processed around 2 · 105 events of the qq̄ → W → τν, qq̄ → W → eν and qq̄ → Z → ττ samples
e f low
and reconstructed around 3000 fake τ1P and 3200 fake τ3P candidates. The ET
distribution is shown in
Figure VI-16. The spectrum is noticeably softer than the one of the dijet35 sample events.
qq → W, Z: QCD ISR fake τ1P
hist2129
Entries
3052
Mean
30.27
RMS
9.185
Underflow
0
Overflow
201
250
qq → W, Z: QCD ISR fake τ3P
hist2229
Entries
3320
Mean
36.28
RMS
11.37
Underflow
0
Overflow
230
140
120
200
100
150
80
60
100
40
50
20
0
20
e f low
Figure VI-16: The ET
25
30
35
40
45
50
55
60
65 70
Eeflow
(GeV)
T
0
20
25
30
35
40
45
50
55
60
65 70
Eeflow
(GeV)
T
distribution of the analyzed fake τ1P and τ3P from the QCD ISR in qq̄ → W, Z events.
Table VI-13: The cumulative acceptances of the fake τ1P and τ3P in the |η| < 1.5 pseudorapidity range. We
processed about 2 · 105 events of the qq̄ → W → τν, qq̄ → W → eν and qq̄ → Z → ττ samples.
Selection/Acceptance
fake τ1P
%
fake τ3P
%
τ
N strips
< 15
τ
W strips < 0.004
f racETR12
< 0.2(τ1P ), < 0.4(τ3P )
Rτem < 0.08
chrgHAD track
ET
/pT < 1.0
97.5
92.7
94.1
86.0
75.6
65.6
62.1
78.7
50.5
49.7
< 0.15(τ1P ), < 0.25(τ3P )
31.0
35.6
ETotherEM +ETotherHAD
ETcalo
We expect that 1.5% of events will give fake one-prong τ and 1.6% will give fake three-prong candidate in
τ in |η| < 1.5 in the inclusive qq̄ → W or qq̄ → Z samples. Identification selection will reduce these numbers to
0.46% and 0.57% respectively.
We checked with simple Atlfast [47] reconstruction that in 18% of events one would expect non-calibrated
jet
jet with threshold pT > 20 GeV. Roughly, the reconstruction and the identification proposed here corresponds
to rejection power of 30 against such a jet for each category separately. It is clearly noticeable that including
three-prong category will increase by a factor of two background from QCD ISR radiation.
90
C VI. T 1P3P A
VI.8 Optimization with multivariate techniques
In this section we present the results of optimization of identification performance with three multivariate analysis
methods: Probability Density Estimation with Range Searching (PDE-RS), Neural Network (NN) and Support
Vector Machine (SVM). The comparison was performed on the same data and the same set of discriminating
variables was used.
VI.8.1
PDE-RS
The standard probability density estimation technique (PDE) with probability calculated in the local volume
range search (RS) was used for optimization of the performance of the tau1P3P algorithm [84]. The method
and implementation is based on publication [85]. The technique combines the observables into a single one,
called discriminant, on which then a cut to separate signal from background is applied. The calculation of the
discriminant is based on sampling the signal and background densities in a multi-dimensional phase space built of
variables described in Section VI.6.4. When taking the number of signal events n s and the number of background
events nb in a small volume V(~x) around point ~x in our 6-dimensional space (built of 6 discriminating variables),
ns
then a discriminant is defined as: D(~x) = ns +c∗n
. This is a good approximation of a probability that given
b
candidate comes from signal event, if the total number of simulated events is equal to constant c times total
number of background events. The event counting was done using multi-dimensional binary trees. The data was
split into two parts. One was used for training and the other - for analysis. As has been stated in [85], this method
was supposed to give comparable results to NN network analysis and that has been confirmed here.
Signal efficiency is defined as a ratio of accepted to all signal events, ε = Naccepted /Nall , and background
rejection as a ratio of rejected to all background events, R = 1 − ǫb = Nre jected /Nall . For comparison, we chose
three configurations of so called “working points” defined by signal efficiency 70%, 80% and 90% respectively.
This represents “identification efficiency” and does not include “reconstruction efficiency” of which a candidate
is built [7].
VI.8.2
Neural Network
The Neural Network is a non-linear discriminating method [69]. In our analysis the Stuttgart Neural Network
Simulator [86] was used.
To each neuron j in the hidden layer n inputs xk (k = 1, .., n) and one output variable (the answer of the
neuron) z j are associated. For the first hidden layer the inputs are the discriminating variables, for the next layers
the inputs are the outputs of the preceding layer. All input variables are normalized to be within the range [−1, 1].
The architecture of the network is optimized to give the proper classification of signal and background and
to avoid over-fitting at the same time. The Neural Network is built with 6 input nodes and two layers of hidden
nodes, each with 10 nodes. After applying the skeletonization pruning algorithm [87] the number of hidden
nodes was reduced to 5 in each of two layers. The skeletonization algorithm is based on the Taylor expansion of
the NN around minimum and eliminating the not contributing units. The method is described in detail in [88].
Finally, we obtained the following network architecture (see Figure VI-17):
- an input layer with 6 input nodes corresponding to 6 discriminating variables;
- two internal hidden layers, each containing 5 nodes;
- an output layer containing a single neuron, since the output is a single discriminating variable.
The neuron sums up the input variables yk , weighted by a factor w jk , plus a threshold θ j . This defines the signal
Z j:
N
X
Zj =
w jk yk + θ j .
(VI.6)
k=1
VI.8. Optimization with multivariate techniques
91
The output of the neuron is a function of Z j : z j = a(Z j ), where a is called the activation function and is chosen
to be of the form a(x) = 1+exp1−(Z j ) (logistic function). The training phase of the Neural Network consists in
determining the weighting factors w jk and the thresholds θ j . This is done by minimizing the following error
function:
n
2
1 X i
(VI.7)
XNN − t1i ,
E=
2 i=1
i
the actual value returned by the network
where t1i is the expected output (0 for background, 1 for signal), XNN
and n is a number of events used for training.
Figure VI-17: The schematic view of the Neural Network.
The training is performed by using half of the available signal data and half of the background sample. The
remaining data is used to estimate the signal detection efficiency and background rejection. It is also used as
a verification sample to check whether the values E obtained for training and verification samples are similar.
This gives useful information when to interrupt the network training. In this analysis the training is stopped after
about 300 training cycles to avoid over-learning. Distributions of the Neural Network output XNN obtained for
signal and background are shown in the left plot in Figure VI-18.
VI.8.3
Support Vector Machine
The Support Vector Machines (SVMs), developed by idea of Vapnik [89], are learning machines that can perform
binary classification (pattern recognition) and real valued function approximation (regression estimation) tasks.
Support Vector Machines map non-linearly their n-dimensional input space into a high dimensional feature
space. In this high dimensional feature space a linear classifier is constructed. A detailed introduction to SVMs
can be found in [90].
In our analysis the libsvm software package was used [91] and a gaussian kernel function was chosen. The
data was divided into two sub-samples: one for training and one for verification and calculating the background
rejection. The performance of the SVM with radial kernel depends on two parameters: the width of the gaussian
kernel g and the cost parameter C. The search in the space of these two parameters was performed and the
optimal signal and background separation was found for g = 1 and C = 256 (see Figure VI-19).
The distributions of both training and verification samples are the same that ensures there was no over
training. The performance of the SVM is shown on the right plot in Figure VI-18.
92
C VI. T 1P3P A
700
300
600
250
500
200
400
150
300
100
200
50
0
100
0
0.2
0.4
0.6
0.8
1
0
0
0.2
0.4
0.6
0.8
1
Figure VI-18: Normalized distributions of the discriminating function XNN (left) and the Support Vector Machine
(right) for signal (red) and background (black).
Figure VI-19: The SVM parameter space of the width of the gaussian kernel g and the cost parameter C. The
parameters g = 1 and C = 256 give the best background rejection.
VI.9. Performance of 1 prong and 3 prong τ-jets identification
93
VI.9 Performance of 1 prong and 3 prong τ-jets identification
The background rejection factors obtained for various τ identification efficiencies ε are presented in Table VI-14
and Figure VI-20 for all the methods presented above, i.e. PDE-RS, Neural Network and Support Vector Machine. For τ1P all methods give very similar results, which indicates that probably all the information from the
six discriminating variables is fully exploit.
When applied to the one-prong and three-prong data, the PDE-RS method for 80% signal identification
efficiency gave background rejection of 75% and (72%) respectively. The Neural Network had six nodes in the
input layer and two hidden layers with five nodes in each layer. The NN rejection power for τ3P was slightly
improved when compared to the PDE-RS. The 80% background rejection for 77% signal efficiency obtained
with the SVM is very similar to the one obtained with use of a NN. In the region of low signal efficiencies the
SVM performs worse than other methods. We suspect that this is because the algorithm might have difficulties
in the region, where nearly all events from one class (background) have to be rejected.
Table VI-14: The background rejection for varying identification efficiency obtained with use of different multivariate analysis methods: PDE-RS, Neural Network and Support Vector Machine.
Method
Efficiency
%
PDE-RS
90
80
70
NN
90
80
70
SVM
90
80
70
Rejection
τ1P
%
Rejection
τ3P
%
58 ± 1
75 ± 1
83 ± 1
54 ± 1
72 ± 1
82 ± 1
64 ± 1
77 ± 1
84 ± 1
64 ± 1
77 ± 1
83 ± 1
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.2
0.4
0.6
0.8
1
65 ± 1
77 ± 1
86 ± 1
0
0
53 ± 1
78 ± 1
86 ± 1
0.2
0.4
0.6
0.8
1
Figure VI-20: The background rejection as a function of signal efficiency for three analysis methods: PDE-RS,
Neural Network (NN) and Support Vector Machine (SVM) for τ1P (left) and τ3P (right).
94
C VI. T 1P3P A
VI.10 Summary
In this chapter we described the new algorithm for hadronic τ reconstruction and identification, based on the
track-seeded reconstruction and energy-flow definition of the energy scale, published initially in [79]. The algorithm is intended for studies of the low mass Higgs (around 120 GeV) and the visible energy from the hadronic
τ decays in the range 20 - 70 GeV. The reconstruction process for the τ visible decay products requires:
• reconstructed, good quality and relatively high pT track(s), and then collected calorimetric energy deposition in a fixed cone seeded by the track η and φ at the vertex (for one-prong mode) or barycenter of
tracks at vertex (for three-prongs mode). The rigorous veto on electron and/or muon tracks by the upstream
reconstruction algorithms is assumed;
• the energy scale of the reconstructed hadronic τ decay. It is obtained from the energy-flow approach:
chrgEM
energy deposited in the calorimeter is classified for its type (e.g. ET
or ETneuEM ), the charged energy
±
is replaced by the track(s) momentum of π and only the neutral electromagnetic energy, consistent with
that originating from π0 decays, is included in the estimate;
• the identification process, for which both calorimetric and energy-flow observables are used. The dedicated
optimization of the one-prong and three-prong decays is assumed.
This algorithm represents a very interesting, complementary approach to the more standard calorimeterbased one, and is now officially used for the data processing.
The use of only qualified tracks and seeding reconstruction by the track(s) at vertex gives a very good
precision for defining direction of the visible decay products of the τ decays. Respectively 83.9% (one-prong)
and 98.1% (three-prongs) candidates are contained within ∆R(τreco , τtruth ) < 0.025 window.
The energy-flow approach used for defining energy scale gives good resolution without any additional calibration, and a stable estimate within few percent over a large range of the nominal energy of the visible τ. About
e f low
88.3% (one-prong) and 93.8% (three-prongs) candidates are contained within window < ET /ETtruth > = 0.8 1.2. An important advantage of the energy-flow procedure is that by construction it significantly underestimates
the energy scale for fake τ from QCD radiation (with respect to the truth) and therefore requires much harder
partons to originate fake candidates than the nominal energy threshold of the accepted hadronic τ’s. As a consequence, the initial level of the fake background is much lower than that with the base line algorithm (the details
of the comparisons are published in [79]).
The identification selection based on the simple cut-based criteria is rather moderate. The separate optimization of the identification of one-prong and three-prongs candidates seems promising and gives better rejection.
The total efficiency achieved with the algorithm presented here is 18.6% with respect to all hadronic decays
in the qq̄ → Z → ττ sample, with one-prong contributing 14.7% and three-prong 3.75%. The rejection against
fake τ′ s originating from hard-process gluons (quarks) in the transverse-momenta range of 35 - 50 GeV is 700
(150) for the τ1P and 100 (30) for τ3P candidates respectively. It is clear that the τ3P category will have much
higher background, with rather small gain for the total signal acceptance.
The comparison of the three multivariate methods, PDE-RS, Neural Network and Support Vector Machine,
shows that all of them give very similar results when applied to the τ identification. This result is an indication
that the obtained background rejection is most probably close to the statistical limit. The information from six
discriminating variables is fully exploit and no significant rejection improvement can be expected.
It was also shown that all those methods can be used in physics data analysis and they give a similar performance. In our comparison, the NN seems to give a slightly better rejection than other methods. The advantage
of the PDE-RS method is short computation time needed for both the training and the analysis phases.
The Neural Network described in the last section is used as a prototype discriminant in the implementation
of the tau1P3P algorithm inside the Athena framework [8].
C VII
R   F S
VII.1 Introduction
The studies presented in Chapter IV were performed with fast simulation of the ATLAS detector response. We
have estimated there the expected number of events for the bb̄H signal and various backgrounds. We established signal significance by defining the excess of events over background in the signal mass window. In the
future, while working with real data, the more sophisticated procedure based on background estimation from
the “sideband" region (far from signal region) should be applied. In our studies, for the Higgs boson mass of
120 GeV:
• in ℓℓ ETmiss , after generic selection, the Z → ττ and tt¯ production processes contribute at the same level
to the total background. However, in the mass window of mH = 120 GeV ± 20 GeV contribution from
Z → ττ becomes dominant, ca. 70% of the total background. This selection passes only 22% of the total
background, while 68% of the signal events;
• in ℓ had ETmiss , after generic selection, apart from the Z → ττ and tt¯ processes, the inclusive W + jet
production contributes to the total background (47%, 37% and 16% respectively). An additional selection
of accepting events only in the same mass window as above leads also to the enhancement of Z → ττ
contribution, but only to ca. 60% of the total background. In ℓ had ETmiss the mass window selection passes
only 25% of the total background, while 74% of the signal events;
• the number of expected signal events, after generic selection, in ℓℓ ETmiss is 1.9 times larger than in
ℓ had ETmiss , while the total background is 2.8 times larger in ℓℓ ETmiss mode. Considering ℓℓ ETmiss and
ℓ had ETmiss final states separately, we evaluated signal significance. We found that ℓℓ ETmiss mode contribution to combined significance is at the level of 14-26% for bb̄H process and 35-41% for gg → H process
and this value varies with the assumed Higgs boson mass.
