Comparison of τ τ Mass Reconstruction
Methods
DPG Tagung 2012
Despoina Evangelakou
in consultation with Ulla Blumenschein, A. Quadt
II. Physikalisches Institut, Georg-August-Universität Göttingen
1. März 2012
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Motivation for Z → τ τ study
• τ τ channel very important for SM/MSSM Higgs discovery
• VBF τ τ : study Higgs couplings
• Z → τ τ is irreducible BG for Higgs@120 GeV ⇒ perfect for understanding mass
reconstruction techniques
• updated cross section measurement with 1.3fb−1 (el) and 1.5fb−1 (mu)1
(a) Higgs decay channels
(b) H → τ τ decay
1
ATLAS-COM-CONF-2012-001
(c) H/Z discrimination (ATLASCONF-2011-132)
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ATLAS Detector
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Z → τ τ Selection
• e/µ: pT > 17. GeV, |η| < 2.47
• τ : pT > 25.(20.) GeV, |η| < 2.47, BDT medium (45%
signal efficiency)
• Trigger e: tau16_loose_e15_medium , µ: mu15i,
mu15i_medium
• lepton isolation in a small (ET or pT ) cone around
the lepton (reject QCD)
• dilepton veto (against Zleplep bg)
• opposite sign between τ -jet and lepton (OS) (against
QCD)
(d) τ
modes
decay
• sum cos dphia > −0.15 + trans massb < 50. GeV
(against W+jets bg)
• τ nr of tracks 1||3 + charge ±1 (against Zleplep fakes
and QCD)
• MET > 20.GeV (ensure MET well-measured)
• reconstruct inv mass
aP
b
(e) τ jet
cos ∆φ = cos(φr
lep − φM ET ) + cos(φhad − φM ET )
“
”
miss · 1 − cos ∆φ(`, E miss )
2 pT (`) · ET
T
miss
mT (`, ET
)=
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diTau mass (mτ τ )
1 visible mass
2 collinear approximation
3 effective mass
4 Missing Mass Calculator (MMC)
5 mass bound
6 mTrue (transverse mass)
7 mass bound or mTrue
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Effective mass
effective mass
p
f
mef
(pvis1 + pvis2 + pM ET )2 , where pM ET = (ETmiss , Exmiss , Eymiss , 0)
ττ =
+ simple full τ mass reconstruction
+ only experiment-related systematics
- very general (can be used in any decay
with 2 vis daughters and MET)
⇒ not tau-system adapted
- doesn’t reconstruct the correct mass
- very broad distribution ⇒ difficult to
separate H/Z
MC signal
Data - BG
mean [GeV]
91.65 ± 0.47
89.66 ± 0.87
width [GeV]
14.13 ± 0.27
13.84 ± 0.61
6 / 43
Collinear Approximation
Collinear Approximation
• assumption 1: H/Z boosted ⇒ τ decay products produced collinearly to taus
• assumption 2: that MET is only coming from ντ
xi =
piT
,
piT +pmis
T
i=visible products
• condition/limitation: no back-to-back decays are allowed (| cos(δφ)| < 0.95)
⇒ mτ τ =
m
√ vis1vis2 ,
xvis1 ∗xvis2
+ good invariant mass
reconstruction
- long tail ⇒ difficult to
separate H/Z
- ∼ 50% of signal events lost
(back-to-back condition)
MC signal
Data - BG
mean [GeV]
94.70 ± 1.07
93.54 ± 1.61
width [GeV]
13.71 ± 0.57
12.58 ± 0.94
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MMC2
Missing Mass Calculator (MMC)
• inv mass of vis+invisible decay products
• best mτ τ per event is weighed by a pdf(∆θ(ν, τ ), tau decay type)a
a
∆θ is the angle between the visible and invisible τ -decay products
+ reconstruction efficiency 90-95%
+ ETmiss resolution taken into account
+ resulting Z peak width ∼ 14%
- slow turn over of results
2
http://arxiv.org/abs/1012.4686
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mBound3
mBound
• inv mass of vis+invisible decay products
• trans mass of τ -decay products < mτ : a desciminator to get the best mτ τ estimate
per event
+ method built to separate H/Z
+ high S/B ratio
+ tau-specific
- large tails at the experimentally not
excluded mH
- method’s condition ⇒ low acceptance
(40-55 % depending on the channel)
MC signal
Data - BG
3
mean [GeV]
88.67 ± 0.70
87.28 ± 1.57
width [GeV]
13.73 ± 0.45
15.92 ± 1.24
http://arxiv.org/abs/1106.2322
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mTrue
mTrue
• trans mass of visible + invisible τ -decay products when the parent is produced
on-shell
+ 100% acceptance
+ narrow distribution
+ steep drop at the experimentally not
excluded mH
- mTrue not tau-system specific method
MC signal
Data - BG
mean [GeV]
83.57 ± 0.25
82.74 ± 0.60
width [GeV]
12.74 ± 0.19
13.30 ± 0.45
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mass bound + mTrue
mBound or mTrue
• use: mBound or mTrue (use mBound and mTrue only when 1st fails)
⇒ make use of tau-system info
⇒ use mTrue when that fails (method constraints)
+ 100% acceptance
- inherits tails from mBound but not
large
MC signal
Data - BG
mean [GeV]
86.32 ± 0.29
86.16 ± 0.67
width [GeV]
12.76 ± 0.21
13.46 ± 0.54
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Summary
MC signal
mef f
mcoll
mbound
mtrue
mcomb
mean [GeV]
91.6
94.7
88.7
83.6
86.3
width [GeV]
14.13
13.71
13.73
12.74
12.76
Data - BG
mef f
mcoll
mbound
mtrue
mcomb
mean [GeV]
89.7
93.5
87.3
82.7
86.3
width [GeV]
13.84
12.58
15.92
13.30
13.46
• use clean and well understood selection from Z → τ τ cross section measurement to
evaluate mass reconstruction methods for diTau events
effective mass
collinear approximation
missing mass calculator
bound mass
true mass
bound or true mass (m-comb)
• best performing mBound combined with mTrue
⇒ fast
⇒ good mass reconstruction
⇒ no large tails
⇒ systematics only shape related and no method related (MMC: JER/METres)
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BackUp
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Mass Methods In More Details
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MMC (1)
A. Elagin, P. Murat, A. Pranko, A. Safonov
http://arxiv.org/abs/1012.4686
miss
Ex
= pmis1 sin θmis1 cos φmis1 + pmis2 sin θmis2 cos φmis2
miss
= pmis1 sin θmis1 sin φmis1 + pmis2 sin θmis2 sin φmis2
q
q
2
2
2
2
2
p2
Mτ = mmis + mvis + 2 p2
vis + mvis
mis + mmis −
•
Ey
1
1
2
2
Mτ
1
2
= mvis
2
1
+2
q
p2
vis
2
1
1
1
−2pvis1 pmis1 cos ∆θvm1
q
2
p2
+ m2
mis + mmis −
vis
2
2
•
pmiss mom, mmiss mass, θmiss
polar angle, φmiss azimuthal angle
miss
of ET
are unknown
∆θ(ν, τvis ) is small but not zero,
depends only on τ decay mode
(lep,1-,or 3-prong jet) and pτ
2
−2pvis2 pmis2 cos ∆θvm2
• more unknowns than equations, but for each (∆φ1 , ∆φ2 ) pair (grid), we can
•
•
•
solve the equations exactly (∆φ the azimuth. difference btwn vis. and invis.