In this chapter the analysis of the bb̄A/H, A/H → ττ signal and the irreducible Z/γ∗ → ττ background process will be presented, based on the full simulation of the ATLAS detector. The main result of the analysis is the
evaluation of the reconstruction efficiencies and the resolution of reconstructed τ pair invariant mass distribution,
the confirmation of the selection “cut-flow” (acceptances and a number of expected events after consecutive cuts)
and the comparisons with results from the fast simulation.
The standard analysis of H/A → ττ decay mode comprises trigger, identification and kinematical selection
of the final state objects: electrons, muons and τ leptons, as well as the reconstruction of the invariant mass of τ
pair. Due to the limited statistics of fully simulated events, as well as a lack of availability of trigger information,
we restricted the analysis presented here to the following steps only:
96
C VII. R   F S
• reconstruction and identification of τ decaying to electron or muon;
• reconstruction and identification of hadronically decaying τ leptons;
• reconstruction of the invariant mass of ττ system;
• optimization of the mass resolution.
VII.2 Analysis framework
The data used in this analysis were prepared with the official ATLAS software of Spring - Summer 2006, the
Athena 11.0.42. The signal bb̄A sample at mA = 120 GeV and tan β = 10 was simulated in four steps. First,
physics events were generated using Pythia data-card as prepared for ATLAS DC3 production. Second, the
passage of particles from these events through the detector was simulated with Geant software and digitized.
Third, the reconstruction algorithms were executed along with the tau1P3P algorithm, from which the ESD and
the AOD data were obtained. The last step was to run the user analysis code in order to arrive to the final results
(histograms, selected events). The data were processed in the distributed grid environment and the analysis was
done in the batch system of the ATLAS Tier 2 site at Cyfronet, Kraków, Poland.
The datasets with Z → ττ events were generated and digitized centrally by the ATLAS Collaboration production system in preparation for the Rome Physics Workshop held in June 2005. We only reprocessed the
reconstruction step along with the tau1P3P package and obtained AOD data and final histograms.
The analysis code used here was written in a form of the Athena package. The candidates for electrons,
muons and the information about missing transverse energy were obtained from executed upstream, official
reconstruction packages. The τ-jets were reconstructed by the tau1P3P package, described in Chapter VI. We
considered two possibilities for the last step of the analysis: either to write analysis code from scratch or to use
the EventView package from the Athena framework.
The EventView is a software package that provides tools which should help the end-user to write the analysis
code. Those tools perform typical analysis tasks like overlap removal, objects selection, object combinations (e.g.
jet pairing), objects association, calculation of physical observables (e.g. invariant mass) and generating output
ntuples. The EventView starting point is the data in the AOD format. The data contain the objects built by
various reconstruction algorithms (tracks, jets and vertexes). It may happen that the same physical object can
be identified by various reconstruction algorithms leading to the redundancy of candidates. The EventView
algorithms on the basis of separation criteria (overlap in (η, φ) plane within distance of 0.3 and 0.1 for jets and
leptons respectively) remove multiple occurrence of candidates and provides objects for further analysis. Then
depending on particular needs, it is up to the user to specify the collection of the so called inferred objects, like
Z, W or Higgs boson, which are "built" of their visible decay products (like electrons or τ-jets) and neutrinos
(whose contribution is estimated with various techniques, in our case with collinear approximation, with the use
of the ETmiss ). However, it often happens that in the complicated topology of events with many jets in the final
state (like in the backgrounds for tt¯ j j) we do not know a priori the best combination of jets. The EventView
offers the possibility of building different views for the same event. Finally, the EventView can also perform
a book-keeping of user defined variables corresponding to all reconstructed quantities and save them for the
permanent storage.
The EventView package is evolving very rapidly and its up-to-date status can be found in [92]. For the
analysis presented in this chapter we decided to use the EventView as the basic framework for the analysis
code.
VII.3. The reconstruction efficiency
97
VII.3 The reconstruction efficiency
The reconstruction efficiency was calculated by matching MC true particle (“daughter” of τ lepton) to a reconstructed object. For each true electron (muon) that passes kinematical selection |η| < 2.5 and pT > 15 GeV for
electron (pT > 10 GeV for muon), the reconstructed and identified electron or muon candidates that pass the
same kinematical selection were searched for. The matching was considered successful if a candidate was found
in the distance smaller than 0.1 in (η, φ) plane to the corresponding MC true particle. In this section, we just report efficiencies for electrons and muons as provided by generic reconstruction algorithms, but the optimization
of their reconstruction and identification was outside the scope of these theses.
In order to evaluate τ identification efficiency, we built visible MC four-momenta of decay products of τ
lepton. For each visible MC τ passing kinematical selection (|η| < 2.5 and pT > 20 GeV) and that has charged
π± with pT > 9 GeV in its decay chain, we matched it to the reconstructed candidates and separately discussed
the performance for single and three prong decays.
VII.3.1
Isolated electrons
m_ele_eff_eta
Entries
9849
Mean
0.01948
Mean y
0.7817
RMS
1.173
RMS y
0.4131
1.2
1
efficiency
efficiency
The reconstruction of electrons is based on identifying clusters of cells in the electromagnetic calorimeter and
on matching them to the track reconstructed in the inner detector. For the purpose of identification, the set of
calorimetric variables (shower shape, energy deposition in each layer of the calorimeter) is built, including the
information from the TRT detector (high threshold hits originating from electrons). Then, the simple discriminant
variable is constructed, on which default cut value is set, as implemented in reconstruction and identification
ATLAS algorithm (the Egamma package).
In Figure VII-1 the overall identification efficiency (reconstruction and identification) for electrons in signal
bb̄A (mA = 120 GeV) sample is presented for the ℓℓETmiss (top line) final state versus pseudorapidity (left) and
transverse momentum (right). The distributions for ℓ had ETmiss final state look similar.
The combined efficiency is stable at the level of 78% in a broad range of the pseudorapidity and transverse
momenta for both ℓℓETmiss and ℓ had ETmiss final states. However, the previous studies reported in the ATLAS
Physics TDR estimated this efficiency at around 85%∗ . Since then, the performance of the algorithms achieved
so far degraded, due to the increased material in the inner detector and more realistic detector description. The
degradation of efficiency close to |η| = 1.5 corresponds to the crack region in the calorimeter between the barrel
and the end-cap sections. The other drop at |η| = 2.5 represents the edge of the inner detector.
1.2
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
-3
-2
-1
0
1
2
3
m_ele_eff_pt
Entries
9849
Mean
31.74
Mean y
0.783
RMS
15.19
RMS y
0.4122
0
10
20
30
40
50
60
η
70
80
90
100
pT [GeV]
Figure VII-1: The overall identification efficiency for true electrons from the bb̄A process and Higgs boson at
mass 120 GeV for ℓℓETmiss , as a function of pseudorapidity η (left) and transverse momentum pT (right).
∗
Fast simulation estimates overall identification efficiency at 90% for both electron and muons.
98
VII.3.2
C VII. R   F S
Isolated muons
m_muo_eff_eta
Entries
12889
Mean
0.02199
Mean y
0.9215
RMS
1.181
RMS y
0.269
1.2
1
efficiency
efficiency
The reconstruction and identification of muons depends on the transverse momentum of the muon. In the pT
range interesting for our studies (10-100 GeV), the information both from the inner detector tracking system and
the muon chambers should be combined to obtain the best performance. The identification of muon is based on
χ2 distribution of track matching between the inner detector and muon spectrometer.
The combined efficiency is presented in Figure VII-2 for muons in signal bb̄A (120 GeV) sample and ℓℓETmiss
finale state (top line). The plots for ℓ had ETmiss mode look similar. The default values of cut thresholds were
used, as implemented in the ATLAS reconstruction algorithms. The degradation of combined efficiency close to
η = 0 is due to services (cables, etc.) provided for the muon spectrometer.
1.2
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
-3
-2
-1
0
1
2
3
m_muo_eff_pt
Entries
12889
Mean
27.83
Mean y
0.9243
RMS
15.91
RMS y
0.2645
0
10
20
30
40
50
60
70
80
η
90
100
pT [GeV]
Figure VII-2: The same as Figure VII-1, but for true muons.
VII.3.3
τ-jet candidates
efficiency
efficiency
The hadronic τ decays were reconstructed with tau1P3P algorithm described in Chapter VI. The reconstruction
and reconstruction plus identification efficiencies are shown in Figure VII-3 for 1 prong and in Figure VII-4 for
3 prong decays respectively.
1.2
1
1.2
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
-3
-2
-1
0
1
2
3
η
0
10
20
30
40
50
60
70
80
90
100
pT [GeV]
Figure VII-3: The overall (reconstruction + identification) efficiency (black dots) for 1 prong τ candidates from
the bb̄A process and Higgs boson at mass 120 GeV versus pseudorapidity η (left) and transverse momentum
pT (right). The plots are normalized respectively to single and three prong decays, with at least one π± with
pT > 9 GeV. The open dots represent reconstruction efficiency only.
99
efficiency
efficiency
VII.4. The ETmiss reconstruction
1.2
1
1.2
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
-3
-2
-1
0
1
2
3
η
0
10
20
30
40
50
60
70
80
90
100
pT [GeV]
Figure VII-4: The same as Figure VII-3, but for 3 prong τ candidates.
We checked that the reconstruction efficiency is flat in the allowed pseudorapidity range for both the bb̄A
and the Z → ττ events: 86% and 88% for 1 prong and 58% and 55% for 3 prong candidates respectively. The
corresponding overall (reconstruction + identification) efficiencies for the bb̄A and Z → ττ is 70% and 75% for
1 prong and 34% and 32% for 3 prong candidates is in agreement with our studies presented in Chapter VI. The
overall efficiency reaches 57%.
The reconstruction and identification procedure is very effective and the fake rate in signal sample is smaller
than 1% (2%) for 1(3)-prong candidates respectively. The more detailed discussion of the 1 and 3 prong fakes
from di-jet events was already presented in Chapter VI.
VII.3.4
Comparison with the fast simulation
The electron and muon efficiencies in the fast simulation studies were set to 90%. For electrons (muons) from
the full simulation we obtained the reconstruction plus identification efficiency of 78% (92%). We hope, that the
ATLAS software will be optimized better and electrons will be reconstructed and identified with higher ultimate
efficiency.
The τ-jet candidates were reconstructed with the track-based algorithm, the tau1P3P, developed as a part of
these theses. The overall efficiency for these candidates in the full simulation of 57% is in agreement with our
fast simulation efficiency of 50%. However, we should keep in mind that the Atlfast parametrization relied on
the calorimter-based algorithm and efficiency distribution was flat and given with respect to all hadronic τ decay
candidates. In the full simulation studies, the efficiency depends on pT and was given with respect to candidates
having π± track with pT > 9 GeV. We consider those numbers as quite consistent, within the precision aimed for
this comparison.
VII.4 The ETmiss reconstruction
The important component of the analysis, of the Higgs boson decay into τ-lepton pair is the reconstruction of
the missing transverse energy (ETmiss ). It is defined as the energy imbalance in the event, due to real physics (neutrinos and other particle escaping detection) as well as detector effects. The latter can be attributed to inaccurate
calorimeter calibration, non-linearity of detector response at low energies, energy losses in the dead material
placed before calorimeters (cryostats) and transition between various calorimeter parts (cracks). In general, the
missing energy is calculated as:
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C VII. R   F S
ETmiss =
r
E miss
x
2
2
+ Eymiss ,
where E miss
and Eymiss is x and y component of the energy imbalance of the event.
x
VII.4.1
Two methods of ETmiss estimation
The ATLAS base-line reconstruction, as in the software release used for these theses, provides two methods for
the calculation of the missing energy. The first one, called the 2 σ approach, calculates the missing energy from
all calorimetric cells within |ηcell | < 5 with the energy deposition above noise threshold |E cell | > 2 σnoise (σnoise
is the resolution expected for electronic noise). This energy is calibrated with Geant4 H1-weights depending
on cell energy density (E/V) and on the calorimeter region. Finally, the estimator of the ETmiss can be written as
follows:
f inal_ETmiss (2 σnoise ) = ETmiss (Calib) + ETmiss (Muon) + ETmiss (Cryo) ,
(VII.1)
where ETmiss (Calib) is the energy calibrated from all calorimetric cells, ETmiss (Muon) is muon contribution from
the muon spectrometer only to avoid energy double-counting (within |η| < 2.5) and ETmiss (Cryo) is an estimate
of the energy lost in the cryostat between LAr and Tile calorimeters (it is obtained from the energy deposited by
jets in the third layer of electromagnetic calorimeter and first layer of Tile detector).
The second approach calculates ETmiss (topological) from all cells in topological clusters. The topological
clusters are created from all the cells that are neighbors (8 surrounding cells around a seed cell in the same layer
and overlapping in η and φ with the seed cell in adjacent layers). Three kinds of noise thresholds are taken into
account:
• Seed Threshold: the calorimetric cells with energy that satisfies |E cell /σnoise | < T seed condition, initiate
cluster building (default for T seed is 4);
• Neighbor Threshold: the calorimetric cells that are the neighbors of cell which are already in the cluster,
with energy that satisfies |E cell /σnoise | < T neighbor condition, expand the cluster (default for T neighbor is 2);
• Cell Threshold: only the calorimetric cells with |E cell /σnoise | < T cell are used in the estimation of the
cluster energy and topology (default for T cell is 0).
In this analysis the default pattern for noise thresholds: 4/2/0 was used. For the topological approach, the calibration is also based on Geant4 H1-weights depending on the cell energy density (E/V) and on the calorimeter region tuned for DC2 di-jets samples. This approach for calculating missing ET can be used in place of
ETmiss (Calib) in Equation VII.1 to calculate final ETmiss :
f inal_ETmiss (topo) = ETmiss (topo) + ETmiss (Muon) + ETmiss (Cryo) .
q
P
The resolution of each component of missing ET vector is defined as σ = σ2x + σ2y and σ x(y) = gen E miss
x(y) −
P
P
miss
miss
rec E x(y) , where gen E x(y) is the sum of all generated particles without any pseudorapidity cut with neutrinos
P
and muons excluded, and rec E miss
x(y) is the sum of x(y) momenta reconstructed by the calorimeter. The studies
miss
over ET resolution performed on samples of Z → ττ, A → ττ in a broad range of Higgs boson masses and
di-jets events with 35 GeV < pT < 1120 GeV report that the resolution of ETmiss : σ(ETmiss ) is proportional to the
P
measured transverse energy ET :
qX
ET ,
(VII.2)
σ(ETmiss ) ∼
P
P
where ET = cell ET . This has a direct impact on the resolution of the invariant mass of di-τ system:
σ(mττ ) ∼
σ(ETmiss )
|sin(∆φ) prod1,prod2 |
,
where (∆φ) prod1,prod2 is the angle between two visible products of τ decays (light leptons or τ-jets) [11].
VII.4. The ETmiss reconstruction
VII.4.2
101
ETmiss calibration
The relative difference: c x(y) between the x and y component of the transverse missing energy E miss
x(y) and the
corresponding x and y component of the neutrinos system, E νx(y) :
c x(y) =
ν
E miss
x(y) −E x(y)
ν
E x(y)
is non-zero (Figure VII-5). Plots are shown only for ℓℓETmiss , since we obtained the similar ones for the ℓ had ETmiss
final state. Thus, since it was not foreseen in the scope of these theses to change/optimize the package for the
ETmiss reconstruction, we introduced calibration factors α x(y) , defined as:
E νx(y) =
800
700
600
500
1
miss
1+c x(y) E x(y)
= α x(y) E miss
x(y) .
h_miss_minus_neutrino_x_ll
h_miss_minus_neutrino_x_t_ll
Entries
7628
Mean
-0.1716
RMS
0.781
χ2 / ndf
9.057 / 5
Prob
0.1068
Constant
664.2 ± 14.1
Mean
-0.1394 ± 0.0100
Sigma
0.2963 ± 0.0106
Entries
7628
Mean
-0.1421
RMS
0.7524
χ2 / ndf
27.97 / 5
Prob
3.695e-05
Constant
714.2 ± 15.4
Mean
-0.1121 ± 0.0076
Sigma
0.2771 ± 0.0089
800
700
600
500
400
400
300
300
200
200
100
100
0-3
-2
-1
0
1
0-3
2
3
miss ν ν
(Ex - Ex)/Ex
-2
-1
0
1
2
3
miss ν ν
(Ex - Ex)/Ex
Figure VII-5: Fit to the relative difference of ETmiss and ETν x-component in (-0.4,0.4) window for ℓℓETmiss . The
2σ (left) or topological (right) approach to calculate ETmiss was used.
The calibration for each x(y) component of ETmiss and for both the 2σ and the topological approaches to
calculate ETmiss was done separately. Fit to distribution was done in (-0.4, 0.4) window. The obtained factors are
summarized in Table VII-1. From this table we can conclude that the topological noise treatment is slightly better
calibrated than the 2σ approach both in ℓℓETmiss and ℓ had ETmiss modes.
Table VII-1: Calibration factors for ETmiss components for bb̄A sample.
Final
state
ETmiss
component
ℓℓ ETmiss
Ex
Ey
Ex
Ey
ℓ had ETmiss
Noise treatment
2σ
Topo
1.162
1.149
1.144
1.147
1.126
1.116
1.095
1.103
102
VII.4.3
C VII. R   F S
ETmiss resolution
It was also interesting to compare the difference between ETmiss for non-interacting particles according to the
MC truth information and reconstructed ETmiss for the bb̄A (mA = 120 GeV) ℓℓ ETmiss (top line), ℓ had ETmiss
(middle line) and Z → ττ (bottom line) presented in Figure VII-6. The 2 σ (left) and the topological (right) noise
treatment was used for the estimation of ETmiss . The peak position is less biased (the mean value from top line
plots in Figure VII-6: 2.7 GeV vs 3.4 GeV) and the resolution is better by 10% (9.3 GeV vs 10.3 GeV) in the case
of the topological noise treatment. The difference in resolution between ℓℓ ETmiss vs ℓ had ETmiss is at the level of
2%.
truth_miss_et_topo_nonint_diff
truth_miss_et_sigma_nonint_diff
Entries
12775
Mean
-3.689
RMS
13.9
χ2 / ndf
34.69 / 13
Prob
0.0009449
Constant
1120 ± 14.4
Mean
-3.373 ± 0.123
Sigma
10.33 ± 0.12
1200
1000
800
Entries
12775
Mean
-2.684
RMS
12.95
χ2 / ndf
82.91 / 13
Prob
3.117e-12
Constant
1249 ± 16.0
Mean
-2.698 ± 0.099
Sigma
9.26 ± 0.10
1400
1200
1000
800
600
600
400
400
200
0-60
200
-40
-20
0
20
40
60
0-60
-40
-20
0
20
ν
Emiss
T - ET [GeV]
40
truth_miss_et_topo_nonint_diff
truth_miss_et_sigma_nonint_diff
Entries
14100
Mean
-2.546
RMS
13.05
χ2 / ndf
21.15 / 13
Prob
0.07001
Constant
1264 ± 15.2
Mean
-2.412 ± 0.112
Sigma
10.45 ± 0.11
1400
1200
1000
60
ν
Emiss
T - ET [GeV]
Entries
14100
Mean
-1.873
RMS
12.02
χ2 / ndf
82.2 / 13
Prob
4.246e-12
Constant
1433 ± 17.2
Mean
-1.912 ± 0.090
Sigma
9.142 ± 0.089
1600
1400
1200
1000
800
800
600
600
400
400
200
0-60
200
-40
-20
0
20
40
60
0-60
-40
-20
0
ν
Emiss
T - ET [GeV]
20
40
truth_miss_et_topo_nonint_diff
truth_miss_et_sigma_nonint_diff
Entries
12477
Mean
2.229
RMS
9.086
χ2 / ndf
41.48 / 13
Prob
7.95e-05
Constant 1473 ± 17.8
Mean
1.976 ± 0.080
Sigma
8.17 ± 0.07
1600
1400
1200
1000
60
ν
Emiss
T - ET [GeV]
Entries
12477
Mean
2.017
RMS
8.413
χ2 / ndf
87.81 / 13
Prob
3.664e-13
Constant 1641 ± 19.7
Mean
1.538 ± 0.069
Sigma
7.281 ± 0.060
1800
1600
1400
1200
1000
800
800
600
600
400
400
200
0
-60
200
-40
-20
0
20
40
60
ν
Emiss
T - ET [GeV]
0
-60
-40
-20
0
20
40
60
ν
Emiss
T - ET [GeV]
Figure VII-6: The difference between ETν for non-interacting particles according to Monte Carlo truth and
reconstructed ETmiss for bb̄A, mA = 120 GeV for ℓℓ ETmiss (top line) and ℓ had ETmiss (middle line) as well as for
Z → ττ combined (bottom line). The 2 σ (left) or topological (right) noise treatment is used for the estimation of
ETmiss .
VII.5. Invariant mass of the di-τ system
103
The resolution of the ETmiss for the Z → ττ events is better (ca. 22%) than for the bb̄A. This is consistent,
because there is more energy
q deposited in the calorimeter for the bb̄A, A → ττ than in the Z → ττ process and
the resolution σ(ETmiss ) ∼
ΣETcalo (Equation VII.2).
For Z → ττ process, the off-set is bigger than in bb̄A: 1.98 ± 0.08 GeV (1.54±0.07 GeV) for 2 σ (topological)
noise treatment. The resolution for this sample is also better in the case of the topological approach: 7.28 ±
0.06 GeV. The corresponding 2 σ approach gives 8.17 ± 0.07 GeV. The results of this analysis are in agreement
with the officially presented ATLAS results [93]. For Z → ττ process, the missing transverse energy was reported
to have 1.36 ± 0.45 GeV (1.62 ± 0.04 GeV) off-set and the resolution of 8.08 ± 0.04 GeV (7.59 ± 0.04 GeV) for
the 2 σ (topological) approach.
VII.5 Invariant mass of the di-τ system
The direct evidence of the Higgs boson existence would be a resonant peak in the distribution of its decay
products (τ-pair in our case). The natural Higgs boson width of 0.126 GeV (0.292 GeV) for the H(A) Higgs boson
contributes only marginally to the τ-pair invariant mass distribution and the mass resolution is dominated by
experimental contributions. Since τ-leptons decay on a visible part and invisible neutrinos, the invariant mass of
τ-system can be reconstructed only in collinear approximation: we assume that τ lepton is massless and neutrinos
and visible decay products propagate in the same direction. We calculated the invariant mass of the two τ leptons
according to the Equation IV.2. The corresponding mass formulas were presented in Section IV.4. The drawback
of the collinear approximation is that it introduces a systematical error which broadens the reconstructed mass
peak.
VII.5.1
The mass resolution using ETν
In order to evaluate the impact of collinear approximation and the precision of the τ reconstruction, we replaced
the reconstructed ETmiss x(y)-components in collinear approximation equation, with the corresponding neutrinos
ETν components. The results are summarized in Table VII-2 and Table VII-3. On the basis of these tables we can
estimate also the mass resolution limit, after generic selection 4.8 GeV for ℓℓ ETmiss and 6.9 GeV for ℓ had ETmiss
mode, that we can obtain from the reconstruction procedure. The exemplary mass distributions are shown in
Figure VII-7 for ℓℓ ETmiss (left) and ℓ had ETmiss (right) final states. We plotted only events which passed selection,
when ETmiss component was used (for ℓℓ ETmiss mode left plot in Figure VII-7 corresponds to the bottom right plot
in Figure VII-8).
The mass peak was fitted with gauss function in mass window of mττ = 120 GeV ± 20 GeV. The peak
position is well reconstructed. The mass resolution for ℓℓ ETmiss mode improves, while for ℓ had ETmiss mode it
remains constant within errors (but this is due to the limited statistics of ℓ had ETmiss events). The resolution for
ℓℓ ETmiss mode is better than for ℓ had ETmiss for a given selection, since collinear approximation works better in
ℓℓ ETmiss mode due to softer neutrinos spectra.
Table VII-2: The mass resolution after consecutive cuts for signal events in ℓℓ ETmiss channel. Fit in reconstructed
mass window mττ = 120 GeV ± 20 GeV. ETν is used instead of ETmiss .
Selection
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
Peak position
[GeV]
119.3 ± 0.1
119.3 ± 0.1
119.6 ± 0.1
119.6 ± 0.1
119.5 ± 0.1
Resolution
[GeV]
6.2 ± 0.1
6.2 ± 0.1
5.4 ± 0.1
4.9 ± 0.1
4.8 ± 0.1
104
C VII. R   F S
Table VII-3: The same as Table VII-2, but for ℓ had ETmiss channel.
Selection
Peak position
[GeV]
Resolution
[GeV]
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
120.0 ± 0.2
119.7 ± 0.2
119.5 ± 0.2
119.8 ± 0.4
119.7 ± 0.3
119.7 ± 0.3
7.4 ± 0.2
7.4 ± 0.2
7.8 ± 0.2
7.9 ± 0.4
7.1 ± 0.3
6.9 ± 0.3
Entries
3072
Mean
122.8
RMS
17.29
χ2 / ndf
97.5 / 5
Prob
0
Constant 1126 ± 30.0
Mean
119.5 ± 0.1
Sigma 4.792 ± 0.088
1400
1200
1000
Entries
475
Mean
121.1
RMS
14.15
χ2 / ndf
11.37 / 5
Prob
0.04453
Constant 126.4 ± 8.5
Mean
119.7 ± 0.3
Sigma 6.926 ± 0.334
160
140
120
100
800
80
600
60
400
40
200
0
0
20
50
100
150
200
250
mττ [GeV]
0
0
50
100
150
200
250
mττ [GeV]
Figure VII-7: The reconstructed invariant mass of τ lepton pair for the signal bb̄A at mass 120 GeV after generic
selection for ℓℓETmiss (left) and ℓ had ETmiss (right). ETν is used instead of ETmiss .
Since we wanted to estimate the Higgs boson mass resolution originating from its physical properties and
detector effects only, and not from "combinatoric effects", we excluded fake electrons, muons or τ-jets from the
plots, since fakes will hopefully be reduced below percent level with the ATLAS offline reconstruction software.
The contribution from fakes at this level to the invariant mass distribution would not change fit parameters within
precision we are discussing here.
VII.5.2
The mass resolution using ETmiss
The quality of reconstruction of invariant mass of τ pair is dominated by the resolution of ETmiss . The impact of
the two approaches for the estimation of ETmiss (“2 σ” and topological) on Higgs boson mass reconstruction is
quantified in Table VII-4 , where fitted parameters to the invariant mass distribution of the reconstructed τ-pair
are summarized: the peak position, resolution, acceptance in mass window (mA = 120 GeV ± 20 GeV). We also
give the mass resolution and the acceptance in the same window, obtained from the fast simulation. The ETmiss
calibration from Section VII.4.2 was also applied. In Figure VII-8 we present the invariant mass distribution for
ℓℓ ETmiss and the topological noise treatment.
From Table VII-4 we can conclude that "topological treatment" in ℓℓ ETmiss gives the same estimate of the
Higgs mass as the "2σ treatment" after generic selection: 120.2 GeV, but the resolution is 15% better in the topological approach. Also the acceptance in the mass window is better in this case. For the ℓ had ETmiss , topological
noise treatment has better (less biased) peak position after generic selection (shift of 2.0 GeV vs 4.5 GeV). After
generic selection the mass resolution is 11% better in ℓℓ ETmiss than in ℓ had ETmiss mode.
VII.5. Invariant mass of the di-τ system
105
In comparison to the fast simulation results (Table VII-4), we can conclude that after generic selection the
fast simulation gives about 1.2% worse (larger) mass resolution for ℓℓ ETmiss channel than the full simulation and
gives smaller (underestimetes) by about 27% resolution for ℓ had ETmiss . The acceptance in the mass window
mττ = 120 GeV ± 20 GeV is comparable with the fast simulation results after | sin ∆φ| < 0.2 selection. The
difference varies between 1% and 5% after consecutive cuts† .
Our results (16.4 GeV ± 1.0 GeV and 18.4 GeV ± 3.2 GeV for ℓℓ ETmiss and ℓ had ETmiss mode respectively)
are in good agreement with the analysis performed by another ATLAS group. These previous studies reported an
off-set of 2.6 GeV and the resolution of 20.4 GeV for MSSM Higgs boson at mass 150 GeV and tan β = 7.5 [11].