decay products)
get a probability density function for each ∆θ point on the grid
(Pi (∆θ, τ decay type))
mτ τ reconstructed for every point on the grid is weighted by Pτ1 ∗ Pτ2
take most probable mτ τ solution as the final estimator
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MMC (2)
A. Elagin, P. Murat, A. Pranko, A. Safonov, D. Varouhas
http://arxiv.org/abs/1012.4686,
ATLAS-CONF-2011-132
mτ τ : best solution for 1 event
mτ τ : all events (H/Z)
mτ τ : all events
(lephad/hadhad)
16 / 43
H/Z mass bound (1)
A. Barr, S.T. French, J. A.Frost, C.G. Lester
http://arxiv.org/abs/1106.2322,
http://xxx.soton.ac.uk/abs/1105.2977
bound
mτ τ
where
H
µ
=
µ
min
q
µ
µ
Q1 ,Q2 |ℵ
µ
H µ Hµ
µ
(1)
Q1 Q1µ = 0
µ
Q2 Q2µ = 0
µ
µ
= P1 + Q1 + P2 + Q2
µ
(P1
µ
(P2
+
+
µ
Q1 )(P1µ
µ
Q2 )(P2µ
2
+ Q1µ ) = mτ
+ Q2µ ) =
2
mτ
• try to minimise the 4-mom vector of all decay products (visible and invisible)
• take advantage of the topology of the event
mνs = 0, mτ = 1.77 GeV
4-mom of τ, pT (νs) from experiment
require mT 2 (pvis1 , pvis2 , pM ET ) < mτ (tau produced on-shell)
• take the maximal lower bound for the mass of mother particle
• the latter is used as a discriminant to get the best mτ τ
17 / 43
H/Z mass bound (2)
A. Barr, S.T. French, J. A.Frost, C.G. Lester
http://arxiv.org/abs/1106.2322,
http://xxx.soton.ac.uk/abs/1105.2977
• Plot at truth level for 1 event
• clear cut at the Higgs mass
• Plot with detector effects accounted for
+ good discriminator
+ good separation btwn H and Z
18 / 43
mTrue
A. Barr, S.T. French, J. A.Frost, C.G. Lester
http://xxx.soton.ac.uk/abs/1105.2977,
http://arxiv.org/abs/1106.2322
2
(mtrue
T )
=
q
m2vis1vis2 + 2 (pmiss (m2vis1vis2 + p
~T,vis1vis2 ) − p
~miss · p
~T,vis1vis2 )
q
( (m2vis1vis2 + p
~T,vis1vis2 ) + pmiss )2 − (~
pT,vis1vis2 + p
~T,vis1vis2 )2
=
m2τ τ .
=
19 / 43
Extras
20 / 43
Systematic Uncertainties
Systematic uncertainty
lepton SF
muon resolution
electron resolution
LAr hole
τ id efficiency
electron-tau jet rate
e, τ , jet and ETmiss energy scale
tau trigger
kW
kZ
QCD estimation
MC normalisations
AZ uncertainties
Total systematic unc.
Statistical uncertainty
δσ/σ (%) τµ τh
1.7
< 0.05
5.2
8.2
< 0.05
< 0.05
0.4
0.1
3.1
9.6
1.1
δσ/σ (%) τe τh
5.0
0.1
0.1
5.2
0.2
9.3
4.7
0.04
< 0.05
0.8
0.2
3.4
12.6
1.5
21 / 43
MMC systematics
Figure: Effect of JER on signal MC
Figure: Effect of MET resolution on
signal MC
22 / 43
Fit Plots (τ - e)
23 / 43
Gaussian Fit Masses - mef f
(a) MC Signal
MC signal
Data - BG
mean [GeV]
91.65 ± 0.47
89.66 ± 0.87
(b) Data - BG
width [GeV]
14.13 ± 0.27
13.84 ± 0.61
24 / 43
Gaussian Fit Masses - mcoll
(c) MC Signal
MC signal
Data - BG
mean [GeV]
94.70 ± 1.07
93.54 ± 1.61
(d) Data - BG
width [GeV]
13.71 ± 0.57
12.58 ± 0.94
25 / 43
Gaussian Fit Masses - mbound
(e) MC Signal
MC signal
Data - BG
mean [GeV]
88.67 ± 0.70
87.28 ± 1.57
(f) Data - BG
width [GeV]
13.73 ± 0.45
15.92 ± 1.24
26 / 43
Gaussian Fit Masses - mtrue
(g) MC Signal
MC signal
Data - BG
mean [GeV]
83.57 ± 0.25
82.74 ± 0.60
(h) Data - BG
width [GeV]
12.74 ± 0.19
13.30 ± 0.45
27 / 43
mtrue
(i) MC Signal
MC signal
Data - BG
mean [GeV]
86.32 ± 0.29
86.16 ± 0.67
(j) Data - BG
width [GeV]
12.76 ± 0.21
13.46 ± 0.54
28 / 43
sum cos dphi - cut sketch
29 / 43
Mass Plots (τ − µ )
30 / 43
Effective mass