For mass points mA = 100 GeV and mA = 150 GeV the other estimation of resolution of 11.7 ± 0.6 and 19.5 ± 0.8
was presented in [38], while for mA = 150 GeV more recent resolution estimation indicated the resolution of
19.9 ± 1.7 in ℓ had ETmiss [37].
500
400
h_amhiggs_topo_calib_100_true_ll
h_amhiggs_topo_calib_101_true_ll
Entries
5845
Mean
125
RMS
32.64
2
χ / ndf
5.534 / 5
Prob
0.3542
Constant 469 ± 11.9
Mean
117 ± 0.7
Sigma
19.59 ± 1.24
Entries
5811
Mean
125
RMS
32.69
2
χ / ndf
5.611 / 5
Prob
0.3459
Constant 465.1 ± 11.9
Mean
117 ± 0.7
Sigma
19.67 ± 1.26
500
400
300
300
200
200
100
100
h_amhiggs_topo_calib_102_true_ll
Entries
3616
Mean
131.6
RMS
31.08
χ2 / ndf
5.864 / 5
Prob
0.3197
Constant 328.6 ± 10.3
Mean
120.2 ± 0.6
Sigma
17.31 ± 1.06
400
350
300
250
200
150
100
50
00
50
100
150
200
250
00
50
100
150
mττ [GeV]
200
250
00
Entries
3207
Mean
129.5
RMS
28.41
χ2 / ndf
5.384 / 5
Prob
0.3708
Constant 312.5 ± 10.1
Mean
120.3 ± 0.6
Sigma
16.66 ± 0.99
350
300
250
300
250
150
150
100
100
50
50
150
200
250
mττ [GeV]
200
250
Entries
3072
Mean
128.5
RMS
27.64
χ2 / ndf
6.565 / 5
Prob
0.2551
Constant 306.9 ± 10.0
Mean
120.2 ± 0.6
Sigma
16.43 ± 0.96
350
200
100
150
h_amhiggs_topo_calib_104_true_ll
400
200
50
100
mττ [GeV]
h_amhiggs_topo_calib_103_true_ll
400
00
50
mττ [GeV]
00
50
100
150
200
250
mττ [GeV]
Figure VII-8: The reconstructed invariant mass of τ lepton pair for the signal bb̄A at mass 120 GeV and tan β =
10 after consecutive cuts for ℓℓETmiss . Plots are shown after resolved neutrino selection (top left), |sin(∆φ)| > 0.2
(top middle), pmiss
> 30 GeV (top right) , cos(∆φ) > −0.9 (bottom left) and ∆Rll < 2.8 (bottom right). The
T
topological approach for estimation of ETmiss and only candidates matched to the MC truth were used.
†
In Table V-4 and Table V-5 (Chapter V) we reported acceptances in the mass window for signal process that yield ca. 10% better
acceptance. We would like to stress that the data samples used to obtain that values were simulated with the AcerDet package, with the
simplified ATLAS detector layout.
106
Table VII-4: The mass resolution after consecutive cuts for signal events in ℓℓ ETmiss and ℓ had ETmiss channels. Fit in reconstructed mass window mττ =
120 GeV ± 20 GeV. Acceptance (Acc) in the same mass window. Only candidates matched with true electron, muon or visible τ were used.
Noise treatment
Selection
2σ
Peak position Resolution
[GeV]
[GeV]
116.0 ± 1.2
116.2 ± 1.2
120.2 ± 0.8
120.4 ± 0.8
120.2 ± 0.8
24.1 ± 2.3
24.1 ± 2.4
19.9 ± 1.7
19.4 ± 1.6
19.4 ± 1.6
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
120.3 ± 1.6
120.2 ± 1.5
116.5 ± 2.4
125.4 ± 2.9
125.3 ± 3.6
124.5 ± 3.6
24.0 ± 3.7
23.2 ± 3.4
24.3 ± 4.7
20.0 ± 4.0
21.4 ± 5.1
21.8 ± 5.6
Acc
[%]
ℓℓ ETmiss
51.7
117.0 ± 0.7
51.7
117.0 ± 0.7
56.2
120.2 ± 0.6
60.1
120.3 ± 0.6
61.4
120.2 ± 0.6
ℓ had ETmiss
54.6
120.6 ± 0.9
54.5
120.5 ± 0.9
52.5
118.3 ± 1.1
52.0
123.1 ± 2.0
57.9
122.4 ± 2.0
58.9
122.0 ± 1.9
Acc
[%]
Fast
simulation
Resolution Acc
[GeV]
[%]
19.6 ± 1.2
19.7 ± 1.3
17.3 ± 1.1
16.7 ± 1.0
16.4 ± 1.0
54.4
54.3
59.6
63.0
64.3
25.8 ± 0.5
23.6 ± 0.4
17.7 ± 0.3
16.8 ± 0.3
16.6 ± 0.2
35.0
47.5
58.7
65.8
67.9
18.1 ± 1.5
18.0 ± 1.5
18.5 ± 2.0
18.8 ± 3.2
18.7 ± 3.3
18.4 ± 3.2
58.7
58.4
56.5
61.2
68.1
70.1
20.0 ± 0.4
18.4 ± 0.3
18.5 ± 0.3
13.9 ± 0.3
13.5 ± 0.3
13.5 ± 0.3
39.2
57.9
58.0
63.2
73.1
74.0
C VII. R   F S
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
Topological
Peak position Resolution
[GeV]
[GeV]
VII.6. Acceptances and expected number of events
107
VII.6 Acceptances and expected number of events
In order to compare the fast and the full simulation results, we summarized the acceptance in Table VII-5, and
the expected number of events in the mass window of mA = 120 GeV ± 20 GeV in Table VII-6, for both ℓℓ ETmiss
and ℓ had ETmiss modes. Only candidates matched to the MC truth are counted. We quote there values for the
"topological treatment" for the ETmiss calculations. The values for the fast simulation were taken from Chapter IV
(Tables IV-3, IV-5, IV-9, IV-10, IV-13, IV-14) and normalized accordingly‡ .
The acceptance for fully simulated samples was calculated according to the formula in Equation IV.3. Since
in the full simulated data we had to conform to official parameters for the MC production, the bb̄A process was
produced with generator cut applied. Thus, we had to take it into account when we consistently normalized the
fast and the full simulation results. We fixed acceptance in the full simulation after |sin(∆φℓℓ )| > 0.2 to the value
of the fast simulation and from the number of events that passed this selection in the full simulation we obtained
the "normalized" number of generated events. This number was used into Equation IV.3 for all other selections,
in order to check the selection “cut-flow” of the analysis.
Table VII-5: The acceptance of signal events after consecutive cuts for ℓℓ ETmiss and ℓ had ETmiss channel. Only
the candidates matched with true τ were used. Statistical errors are typically less than 1%.
Acceptance
Selection
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
Acceptance
in mass window
Simulation
Full
Fast
Full
[%]
[%]
[%]
Fast
[%]
ℓℓ ETmiss
6.55
6.55
2.29
2.29
1.81
2.03
1.68
1.95
miss
ℓ had ET
1.30
1.30
1.22 0.935
0.327 0.364
0.254 0.297
0.248 0.285
3.10
1.34
1.18
1.14
3.56
1.36
1.28
1.25
0.749
0.709
0.206
0.185
0.183
0.760
0.528
0.223
0.202
0.200
The expected number of events and the events in the mass window are estimated with Equation IV.4, where
acceptance is taken from Table VII-5. The errors are calculated according to the total derivative and are dominated by 10% uncertainty on the cross-section, following what was estimated in [17] and applied also in the fast
simulation studies. The difference between the fast and full simulation is in a constant of this equation: for the
fast simulation the fixed electron or muon reconstruction efficiency 90% was assumed, while for the full simulation data this factor was omitted, since already reconstructed and identified leptons were used). The production
cross-section for the MSSM bb̄A, A → ττ Higgs boson of 2.345pb at tan β = 10 was multiplied by the same
branching ratio as fast simulation data for configuration with both τ → ℓνν (BR = 0.127) and for one τ → ℓνν
and one τ → had ν (BR = 0.459) yielding 3.0 · 10−1 pb (2.2 · 10−3 pb) and 1.1 · 100 pb (7.9 · 10−3 pb), where
the numbers in brackets are the values used in the fast simulation analysis with the SM couplings. The effective
cross-section§ is ∼ 137 times larger in the MSSM than in the SM case.
‡
The acceptance from the fast simulation did not contain efficiency for light leptons and τ-jet reconstruction, so they were multiplied
by efficiencies 90% and 50% respectively.
§
The ratio of σ MS S M · BR MS S S M /σS M · BRS M is equal 2.345 pb/17.17 · 10−3 pb = 136.6.
108
C VII. R   F S
Table VII-6: The expected number of signal events and events inside the mass window mA = 120 GeV ± 20 GeV
after consecutive cuts for ℓℓ ETmiss and ℓ had ETmiss channel at tan β = 10 and for an integrated luminosity 10 f b−1 .
Only candidates matched with true τ were used.
Expected events
Selection
Fast
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
Expected events in mass window
Simulation
Fast
Full
Full
ℓℓ ETmiss
196.8 ± 21.0 196.8 ± 40.0
68.8 ± 7.2
68.8 ± 11.0
54.4 ± 5.7
61.0 ± 9.9
50.5 ± 5.3
58.6 ± 9.5
ℓ had ETmiss
140.4 ± 15.0 140.4 ± 22.0
131.8 ± 14.0 101.0 ± 16.0
35.3 ± 3.7
39.3 ± 6.3
27.4 ± 2.9
32.1 ± 5.1
26.8 ± 2.8
30.8 ± 4.9
93.2 ± 9.8
40.3 ± 4.2
35.5 ± 3.7
34.3 ± 3.6
107.0 ± 22.0
40.9 ± 6.6
38.5 ± 6.3
37.6 ± 6.1
80.9 ± 8.5
76.6 ± 8.0
22.2 ± 2.3
20.0 ± 2.1
19.8 ± 2.1
82.1 ± 13.0
57.0 ± 9.1
24.1 ± 3.9
21.8 ± 3.5
21.6 ± 3.5
The results of the fast and the full simulation conform very well, and the small difference should be attributed
to the manner the reconstruction efficiency is estimated (fixed in the fast simulation studies, and effective - for
the full simulation).
VII.7 Summary
In this chapter the results for the signal reconstruction of events processed with the full simulation of the ATLAS
detector were presented. As a reference point, the bb̄A Higgs boson with mass mA = 120 GeV, tan β = 10 was
used. The discussed analysis consisted of identifying isolated lepton (electron or muon) from decay of one or
two tau leptons, identifying hadronically decaying second tau lepton (in the case of ℓ had ETmiss final state). In
the following information on the reconstructed transverse missing energy was analyzed and the invariant mass
reconstruction of ℓℓ ETmiss or ℓ had ETmiss was performed. As the last step, the optimization of the selection
criteria resulting in improving resolution on the reconstructed invariant mass was discussed. Due to the limited
availability of fully simulated events at the time when theses were completed, the studies of background events
or further steps of the analysis (b-jet tag, b-jet veto) were not possible. The results obtained in this section can
be summarized as follows:
• on average, identification efficiency for isolated electron of 78% (instead of expected 85% ) was observed;
hopefully it will be further improved with the next versions of the ATLAS offline software;
• on average, the better muon efficiency of 92% instead of expected 90% was observed;
• the tau1P3P algorithm for reconstruction of τ-jets in signal sample with Higgs boson was used and the
reconstruction efficiency is in agreement with the results obtained in Chapter IV for Z and W bosons
samples;
• we discussed two (the topological and the 2σ) treatments for ETmiss calculation. The topological ETmiss
treatment gives a better (by 15%) estimate of the missing transverse energy and it was used in the analysis;
VII.7. Summary
109
• the missing transverse energy is the key ingredient of the invariant mass reconstruction. We showed in this
chapter that the invariant mass distribution of the τ pair depends significantly on the quality of ETmiss reconstruction. The use of the collinear approximation convoluted with the resolution of the τ reconstruction
contributes only 25% - 30% to the total experimental resolution and rather marginal to the level of tails.
The dominant contribution comes from the experimental ETmiss resolution;
• the invariant mass resolution obtained from the fast simulation is comparable to the full simulation result.
The highest discrepancy is observed in ℓ had ETmiss channel after three last cuts, but this might be due to
a lower statistic of the available events after the whole selection. The acceptance in the mass window of
mH = 120 GeV ±20 GeV is also comparable in the fast and the full simulation. However, the full simulation
data have 3-4% more events in the tail of the distribution;
• at the mass point mA = 120 GeV the obtained mass resolution 18.1 GeV ± 1.1 GeV in ℓℓ ETmiss and
16.2 GeV ± 2.0 GeV in ℓ had ETmiss are in agreement with the previous studies done by the ATLAS Collaboration.
We can conclude that the selection “cut-flow” in the full simulation is consistent with the results from the
fast simulated data. The interpretation of the MSSM parameter scan, presented in Section IV.8, based on the
acceptances and reconstruction efficiencies from the fast simulation, is valid. The analysis based on the full
simulation stopped at this point, due to the limited statistics of the fully simulated data. The large statistics
samples, with various processes comprising background for the associated Higgs boson production with bottom
quark, are becoming available just at the time of submitting these theses and can not be included in the results
presented here. We are also fully aware of the limitations in the trigger information discussed here. Also, as this
part of the information available for off-line analysis is becoming available just now, it is already too late to
properly include it in these theses.
For the selection discussed for this analysis (see Chapter IV), the trigger inefficiency (single or double electron, muon) is expected on the level of 90% at most. In the ℓ had ETmiss channel, it can be still partially recovered
with the hadronic Tau trigger. Given overall uncertainties from understanding the exact performance of the different reconstruction components, or theoretical uncertainty on the signal and background modeling, we decided
not to introduce it as yet another correction factor for the expected signal observability.
110
C VII. R   F S
C VIII
C
In these theses, we have discussed the observability potential of the ATLAS experiment at the LHC for the
bb̄h/H/A → ττ channel in the MSSM model in the mass range below 200 GeV.
The Monte Carlo predictions for signal and different backgrounds have been discussed, including a variety
of available generators and quantifying the impact of theoretical uncertainty on the final sensitivity of the experimental analysis. The need for the fully exclusive Monte Carlo predictions for the signal has been explicitly
shown (about factor 10 difference in acceptances in the most extreme case). It has been also shown that for the
background the effect from including full (2 → 6) matrix element in the tt¯ production is less crucial, and that
both W + jet and Z + jet background is dominated by the reducible contributions. The estimates from bb̄W and
bb̄Z matrix elements simulations have been found well below the inclusive W or Z estimates.
For the first time for the ATLAS experiment a complete analysis of the bb̄h/H/A → ττ → ℓℓ ETmiss mode
has been performed. The discussion of the observability prospects of the ℓℓ ETmiss and already well established
ℓ had ETmiss channel has been carried out in parallel. That allowed us to assess at each step the relative importance
and the detector performance for each decay mode. The complete analysis for the signal and background has been
performed with the fast simulation of the ATLAS detector. Then, it has been confirmed with the full simulation
of the detector for the bb̄A signal process and the reference mass point mA = 120 GeV only. The estimate for the
expected number of signal and background events in each mode (ℓℓ ETmiss and ℓ had ETmiss ) has been presented.
The results obtained for the reference cross-section from the SM have been interpreted in the MSSM and the full
scan of the parameter space has been completed. The improvement due to inclusion of ℓℓ ETmiss mode depends
on the Higgs boson mass studied (120 GeV - 200 GeV). We found, that the signal significance at tan β where
combined 5σ significance is obtained, was increased between 26% - 14%. The same result interpreted as an
extension in the tan β reach for 30 f b−1 , was found between 11% - 8%. The achieved result is quite important,
since in this tan β range the discussed channel may provide the only discovery signature that the discovered
Higgs boson is the MSSM Higgs boson, as in the SM the bb̄H process rates are too low and are not detectable at
the LHC. The possibility of extending discovery range by about 10% is a very satisfactory result.
As an important part of these theses, the reconstruction algorithm of the hadronically decaying tau leptons
has been proposed and implemented in the ATLAS offline software. The algorithm starts the reconstruction from
tracks found in the ATLAS tracker system and then associates the calorimeter clusters with the τ candidate, using
the energy-flow method to define its energy scale. It leads to much higher purity sample at the reconstruction step
than for the calorimeter-based algorithm used so far, and the required rejection at the identification step is less
stringent. The discriminating variables are calculated with use of the calorimeter and the tracker information and
four identification methods are applied: standard one, based on consecutive cuts and three multivariate methods the Neural Networks, the Probability Density Estimation with Range Searching algorithm or the Support Vector
Machine. For the efficiency of 50%, rejection of 100 - 500 is achieved with the cuts selection, depending on the
origin of fake candidates. The very first version of this algorithm has been used for the results presented here.
The proposed algorithm has been developed further, already beyond the scope of these theses, it has become a
part of the ATLAS production software since Spring 2007 and has been proved to be very promising for searches
in several SUSY scenarios, with an enhancement of the stau production decaying to the soft tau leptons.
112
C VIII. C
A A
A.1 Energy calibration for τ-jets in fast simulation
The energy calibration for τ-jets is realized in a relatively simple way, following the method described in [50]. It
is based on 1-dimension calibration function, which gives the scale function to energy-momentum four-vector of
a reconstructed jet. The function is exclusively dependent on the raw transverse momentum of the reconstructed
jet
jet. It has been derived by fitting with gaussian function peak position of the pT /pτ−had
distribution and by
T
taking a calibration factor as a value needed to rescale this position to one. Such fit was performed for several
bins of the raw transverse momentum of jets and yielded the calibration factor as a function of raw pT of the
jet. This calibration gives very good overall results in the absence of inhomogeneity of the detector, which is the
case in the fast simulation where several detector effects are absent or averaged.
The scaling function for τ-jets is shown in Figure A-1. For comparison, calibration factors for b-jets and
light-jets, as presently parametrized for the results from the fast simulation and implemented in Atlfast-b, are
also presented [47].
1.8
1.6
b-jets
1.4
1.2
1
light-jets
τ-jets
0.8
0.6
0.4
0.2
0
0
20
40
60
80
100
120
140
160 180 200
praw
(GeV)
T
Figure A-1: The calibration factor as function of raw jet transverse momentum praw
T for τ − jets (derived here)
and for b-jets and light-jets (as presently in Atlfast-b).
114
A A.
jet
jet
Figure A-2 shows the ratio of pT /pτ−had
as a function of pT (left) and as a function of pseudorapidity
T
(right) for the bb̄H, H → ττ events. Both distributions are flat and close to one (the precision from Atlfast
reconstruction should not be pushed too far of course). So just very small calibration factor is necessary to bring
τ-jets back to the energy scale of the hadronic τ-decay products.
prof303
Entries 60360
Mean
36.64
Mean y 0.9977
RMS
16.8
RMS y 0.0727
1.1
1.08
1.06
1.08
1.06
1.04
1.04
1.02
1.02
1
1
0.98
0.98
0.96
0.96
0.94
0.94
0.92
0.92
0.90
20
40
60
80
100
120
140
160
180 200
pjet (GeV)
T
prof304
Entries 60360
Mean 0.002827
Mean y 0.9978
RMS
1.272
RMS y 0.0727
1.1
1.08
1.06
0.90
1
0.98
0.98
0.96
0.96
0.94
0.94
0.92
0.92
0
0.5
1
1.5
2
2.5
jet
0.9-2.5
η
jet
100
120
140
160
180
200
prof306
Entries 60360
Mean 0.002827
Mean y 0.9985
RMS
1.272
RMS y 0.07248
1.06
1.02
-0.5
80
1.08
1
-1
60
1.1
1.04
-1.5
40
T
1.02
-2
20
pjet (GeV)
1.04
0.9-2.5
prof305
Entries 60348
Mean
36.64
Mean y
0.999
RMS
16.8
RMS y 0.07222
1.1
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
ηjet
jet
Figure A-2: The ratio of pT /pτ−had
as a function of pT (top) and as a function of pseudorapidity (bottom)
T
before (left) and after (right) energy calibration for τ-jets. The results are shown for bb̄H, H → ττ events.
A.2. Reconstruction of ETmiss in fast simulation
115
A.2 Reconstruction of ETmiss in fast simulation
A very important ingredient to the quality of the signal reconstruction will be the reconstruction of the total missing energy. In the fast simulation approach [47] this energy is not calibrated with any dedicated procedure, but
just recalculated from the total energy balance of reconstructed quantities. In Figure A-3 we show ETmiss /ETν for
different Higgs production mechanisms. The mean value is relatively well centered around one (only 2% offset),
the gaussian peaks are symmetric, but the resolution is different for different production mechanisms (topologies), varying on average from 13% for VBFqproduction to 21% for gg → bb̄H production. This is consistent
P calo
with the proportionality relation σ(ETmiss ) ∼
ET , a well known feature of the ETmiss reconstruction based
on calorimetry.
5000
4000
3000
300
300
Entries
150000
Mean
1.014
RMS
0.3249
2
25.03 / 17
χ / ndf
Prob
0.09397
Constant
4634 ± 23.9
Mean
0.9822 ± 0.0011
Sigma 0.1776 ± 0.0019
Entries
100000
Mean
1.018
RMS
0.3394
2
25.17 / 17
χ / ndf
Prob
0.09095
Constant
2725 ± 18.0
Mean
0.9777 ± 0.0020
Sigma 0.2109 ± 0.0039
2500
2000
300
Entries
200000
Mean
1.005
RMS
0.2598
2
281.6 / 17
χ / ndf
Prob
0
Constant
9092 ± 35.2
Mean
0.9848 ± 0.0005
Sigma 0.1327 ± 0.0007
10000
8000
6000
1500
2000
4000
1000
1000
0
0
2000
500
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6 1.8 2
ν
Emiss
T /ET(GeV)
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6 1.8 2
ν
Emiss
T /ET(GeV)
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
ν
Emiss
T /ET(GeV)
Figure A-3: The ratio ETmiss /ETν is shown for different production processes: gg → H (left), bb̄H (middle) and
qqH (right) in ℓ had E miss channel.
T
A.3 Calculation of invariant mass of reconstructed τ leptons pair
Let us start with the expression on product of 4-momenta of two particles:
→
→
p1 p2 = E1 E2 − −
p1 · −
p2 = m212 ,
→
→
where p1(2) are 4-momenta of two particles p1 =(E1 ,−
p1 ) and p2 =(E2 ,−
p2 ), m12 is invariant mass of both particles
and "·" represents an inner product, so
→
→
p1 ||−
p1 | cos φ12 ,
m212 = E1 E2 − |−
where we denoted by φ12 the angle between particle 1 and 2. Let us now calculate a ratio squared of τ-lepton
pair mττ and their visible decay products (denoted here by indices 1 and 2), mvis :
m 2
ττ
mvis
since
−
|→
pi |
Ei
=
−−→
Eτ1 Eτ2 −|−
p−→
τ1 || pτ1 | cos φτ1 τ2
−
→
→
E E −| p ||−
p | cos φ
1 2
1
2
12
=
|−
p−τ−→| |−
p−τ−→
2 | cos φ
τ1 τ2 )
1 E τ2
−
→|
|−
p→
|
|
p
E1 E2 (1− E1 E2 cos φ12 )
1 2
Eτ1 Eτ2 (1− Eτ1
→
−
= | βi | = βi is a velocity of particle i:
=
Eτ1 Eτ2 (1−βτ1 βτ2 cos φτ1 τ2 )
E1 E2 (1−β1 β2 cos φ12 )
=
=
116
A A.
since Ei = ET i cosh ηi :
=
ET τ1 cosh ητ1 ET τ2 cosh ητ2 (1−βτ1 βτ2 cos φτ1 τ2 )
ET 1 cosh η1 ET 2 cosh η2 (1−β1 β2 cos φ12 )
=
ET τ1 ET τ2 cosh ητ1 cosh ητ2 (1−βτ1 βτ2 cos φτ1 τ2 )
ET 1 ET 2 cosh η1 cosh η2 (1−β1 β2 cos φ12 )
=
.
Now, from assumption that τ is massless (so its decay products as well), βτ1 = βτ2 = β1 = β2 = 1, and from
assumption that decay products decay collinearly (which is consequence of mτ = 0), ητ1 = η1 , ητ2 = η2 and
φτ1 τ2 = φ12 :
m 2
ττ
mvis
and if we denote
ETi
E T τi
= xτi :
=
=
E T τ1 E T τ2
ET1 ET2
1 1
xτ1 xτ2
=
.
In the end we obtain:
m 2
ττ
mvis
and we can express mττ as:
mττ =
=
√
1 1
xτ1 xτ2
mvis
xτ1 xτ2
.
Figures A-4 and A-5 show the reconstructed invariant mass of the τ-lepton system in the situation where either
true missing energy (left) or reconstructed missing energy (right) is used for calculating xτ1 , xτ2 , which enter
the formula for the mττ invariant mass. We can notice that about 30% contribution to the final resolution comes
already from the assumption of τ-leptons decaying collinearly. The reconstruction of ETmiss itself adds remaining
70% to the total resolution. Comparing reconstruction in the ℓℓETmiss and ℓ had ETmiss channels one can easily
notice that the absolute and relative contribution from the ETmiss reconstruction is smaller in the ℓ had ETmiss one,
due to the harder spectrum of hadronic τ decays with respect to the lepton ones (Figure V-2). Obviously, the
results concerning the impact of ETmiss reconstruction are indicative only. These effects should be studied with
the full simulation of the detector.
A.3. Calculation of invariant mass of reconstructed τ leptons pair
117
301
×10
-1
173
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Mean
119.4
RMS
5.503
χ2 / ndf
0.005
145.9 / 6
Prob
0
Constant 0.0005823 ± 0.0000095
0.004
×10
-1
7164
119.8 ± 0.0
Mean
3.9 ± 0.0
Sigma
Entries
0.002
7164
Mean
120
RMS
15.68
χ2 / ndf
0.0018
29.65 / 6
Prob
4.586e-05
Constant 0.0001922 ± 0.0000035
0.0016
0.0014
Mean
118.3 ± 0.2
Sigma
11.12 ± 0.25
0.0012
0.003
0.001
0.0008
0.002
0.0006
0.0004
0.001
0.0002
0
0
20
40
60
80
0
0
100 120 140 160 180 200
20
40
60
80
100 120 140 160 180 200
mττ(GeV)
mττ(GeV)
301
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-5
0.25
173
Entries
836
Mean
116
RMS
11.25
χ2 / ndf
0.2
-5
0.1
18.66
4.479 / 6
0.6122
Constant 8.305e-07 ± 4.551e-08
114 ± 2.1
Mean
5.995 ± 0.222
Sigma
117.9
Prob
0.08
118.2 ± 0.2
Mean
836
Mean
χ2 / ndf
0.0005019
Constant 1.953e-06 ± 9.969e-08
Entries
RMS
24.09 / 6
Prob
0.15
×10
16.79 ± 2.36
Sigma
0.06
0.1
0.04
0.05
0.02
0
0
20
40
60
80
0
0
100 120 140 160 180 200
20
40
60
80
100 120 140 160 180 200
mττ(GeV)
mττ(GeV)
301
×10
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0.005
173
Entries
18608
Mean
119.4
RMS
5.2
χ / ndf
2
378.9 / 6
Prob
0.004
0
Constant 0.0005387 ± 0.0000054
Mean
Sigma
119.7 ± 0.0
3.619 ± 0.025
×10
-1
0.002
Entries
18608
Mean
119.4
RMS
13.84
0.0018
χ / ndf
0.0016
Prob
0.0014
Mean
118.4 ± 0.1
Sigma
10.16 ± 0.12
0.003
0.0012
0.002
0.0008
2
48.82 / 6
8.104e-09
Constant 0.0001834 ± 0.0000020
0.001
0.0006
0.0004
0.001
0.0002
0
0
20
40
60
80
100 120 140 160 180 200
mττ(GeV)
0
0
20
40
60
80
100 120 140 160 180 200
mττ(GeV)
Figure A-4: The reconstructed invariant mass of the ττ system mττ in ℓℓE miss channel and different production
T
modes: gg → H (top), bb̄H (middle) and qqH (bottom), if the true neutrino (left) or ETmiss (right) was used for
mττ reconstruction.
118
A A.
301
173
Entries
0.0035
0.003
2725
Mean
119.5
RMS
5.626
χ2 / ndf
14.42 / 6
Prob
0.02528
Constant 0.003802 ± 0.000093
119.7 ± 0.1
Mean
0.0025
Sigma
4.742 ± 0.072
Entries
0.0018
0.0016
0.0014
2725
Mean
122.7
RMS
13.74
χ2 / ndf
13.4 / 6
Prob
0.03716
Constant 0.001656 ± 0.000046
0.0012
Mean
120.9 ± 0.3
Sigma
10.27 ± 0.29
0.001
0.002
0.0008
0.0015
0.0006
0.001
0.0004
0.0005
0.0002
0
0
20
40
60
80
0
0
100 120 140 160 180 200
20
40
60
80
100 120 140 160 180 200
mττ(GeV)
mττ(GeV)
301
×10
-4
173
Entries
684
Mean
117.4
RMS
0.14
0.12
-5
9.936
χ2 / ndf
11.48 / 6
Prob
0.07466
Constant 1.297e-05 ± 6.850e-07
0.1
0.8 ×10
Mean
118.3 ± 0.3
Sigma
6.036 ± 0.221
0.3
0.2
0.02
0.1
80
100 120 140 160 180 200
0
0
0.1345
Constant 6.003e-06 ± 3.765e-07
0.5
0.04
60
17.01
20
40
60
80
Mean
118.6 ± 1.0
Sigma
13.4 ± 1.3
100 120 140 160 180 200
mττ(GeV)
mττ(GeV)
301
0.0035
13790
Mean
119.4
RMS
5.639
χ / ndf
0.003
173
Entries
2
Prob
65.38 / 6
Mean
Sigma
Entries
0.0018
0.0016
119.7 ± 0.0
4.605 ± 0.031
0.002
0.0014
13790
Mean
121.4
RMS
12.22
χ / ndf
36.87 / 6
Prob
1.87e-06
2
3.613e-12
Constant 0.003664 ± 0.000040
0.0025
9.774 / 6
Prob
0.4
40
122.3
χ2 / ndf
0.6
0.06
20
684
Mean
RMS
0.7
0.08
0
0
Entries
Constant 0.001693 ± 0.000021
Mean
0.0012
Sigma
120 ± 0.1
9.638 ± 0.111
0.001
0.0008
0.0015
0.0006
0.001
0.0004
0.0005
0
0
0.0002
20
40
60
80
100 120 140 160 180 200
0
0
20
40
60
80
100 120 140 160 180 200
mττ(GeV)
mττ(GeV)
Figure A-5: The same as Figure A-4, but for ℓ had E miss channel.
T
A.4. The mass reconstruction for background events
119
A.4 The mass reconstruction for background events
The signal events at 120 GeV will have to be detected above the steeply falling resonant background. For the
irreducible qq̄ → Z/γ∗ → ττ background, respective distribution of the reconstructed mττ invariant mass based
on fast simulation is shown in Figure A-6 (left column).
173
Entries
25219
Mean
95.06
RMS
0.03
18.52
χ / ndf
17.33 / 6
Prob
0.008154
2
6
Constant 0.03073 ± 0.00038
0.025
0.02
Mean
91.31 ± 0.11
Sigma
10.13 ± 0.12
5.5
5
0.015
4.5
0.01
4
0.005
3.5
0
0
20
40
60
80
100 120 140 160 180 200
100
110
120
130
140
150
mττ(GeV)
160
mττ(GeV)
173
Entries
9606
Mean
98.35
RMS
18.43
10.5 / 6
χ2 / ndf
Prob
0.1052
Constant 0.1914 ± 0.0037
Mean
93.16 ± 0.16
8.784 ± 0.144
Sigma
0.2
0.18
0.16
0.14
0.12
5
4
3
0.1
0.08
2
0.06
0.04
1
0.02
0
0
20
40
60
80
100 120 140 160 180 200
mττ(GeV)
0
100
110
120
130
140
150
160
mττ(GeV)
Figure A-6: The reconstructed mass of the ττ system in ℓℓE miss (upper line) and ℓ had E miss (bottom line) for
T
T
the qq̄ → Z/γ∗ → ττ events (left column) normalization to total σ × BR [pb]. The ratio of the reconstructed
to the generated mass for accepted events as a function of the reconstructed mass is shown on the right column
plots. In decreasing order come ratios after consecutive selection.
The ratio of the generated to reconstructed mass for accepted events as a function of the generated ττ pair
mass is shown in Figure A-6 (right column). For the primary selection the background shape will not reproduce
the original line shape of the Z/γ∗ (the ratio is not flat in the range mττ = 100 − 140 GeV) and the ratio is of a few.
Just at 120 GeV, the background is dominated by events generated with on-shell Z-boson and misreconstructed
at higher masses. This is also the case after additional selection.
Given this behaviour, one of the important experimental issue will be therefore the evaluation of the procedure to predict/control precisely the expected background shape. It will be dominated, for individual background
events, by the tails contribution in mass reconstruction of the on-shell Z-boson.
The studies on the reconstruction of the resonant irreducible Z/γ∗ → ττ background clearly show that the
ratio of the reconstructed to generated events in the mass window around Z peak varies by factor few with
different selection criteria. Controlling this background for the Higgs masses not very far from the Z-boson mass
will be a challenge at the LHC.
120
A A.
A.5 List of variables
Throughout this thesis we will use following variables:
• pseudorapidity: η = −ln tan 2θ , where θ is a polar angle from the beam direction;
• azimuthal angle: tan φ =
py
px ,
• transverse momentum: pT =
• transverse energy: ET =
where p x and py are x and y component of particle momentum;
q
p2x + p2y ;
E
cosh η ;
• distance in the pseudorapidity and azimuthal angle plane: ∆R =
p
(∆η)2 + (∆φ)2 .
A B
B.1 Acceptance and expected number of events for the mass point mH = 150 GeV
The evaluation of signal and background for associated Higgs production, bb̄H was performed at three mass
points. The most challenging, due to irreducible Z → ττ background, is the observability of the Higgs boson at
120 GeV and the results were presented in Chapter IV. Here, we briefly discuss the cases of Higgs boson masses
of 150 GeV and 200 GeV (in Appendix B.2).
The acceptance of events after consecutive cuts is shown in Table B-1 and Table B-3 for ℓℓETmiss and
ℓ had ETmiss modes respectively. After primary selection (Section IV.4), the acceptance for all signal production process is similar ∼ 29% and ∼ 18% for ℓℓETmiss and ℓ had ETmiss modes respectively. However, after generic
selection, the gg → H has 5.73/2.85 = 2.0 (2.37/0.992 = 2.4) times higher acceptance than bb̄H process. This
is due to softer pT spectra of Higgs boson produced in gluon fusion process. What is worth noticing is a disperse
of values for different approaches to associated production: in the most extreme case acceptance for bb̄ → H
process is 4.18/2.06 = 2 times higher in respect to gb → bH for ℓℓETmiss and 1.61/0.668 = 2.4 for ℓ had ETmiss
respectively. In the case of b-jet veto/tag analysis, the events of gluon fusion process mainly accepted as the ones
that do not have b-jet veto (ca. 93%) for both final states, which is expected as they do not have b-quarks in
the hard process. The Yukawa induced Higgs production is more frequently assigned as b-jet tag events (at least
50%). However, we spotted that bb̄H approach in all cases (SF and NSF of ℓℓETmiss and ℓ had ETmiss ) has constant
10% higher acceptance: for example, in the case of NSF leptons, a ratio of b-jet tag versus after generic selection equals 0.845/1.42 = 60% (instead of 50%) in respect to other approaches for Yukawa induced production.
This might be due to the tagging procedure that is pT -dependent, and for processes with various b-quark’s pT
distributions can lead to such discrepancy.
The number of expected events for 10 f b−1 , with assumed reconstruction efficiencies for electrons, muons
and τ-jet included, is presented in Table B-2 (B-4). One can notice that after generic selection values for ℓℓETmiss
and ℓ had ETmiss for the same process are quite similar: for example 0.0589 versus 0.0409 for bb̄H or 13.6 versus
11.2 for gg → H. This is an important feature, since the ratio of expected background between ℓℓETmiss and
ℓ had ETmiss drops even by one third.
The mass resolution, fitted in mass window of 150 GeV ± 30 GeV is summarized in Table B-5 (B-6).
After generic selection the mass resolution in ℓℓETmiss improves (32.3 GeV-20.6 GeV)/32.3 GeV ∼ 36% and
in ℓ had ETmiss by (26.6 GeV-17.7 GeV)/26.6 GeV ∼ 33%. The b-jet veto in ℓ had ETmiss improves nominally
(14.2 GeV-14.0 GeV)/14.2 GeV ∼ 1%, but this change is inside the error bars of the fitted values.
The number of expected events in a mass window of 150 GeV ± 30 GeV for 10 f b−1 is demonstrated in Table
B-7 (B-8). The expected events for signal is the same in both ℓℓETmiss and ℓ had ETmiss , but the backgroud in
ℓ had ETmiss is suppressed on average by 30%. An interesting observation can be made concerning the contribution
of bb̄Z to inclusive Z/γ∗ production. For both ℓℓETmiss and ℓ had ETmiss modes, this ratio is the same: after generic
selection (6-7%), after b-jet veto (2%) and after b-jet tag (36-46%). The statistics for W background in ℓℓETmiss
is limited and the contribution of bb̄W to W + jet events can not be estimated. For ℓ had ETmiss after generic
selection this ratio equals 2.57/529= 0.5% and for b-jet tag it increases to 0.77/18.9= 4%.
122
A B.
The final values for expected signal and background in the corresponding mass window was used in Section IV.7 in the estimation of combined significance.
Table B-1: The cumulative acceptance after consecutive selections for signal mH = 150 GeV events in ℓℓE miss
T
channel. After applying a common set of selections the analysis splits into two streams. One selects only the
not same flavour leptons NSF and performs b-tagging procedure directly, while the other takes the same flavour
leptons SF and introduces additional selections against Z → ℓℓ events and applies b-jet tagging procedure.
Statistical errors at the level of the generic selection are less than 1%; they increase to 1-3% for b-jet veto and
b-jet tagged analyses.
Analysis
type
NSF+SF
only NSF
only SF
Selection
gg → bb̄H
%
bb̄ → H
%
gb → bH
%
gg → H
%
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
46.9
29.1
18.1
10.2
4.55
3.25
2.85
46.5
28.6
17.8
9.58
3.81
2.46
2.06
46.8
28.2
18.7
11.5
6.13
4.65
4.18
48.4
28.8
19.9
12.6
7.61
6.21
5.73
after generic selection
1.42
1.02
2.08
2.86
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.577
0.348
0.312
0.507
0.34
0.306
1.02
0.584
0.515
2.67
1.38
1.19
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.845
0.634
0.56
0.516
0.417
0.371
1.06
0.751
0.653
0.189
0.102
0.0887
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
1.43
1.25
0.681
1.03
0.926
0.377
2.1
1.83
1.14
2.87
2.44
1.71
b-jet veto
3rd jet veto
0.263
0.139
0.178
0.112
0.506
0.267
1.6
0.77
b-jet tagged
3rd jet veto
0.419
0.291
0.199
0.158
0.634
0.442
0.114
0.0571
B.1. Acceptance and expected number of events for the mass point mH = 150 GeV
123
Table B-2: The expected number of signal mH = 150 GeV events for an integrated luminosity 10 f b−1 after
consecutive cuts in ℓℓE miss channel. Efficiencies for leptons and b-jet identification are included (90% and 60%
T
respectively). Statistical errors are typically at 10% level.
Analysis
type
NSF + SF
only NSF
only SF
Selection
gg→ bb̄H
bb̄ → H
gb → bH
gg → H
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
0.969
0.601
0.374
0.211
0.094
0.0671
0.0589
3.87
2.38
1.48
0.798
0.318
0.205
0.171
3.3
1.99
1.32
0.81
0.432
0.328
0.295
115.0
68.2
47.0
29.9
18.0
14.7
13.6
after generic selection
0.0294
0.0852
0.147
6.77
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.0119
0.0072
0.00646
0.0422
0.0283
0.0255
0.0723
0.0412
0.0363
6.33
3.26
2.8
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.0175
0.0131
0.0116
0.043
0.0347
0.0309
0.0746
0.053
0.046
0.448
0.241
0.21
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
0.0295
0.0259
0.0141
0.0861
0.0771
0.0314
0.148
0.129
0.0804
6.79
5.79
4.06
b-jet veto
3rd jet veto
0.00543
0.00287
0.0148
0.00931
0.0357
0.0188
3.79
1.82
b-jet tagged
3rd jet veto
0.00866
0.00601
0.0166
0.0132
0.0447
0.0312
0.27
0.135
124
A B.
Table B-3: The same as Table B-1, but for ℓ had E miss channel. Statistical errors at the level of the generic
T
selection are typically less than 1%; they increase to 2-3% for b-jet veto and b-jet tagged analyses.
Selection
gg → bb̄H
%
bb̄ → H
%
gb → bH
%
gg→ H
%
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
33.4
18.2
9.18
4.75
4.26
1.57
1.06
0.992
32.9
18.0
9.03
4.44
4.01
1.26
0.733
0.668
33.2
17.8
9.83
5.64
5.01
2.26
1.69
1.61
34.3
18.2
10.6
6.53
5.75
2.98
2.45
2.37
b-jet veto
3rd jet veto
0.398
0.233
0.326
0.215
0.757
0.416
2.2
1.11
b-jet tagged
3rd jet veto
0.594
0.433
0.342
0.277
0.853
0.599
0.17
0.09
Table B-4: The same as Table B-2, but for ℓ had E miss channel. Statistical errors are typically at 10% level.
T
Selection
gg→ bb̄H
bb̄ → H
gb → bH
gg→ H
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
0.379
0.196
0.176
0.0648
0.0437
0.0409
1.5
0.738
0.666
0.21
0.122
0.111
1.39
0.796
0.707
0.318
0.239
0.227
50.2
31.0
27.3
14.1
11.6
11.2
b-jet veto
3rd jet veto
0.0164
0.00962
0.0542
0.0358
0.107
0.0587
10.4
5.27
b-jet tagged
3rd jet veto
0.0245
0.0179
0.0569
0.0461
0.12
0.0845
0.806
0.427
B.1. Acceptance and expected number of events for the mass point mH = 150 GeV
125
Table B-5: The resolution of the reconstructed invariant mass of the τ system for signal events in ℓ had E miss
T
channel. The results from gaussian fit in mass window mH = 150 GeV ± 30 GeV.
Analysis
type
NSF+SF
Selection
gg→ bb̄H
[GeV]
bb̄ → H
[GeV]
gb → bH
[GeV]
gg → H
[GeV]
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
32.3 ± 0.4
28.9 ± 0.3
23.2 ± 0.2
21.4 ± 0.2
20.6 ± 0.2
35.7 ± 0.5
31.7 ± 0.4
25.5 ± 0.3
22.9 ± 0.3
21.9 ± 0.3
27.1 ± 0.2
24.9 ± 0.2
20.7 ± 0.1
19.4 ± 0.1
18.7 ± 0.1
22.6 ± 0.1
20.8 ± 0.1
17.7 ± 0.1
16.8 ± 0.1
16.4 ± 0.1
20.6 ± 0.3
20.8 ± 0.4
21.5 ± 0.5
20.5 ± 0.4
20.0 ± 0.4
20.3 ± 0.5
17.8 ± 0.2
17.6 ± 0.2
17.8 ± 0.3
17.4 ± 0.5
17.6 ± 0.6
17.9 ± 0.7
b-jet veto
3rd jet veto
19.3 ± 0.3
19.6 ± 0.7
19.1 ± 0.6
18.0 ± 0.5
18.2 ± 0.3
18.1 ± 0.4
15.1 ± 0.1
14.7 ± 0.1
b-jet tagged
3rd jet veto
18.4 ± 0.3
18.2 ± 0.4
20.9 ± 0.7
20.5 ± 0.7
16.8 ± 0.2
16.7 ± 0.3
16.1 ± 0.5
15.8 ± 0.7
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
only NSF
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
only SF
20.9 ± 0.4
21.2 ± 0.6
21.6 ± 0.6
21.1 ± 0.3
18.8 ± 0.3
22.9 ± 0.6
22.1 ± 0.6
22.6 ± 0.7
22.4 ± 0.4
20.1 ± 0.5
19.3 ± 0.3
19.3 ± 0.3
19.3 ± 0.4
19.4 ± 0.2
17.4 ± 0.2
16.4 ± 0.1
16.2 ± 0.1
16.5 ± 0.2
16.6 ± 0.1
15.2 ± 0.1
Table B-6: The same as Table B-5, but for ℓ had E miss channel.
T
Selection
gg→ bb̄H
[GeV]
bb̄ → H
[GeV]
gb → bH
[GeV]
gg→ H
[GeV]
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
26.6 ± 0.3
24.3 ± 0.2
24.4 ± 0.3
19.3 ± 0.2
18.0 ± 0.2
17.7 ± 0.2
29.1 ± 0.5
26.5 ± 0.3
26.6 ± 0.3
20.3 ± 0.3
18.8 ± 0.6
18.7 ± 0.3
23.2 ± 0.2
21.5 ± 0.2
21.5 ± 0.2
17.6 ± 0.1
16.7 ± 0.1
16.5 ± 0.1
19.5 ± 0.1
18.2 ± 0.1
18.2 ± 0.1
15.0 ± 0.1
14.3 ± 0.1
14.2 ± 0.1
17.6 ± 0.3
17.7 ± 0.2
18.6 ± 0.4
18.7 ± 0.4
16.1 ± 0.2
16.2 ± 0.2
14.7 ± 0.3
14.9 ± 0.4
b-jet veto
3rd jet veto
b-jet tagged
3rd jet veto
17.9 ± 0.3
17.8 ± 0.4
18.7 ± 0.4
18.5 ± 0.5
16.9 ± 0.2
17.0 ± 0.3
14.2 ± 0.1
14.0 ± 0.1
Analysis
type
NSF+SF
only NSF
only SF
gg → bb̄H
gg → H
bb̄Z
Z/γ∗
qq̄ → W
W + jet
bb̄W
tt¯
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
0.155
0.119
0.0627
0.0506
0.0459
23.9
20.2
13.8
12.3
11.6
403
302
134
111
101
1.77·104
9.48·103
2.51·103
1.79·103
1.58·103
133
83.1
83.1
33.4
6.19
191
180
160
154
12.5
8.99
7.53
4.55
3.37
3.14
4.39·103
4.3·103
3.27·103
3.15·103
3.03·103
after generic selection
0.023
5.81
50.5
790
6.19
7.69
1.84
1.62·103
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.00919
0.00553
0.00492
5.43
2.81
2.41
23.4
9.3
9.15
735.0
440.0
431.0
5.82
0.0
0.0
6.95
1.22
0.0
1.71
1.1
1.02
427.0
60.7
37.4
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.0138
0.0103
0.00904
0.378
0.204
0.177
27.1
13.4
13.2
55.1
36.8
36.0
0.372
0.0
0.0
0.742
0.148
0.148
0.13
0.0841
0.078
1.19·103
503.0
313.0
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
0.0229
0.0199
0.0115
5.8
4.92
3.57
50.3
49.4
23.7
791
773.0
238.0
0
0.0
0.0
4.8
3.36
1.93
1.3
0.841
0.0765
1.41·103
907.0
725.0
b-jet veto
3rd jet veto
0.00437
0.00229
3.33
1.62
10.0
3.13
215.0
120.0
0.0
0.0
1.83
1.22
0.0642
0.0344
161.0
30.6
b-jet tagged
3rd jet veto
0.00709
0.00496
0.237
0.12
13.7
6.24
22.7
13.4
0.0
0.0
0.1
0.1
0.0122
0.0122
564.0
192.0
A B.
Selection
126
Table B-7: The expected number of signal and background events within mass window mH = 150 GeV ± 30 GeV for an integrated luminosity 10 f b−1 after
consecutive cuts in ℓℓE miss channel. Efficiencies for lepton and b-jet identification are included (90% and 50% respectively). Statistical errors are typically
T
at the level of 10%. Throughout the b-jet veto and b-jet tag analysis statistical errors for all backgrounds increase to 15%, while signal uncertainty stays at
the level of 10%. The background from W (qq̄ → W and W + jet) suffers a lack of statistics and at the level of generic selection the statistical errors are at the
level of 14% and they increase to 82% and more throughout the rest of the analysis. For tt¯ background in b-jet veto analysis numbers have 25% uncertainty.
Selection
gg → bb̄H
gg→ H
bb̄Z
Z/γ∗
qq̄ → W
W + jet
bb̄W
tt¯
resolved neutrino
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
pmiss
>
30 GeV
T
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
0.17
0.129
0.116
0.0457
0.0358
0.0343
27.2
23.1
20.4
11.3
10.2
10
172
126
119
39.8
35.6
35.2
8.35·103
4.19·103
4.02·103
702
524
508
1.16·104
8.51·103
4.96·103
838
681
633
1.26·104
8.68·103
4.86·103
680
563
529
28.6
23.7
12.3
3.11
2.71
2.57
2.79·103
2.75·103
1.72·103
1.07·103
1.04·103
1.03·103
b-jet veto
3rd jet veto
0.0136
0.00793
9.32
4.72
15.5
5.69
474.0
271.0
581.0
307.0
496.0
269.0
1.37
0.688
331.0
38.6
b-jet tagged
3rd jet veto
0.0207
0.0152
0.719
0.386
19.7
9.09
33.9
21.3
52.2
31.3
33.1
18.9
1.2
0.77
702.0
146.0
B.1. Acceptance and expected number of events for the mass point mH = 150 GeV
Table B-8: The same as Table B-7, but for ℓ had E miss channel. Statistical errors are typically at the level of 10%. Throughout the b-jet veto and b-jet tag
T
analysis statistical errors for all backgrounds increase to 15%, while signal uncertainty stays at the level of 10%. For tt¯ background in b-jet veto analysis
numbers have 25% uncertainty.
127
128
A B.
B.2 Acceptance and expected number of events for the mass point mH = 200 GeV
The acceptance of events after consecutive cuts for the Higgs mass of 200 GeV is shown in Table B-9 and
Table B-11 for ℓℓETmiss and ℓ had ETmiss mode respectively. After primary selection the acceptance for all signal
production processes is comparable ∼ 37% and ∼ 28% for ℓℓETmiss and ℓ had ETmiss mode respectively. However,
after generic selection the gg → H has 7.21/3.52 = 2 (3.53/1.54 = 2.3) times higher acceptance than bb̄H
process. This is due to softer pT spectra of gluon fusion process. What is worth noticing is a disperse of values
for different approaches to associated production: in the most extreme case, the acceptance for bb̄ → H is
5.49/2.99 = 1.8 and 2.52/1.3 = 1.9 times higher than gb → bH for ℓℓETmiss and ℓ had ETmiss mode respectively.
In the case of b-jet veto/tag analysis, the events of gluon fusion process are mainly accepted as b-jet veto (ca.
93%) for both final states, which is expected as they have no b-jet in the final state of the hard process. The
Yukawa induced Higgs production is more frequently assigned as b-jet tag events (at least 50%). However, we
observed that bb̄H approach in both ℓℓETmiss and ℓ had ETmiss mode has ∼ 10% higher acceptance. For example,
a ratio of acceptance after b-jet tag for NSF (Table B-9) 1.06 and acceptance after generic selection 1.75 equals
60% (instead of 50% as for the other approaches for Yukawa induced production). This might be due to the
tagging procedure, that is pT -dependent, and for processes with different pT distributions of b-quarks, can lead
to such discrepancy.
The number of expected events for 10 f b−1 with assumed reconstruction efficiencies for electrons, muons
and τ-jet included is presented in Table B-10 (B-12). One can notice that after generic selection the values for
ℓℓETmiss and ℓ had ETmiss for the same process are quite similar, for example 0.000406 versus 0.000357 for bb̄H
or 0.171 versus 0.156 for gg → H. This is the important feature, since the ratio of expected background between
ℓℓETmiss and ℓ had ETmiss drops even by one third.
The mass resolution is summarized in Table B-13 (B-14). After generic selection, in ℓℓETmiss channel the
mass resolution improves by (41.6 GeV-25.2 GeV)/41.6 GeV ∼ 39% and in ℓ had ETmiss channel by (34.7 GeV23.3 GeV)/34.7 GeV ∼ 33%. The sensitivity of b-jet tag analysis for both final states improves by 1-2% (for
example NSF ℓℓETmiss 25.2 GeV-24.9 GeV)/25.2 GeV = 1.2%).
The number of expected events in a mass window of 200 ± 40 GeV for 10 f b−1 is shown in Table B-15
(B-16). The number of expected events for signal is comparable in both ℓℓETmiss (0.000320) and ℓ had ETmiss
(0.000307) respectively, but the backgroud in ℓ had ETmiss is suppressed on average by 30%, thus giving better
significance.
For this Higgs boson mass, we also observe higher acceptance in b-jet tag analysis with respect to generic
selection (60% for bb̄H versus 50% for bb̄ → H or gb → bH). The 93% acceptance is the same for gluon fusion
in b-jet veto as for 150 GeV (in all modes).
Another important aspect of the analysis is the ratio of bb̄Z and inclusive Z production. In ℓℓETmiss channel,
after generic selection, this ratio was 19.1/290= 6.5% in the b-jet veto case. It stayed at the level of 3% for b-jet
veto case, while depending if NSF and SF contribution, raised in b-jet tag analysis to 40% and 85% respectively.
In the case of ℓ had ETmiss ,after generic selection the contribution of bb̄Z was about 10%; it was reduced to 2%
for b-jet veto, but increased to 30% in b-jet tag analysis.
The bb̄W background in ℓ had ETmiss after generic selection contributed only at the level of 0.5% to W + jet.
In b-jet veto the ratio dropped to 0.3% and in b-jet tagged was raised to 4% as for mass point mH = 150 GeV.
The final values for expected signal and background in the corresponding mass window was used in Section IV.7 in the estimation of combined significance.
B.2. Acceptance and expected number of events for the mass point mH = 200 GeV
129
Table B-9: The cumulative acceptance after consecutive selections for signal mH = 200 GeV events in ℓℓE miss
T
channel. After applying a common set of selections the analysis splits into two streams. One selects only not
the same flavour leptons NSF and performs b-tagging procedure directly, while the other takes the same flavour
leptons SF and introduces additional selections against Z → ℓℓ events and applies b-jet tagging procedure.
Statistical errors at the level of the generic selection are less than 1%; they increase to 1-3% for b-jet veto and
b-jet tagged analyses.
Analysis
type
NSF+SF
only NSF
only SF
Selection
gg → bb̄H
%
bb̄ → H
%
gb → bH
%
gg → H
%
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
57.4
37.3
24.1
12.4
7.19
4.43
3.52
57.3
37.0
24.2
12.3
6.91
3.99
2.99
57.4
36.2
25.2
14.8
9.83
6.67
5.49
59.2
36.9
26.5
15.9
11.4
8.4
7.21
after generic selection
1.75
1.48
2.75
3.6
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.686
0.396
0.262
0.703
0.435
0.285
1.34
0.694
0.442
3.35
1.6
0.974
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
1.06
0.767
0.488
0.778
0.602
0.391
1.41
0.939
0.582
0.251
0.126
0.0757
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
1.77
1.13
0.812
1.51
0.981
0.637
2.74
1.72
1.35
3.61
2.19
1.86
b-jet veto
3rd jet veto
0.306
0.163
0.298
0.177
0.616
0.308
1.72
0.785
b-jet tagged
3rd jet veto
0.507
0.352
0.339
0.258
0.729
0.476
0.133
0.0656
130
A B.
Table B-10: The expected number of signal mH = 200 GeV events for an integrated luminosity 10 f b−1 after
consecutive cuts in ℓℓE miss channel. Efficiencies for leptons and b-jet identification are included (90% and 60%
T
respectively). Statistical errors are typically at 10% level.
Analysis
type
NSF+SF
only NSF
only SF
Selection
gg→ bb̄H
bb̄ → H
gb → bH
gg → H
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
0.00663
0.00431
0.00279
0.00143
0.00083
0.000512
0.000406
0.0252
0.0163
0.0107
0.00542
0.00304
0.00176
0.00132
0.0368
0.0232
0.0162
0.00949
0.00631
0.00428
0.00352
1.4
0.877
0.629
0.379
0.271
0.199
0.171
after generic selection
0.000202
0.000652
0.00177
0.0854
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
7.93·10−5
4.57·10−5
3.03·10−5
0.00031
0.000192
0.000126
0.00086
0.000446
0.000284
0.0794
0.0379
0.0231
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
0.000123
8.86·10−5
5.63·10−5
0.000343
0.000265
0.000172
0.000907
0.000603
0.000373
0.00597
0.00299
0.0018
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
0.000204
0.000131
9.39·10−5
0.000664
0.000432
0.00028
0.00176
0.0011
0.000863
0.0858
0.052
0.0441
b-jet veto
3rd jet veto
3.53·10−5
1.89·10−5
0.000131
7.79·10−5
0.000395
0.000198
0.0409
0.0186
b-jet tagged
3rd jet veto
5.85·10−5
4.07·10−5
0.000149
0.000114
0.000468
0.000306
0.00316
0.00156
B.2. Acceptance and expected number of events for the mass point mH = 200 GeV
131
Table B-11: The same as Table B-9, but for ℓ had E miss channel. Statistical errors at the level of the generic
T
selection are typically less than 1%, they increase to 1-2% for b-jet veto and b-jet tagged analyses.
Selection
gg → bb̄H
%
bb̄ → H
%
gb → bH
%
gg→ H
%
trigger selection
primary selection
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
43.3
28.4
15.0
7.22
6.01
3.12
1.81
1.54
43.2
28.2
15.1
7.16
6.0
3.0
1.59
1.3
43.0
27.5
16.1
9.02
7.38
4.39
2.85
2.52
44.3
28.3
17.2
10.2
8.22
5.29
3.87
3.53
b-jet veto
3rd jet veto
0.597
0.335
0.62
0.382
1.2
0.616
3.26
1.55
b-jet tagged
3rd jet veto
0.948
0.679
0.683
0.53
1.32
0.88
0.266
0.133
Table B-12: The same as Table B-10, but for ℓ had E miss channel. Statistical errors are typically at 10% level.
T
Selection
gg→ bb̄H
bb̄ → H
gb → bH
gg→ H
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
0.00347
0.00167
0.00139
0.000721
0.000417
0.000357
0.0133
0.0063
0.00528
0.00264
0.00139
0.00115
0.0207
0.0115
0.00945
0.00562
0.00365
0.00323
0.762
0.449
0.364
0.234
0.171
0.156
b-jet veto
3rd jet veto
0.000138
7.73·10−5
0.000545
0.000336
0.00154
0.000788
0.144
0.0688
b-jet tagged
3rd jet veto
0.000219
0.000157
0.0006
0.000466
0.00169
0.00113
0.0118
0.00587
132
A B.
Table B-13: The resolution of the reconstructed invariant mass of the τ system for signal events in ℓ had E miss
T
channel. The results from gaussian fit in mass window mH = 200 GeV ± 40 GeV.
Analysis
type
NSF+SF
Selection
gg→ bb̄H
[GeV]
bb̄ → H
[GeV]
gb → bH
[GeV]
gg → H
[GeV]
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
41.6 ± 0.4
35.3 ± 0.3
30.6 ± 0.2
26.7 ± 0.2
25.2 ± 0.2
43.2 ± 0.4
37.3 ± 0.3
32.5 ± 0.3
27.9 ± 0.2
26.4 ± 0.2
35.5 ± 0.1
31.7 ± 0.2
28.2 ± 0.2
25.2 ± 0.1
24.0 ± 0.1
28.8 ± 0.1
26.1 ± 0.1
23.4 ± 0.1
21.4 ± 0.1
20.4 ± 0.1
24.9 ± 0.3
25.1 ± 0.4
26.5 ± 0.6
26.0 ± 0.4
25.6 ± 0.4
26.7 ± 0.6
23.6 ± 0.2
23.3 ± 0.3
24.4 ± 0.4
21.5 ± 0.4
21.2 ± 0.6
21.7 ± 0.8
b-jet veto
3rd jet veto
25.8 ± 0.6
25.5 ± 0.8
25.2 ± 0.6
24.7 ± 0.7
23.7 ± 0.3
23.3 ± 0.5
19.8 ± 0.1
19.4 ± 0.2
b-jet tagged
3rd jet veto
24.4 ± 0.4
24.4 ± 0.5
25.8 ± 0.6
25.5 ± 0.6
22.3 ± 0.3
21.8 ± 0.3
21.4 ± 0.6
20.5 ± 0.7
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
only NSF
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
only SF
25.4 ± 0.4
25.6 ± 0.5
27.1 ± 0.8
26.3 ± 0.3
24.9 ± 0.4
26.5 ± 0.4
26.0 ± 0.5
26.4 ± 0.7
24.9 ± 0.3
24.9 ± 0.4
25.4 ± 0.5
27.4 ± 0.4
25.6 ± 0.4
24.2 ± 0.2
22.9 ± 0.2
20.2 ± 0.1
20.0 ± 0.1
20.4 ± 0.2
20.9 ± 0.1
19.9 ± 0.1
Table B-14: The same as Table B-13, but for ℓ had E miss channel.
T
Selection
gg→ bb̄H
[GeV]
bb̄ → H
[GeV]
gb → bH
[GeV]
gg→ H
[GeV]
resolved neutrinos
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
miss
pT > 30 GeV
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
34.7 ± 1.4
31.2 ± 1.2
31.8 ± 1.4
25.9 ± 1.1
23.6 ± 1.2
23.3 ± 1.0
37.3 ± 1.7
33.5 ± 1.4
33.7 ± 1.6
28.2 ± 1.4
25.5 ± 1.3
24.7 ± 1.3
32.9 ± 1.1
30.0 ± 0.9
30.0 ± 1.1
24.5 ± 0.8
23.0 ± 0.7
22.6 ± 0.8
33.9 ± 1.1
30.5 ± 0.9
30.6 ± 1.0
24.0 ± 0.7
21.8 ± 0.6
21.7 ± 0.5
22.3 ± 1.1
23.4 ± 0.3
25.1 ± 1.7
23.5 ± 0.3
22.5 ± 1.1
20.6 ± 0.2
20.3 ± 1.7
20.0 ± 0.5
b-jet veto
3rd jet veto
b-jet tagged
3rd jet veto
25.2 ± 2.0
24.2 ± 0.5
24.2 ± 1.7
24.0 ± 0.4
22.8 ± 1.1
22.1 ± 0.3
21.8 ± 0.6
18.8 ± 0.1
Analysis
type
NSF+SF
only NSF
only SF
gg → bb̄H
gg → H
bb̄Z
Z/γ∗
qq̄ → W
W + jet
bb̄W
tt¯
resolved neutrinos
|sin(∆φℓℓ )| > 0.2
pmiss
> 30 GeV
T
cos(∆φℓℓ ) > −0.9
∆Rℓℓ < 2.8
0.00118
0.00085
0.000562
0.000394
0.00032
0.328
0.267
0.208
0.171
0.15
202
104
47
25.7
19.1
1.14·104
3.53·103
983
421
290
113
13.6
13.6
13.6
0
78.3
60.9
43.2
28.1
20.4
9.1
6.46
4.59
2.83
2.26
5.31·103
5.16·103
4.25·103
4.02·103
3.65·103
after generic selection
0.000159
0.075
9.43
144
0
13.7
1.45
1.89·103
b-jet veto
3rd jet veto
20 GeV < mℓℓ < 80 GeV
6.12·10−5
3.47·10−5
2.16·10−5
0.0699
0.0334
0.02
4.32
1.64
1.54
134
67.7
56.6
0
0
0
13.2
6.48
3.85
1.35
0.74
0.629
479
73.3
31.3
b-jet tagged
3rd jet veto
20 GeV < mℓℓ < 80 GeV
9.77·10−5
7.05·10−5
4.28·10−5
0.00513
0.00258
0.00149
5.11
2.2
1.95
10.7
6.82
5.87
0
0
0
0.498
0.392
0.0143
0.101
0.0398
0.0298
1.41·103
558
233
after generic selection
20 GeV < mℓℓ < 80 GeV
pmiss
> 50 GeV
T
0.000161
9.85·10−5
7.61·10−5
0.0755
0.0449
0.0391
9.64
8.82
5.05
145
124
45.9
0
0
0
6.73
4.58
3.86
0.803
0.382
0.115
1.76·103
661
582
b-jet veto
3rd jet veto
2.86·10−5
1.52·10−5
0.0364
0.0167
2.23
0.577
42.9
22.6
0
0
3.66
2.36
0.109
0.109
153
28.8
b-jet tagged
3rd jet veto
4.75·10−5
3.31·10−5
0.00274
0.00134
2.82
1.19
2.98
1.41
0
0
0.202
0.173
0.00535
0.00535
430
165
133
Selection
B.2. Acceptance and expected number of events for the mass point mH = 200 GeV
Table B-15: The expected number of signal and background events within mass window mH = 200 GeV ± 40 GeV for an integrated luminosity 10 f b−1 after
consecutive cuts in ℓℓE miss channel. Efficiencies for lepton and b-jet identification are included (90% and 50% respectively). Statistical errors are typically
T
at the level of 10%. Throughout the b-jet veto and b-jet tag analysis statistical errors for all backgrounds increase to 15%, while signal uncertainty stays at
the level of 10%. The background from W (qq̄ → W and W + jet) suffers a lack of statistics and at the level of generic selection the statistical errors are at the
level of 13% and they increase to 47% and more throughout the rest of the analysis. For tt¯ background in b-jet veto analysis numbers have 25% uncertainty.
134
Table B-16: The same as Table B-15, but for ℓ had E miss channel. Statistical errors are typically at the level of 10%. Throughout the b-jet veto and b-jet tag
T
analysis statistical errors for all backgrounds increase to 15%, while signal uncertainty stays at the level of 10%. For tt¯ background in b-jet veto analysis
numbers have 25% uncertainty.
Selection
gg → bb̄H
gg→ H
bb̄Z
Z/γ∗
qq̄ → W
W + jet
bb̄W
tt¯
resolved neutrino
|sin(∆φℓτ− jet )| > 0.2
mℓ,miss
< 50 GeV
T
pmiss
>
30 GeV
T
cos(∆φℓτ− jet ) > −0.9
∆Rℓτ− jet < 2.8
0.0016
0.00113
0.000941
0.000525
0.00035
0.000307
0.419
0.343
0.277
0.189
0.153
0.142
87.7
45.2
40.7
13.1
8.14
7.61
5.49·103
1.58·103
1.46·103
346
172
148
1.25·104
8.22·103
4.23·103
1.04·103
758
592
1.46·104
8.82·103
4.28·103
991
724
579
35.2
27.4
12
4.29
3.38
2.79
3.68·103
3.58·103
1.85·103
1.35·103
1.27·103
1.18·103
b-jet veto
3rd jet veto
0.000118
6.58·10−5
0.132
0.063
3.31
0.932
134.0
76.6
538.0
281
544.0
277
1.43
0.67
379.0
31.3
b-jet tagged
3rd jet veto
0.000189
0.000136
0.0106
0.00532
4.31
2.09
13.6
8.71
54.7
33.3
34.9
18.6
1.36
0.857
800.0
184.0
A B.
A C
C.1 List of abbreviations and names
AOD
- Analysis Object Data - data prepared for user analysis in ATLAS
ALICE
- A Large Ion Collider Experiment
ATLAS
- A Toroidal LHC ApparatuS (ATLAS)
Σ(η(φ)i ET )
barycenter
- mean value of η and/or φ, weighted with ET , calculated as: η(φ)barycenter = ΣET i
i
C++
- one of computer programming languages
CBNT
- ComBined NTuple - output data format of analysis tool
CDF
- Collider Detector at Fermilab, one of experiments placed at the Tevatron
CKM
- Cabibbo-Kobayashi-Maskawa
CLEO
- name of the experiment at Cornell Electron Storage Ring (CESR)
CMS
- Compact Muon Spectrometer
CSC
- Cathode Strip Chambers - part of the ATLAS muon system
DØ
- one of experiments placed at the Tevatron
DC1
- Data Challenge 1 of ATLAS Collaboration (summer 2002 - spring 2003)
DC2
- Data Challenge 2 of ATLAS Collaboration (summer 2004 - spring 2005)
DESY
- Deutsches Synchrotron
ESD
- Event Summary Data - output of ATLAS reconstruction
EventView
- ATLAS software helper tool in user analysis
FSR
- Final State Radiation
Gbps
- Gigabit per second - speed of the internet link, 1 bit is transferred in 1 ns
Geant
- also Geant4, toolkit for simulation the passage of particles through matter
had had ETmiss - final state of the Higgs boson decay into τ leptons pair with two τ-jet and the missing energy
HERA
- accelerator at Hamburg, Germany
ISR
- Initial State Radiation
LAr
- Liquid Argon - material used in calorimeters
LEP
- Large Electron and Positron collider at CERN
LHC
- Large Hadron Collider at CERN
LHCb
- Large Hadron Collider beauty experiment
miss
ℓ had ET
- final state of the Higgs boson decay into τ leptons pair with one lepton (e or µ),
τ-jet and the missing energy
miss
ℓℓET
- final state of the Higgs boson decay into τ leptons pair with two leptons (e, µ) and
the missing energy
LO
- Leading Order - calculations based on the tree level of QCD diagrams
LVL1
- first level of the trigger system
LVL2
- second level of the trigger system
136
LVL3
MDT
MSSM
NLO
NN
NNLO
NSF
PB
PDE-RS
QCD
RMS
RoI
RPC
SCT
SF
SM
SUSY
SVM
tau1P3P
tauRec
TDR
Tevatron
TGC
TOTEM
TR
TRT
VBF
VO
A C.
- third level of the trigger system
- Monitored Drift Tubes - part of the ATLAS muon system
- Minimal Supersymetric Standard Model
- Next to Leading Order - 1-loop corrections to QCD diagrams
- Neural Network
- Next to Next to Leading Order - 2-loop corrections to QCD diagrams
- Not Same Flavour (description of two leptons from Z/H decay:eµ)
- PetaByte - unit of information, equal to 106 GB
- Probability Density Estimation with Range Searching algorithm
- Quantum ChromoDynamics q
Pn
x2
i=1 i
- Root Mean Square, defined as
n , where xi are measured values for n entries
- Region of Interest
- Resistive Plate Chambers - part of the ATLAS muon system
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- Same Flavour (description of two leptons from Z/H decay: ee or µµ)
- Standard Model
- SUperSYmmetry
- Support Vector Machine
- track-based algorithm for hadronic τ reconstruction in ATLAS
- calorimeter-based algorithm for hadronic τ reconstruction in ATLAS
- Technical Design Report
- proton - antiproton collider at Fermilab
- Thin Gap Chambers - part of the ATLAS muon system
- Experiment at the LHC for the diffractive physics and the luminosity measurements
- Transition Radiation
- Transition Radiation Tracker
- Vector Boson Fussion - Higgs production from fussion of two Z 0 or pair W ±
- Virtual Organisation - collaboration of institutes in Grid environment
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