effective mass
p
f
mef
(pvis1 + pvis2 + pM ET )2 , where pM ET = (ETmiss , Exmiss , Eymiss , 0)
ττ =
+ simple full τ mass reconstruction
+ only experiment-related systematics
- very general (can be used in any decay
with 2 vis daughters and MET)
⇒ not tau-system adapted
- doesn’t reconstruct the correct mass
- very broad distribution ⇒ difficult to
separate H/Z
MC signal
Data - BG
mean [GeV]
92.37 ± 0.49
91.91 ± 0.92
width [GeV]
14.81 ± 0.33
14.68 ± 0.67
31 / 43
Collinear Approximation
Collinear Approximation
• assumption 1: H/Z boosted ⇒ τ decay products produced collinearly to taus
• assumption 2: that MET is only coming from ντ
xi =
piT
,
piT +pmis
T
i=visible products
• condition/limitation: no back-to-back(b2b) decays are allowed (| cos(δφ)| < 0.95)
⇒ mτ τ =
m
√ vis1vis2 ,
xvis1 ∗xvis2
+ good invariant mass
reconstruction
- long tail ⇒ difficult to
separate H/Z
- ∼ 50% of signal events lost
(b2b condition)
MC signal
Data - BG
mean [GeV]
91.50 ± 0.72
93.15 ± 1.84
width [GeV]
13.02 ± 0.58
14.90 ± 1.32
32 / 43
MMC4
Missing Mass Calculator (MMC)
• inv mass of vis+invisible decay products
• best mτ τ per event is weighed by a pdf(∆θ(ν, τ ), tau decay type)a
a
∆θ is the angle between the visible and invisible τ -decay products
+ reconstruction efficiency 90-95%
+ ETmiss resolution taken into account
+ resulting H/Z peak resolution ∼ 18%
- slow turn over of results
MC signal
Data - BG
4
mean [GeV]
92.60 ± 0.45
93.11 ± 0.85
width [GeV]
14.60 ± 0.32
14.37 ± 0.66
http://arxiv.org/abs/1012.4686
33 / 43
mBound5
mBound
• inv mass of vis+invisible decay products
• trans mass of τ -decay products < mτ : a desciminator to get the best mτ τ estimate
per event
+ method built to separate H/Z
+ high S/B ratio
+ tau-specific
- large tails @ mH
- method’s condition ⇒ low acceptance
(40-55 % depending on the channel)
MC signal
Data - BG
5
mean [GeV]
88.26 ± 0.62
88.48 ± 0.98
width [GeV]
13.47 ± 0.40
13.93 ± 0.78
http://arxiv.org/abs/1106.2322
34 / 43
mTrue
mTrue
• trans mass of visible + invisible τ -decay products when the parent is produced
on-shell
+ 100% acceptance
+ narrow distribution
+ steep drop @ mH
- mTrue not tau-system specific method
MC signal
Data - BG
mean [GeV]
84.59 ± 0.23
84.28 ± 0.44
width [GeV]
9.82 ± 0.10
10.76 ± 0.29
35 / 43
mass bound + mTrue
mBound or mTrue
• use: mBound or mTrue (use mBound and mTrue only when 1st fails)
⇒ make use of tau-system info
⇒ use mTrue when that fails (method constraints)
+ 100% acceptance
- inherits tails from mBound but not
large
MC signal
Data - BG
mean [GeV]
85.93 ± 0.30
85.97 ± 0.57
width [GeV]
11.73 ± 0.18
12.12 ± 0.43
36 / 43
Fit Plots (τ − µ)
37 / 43
Gaussian Fit Masses - mef f
(k) MC Signal
MC signal
Data - BG
mean [GeV]
92.37 ± 0.49
91.91 ± 0.92
(l) Data - BG
width [GeV]
14.81 ± 0.33
14.68 ± 0.67
38 / 43
Gaussian Fit Masses - mcoll
(m) MC Signal
MC signal
Data - BG
mean [GeV]
91.50 ± 0.72
93.15 ± 1.84
(n) Data - BG
width [GeV]
13.02 ± 0.58
14.90 ± 1.32
39 / 43
Gaussian Fit Masses - mM M C
(o) MC Signal
MC signal
Data - BG
mean [GeV]
92.60 ± 0.45
93.11 ± 0.85
(p) Data - BG
width [GeV]
14.60 ± 0.32
14.37 ± 0.66
40 / 43
Gaussian Fit Masses - mbound
(q) MC Signal
MC signal
Data - BG
mean [GeV]
88.26 ± 0.62
88.48 ± 0.98
(r) Data - BG
width [GeV]
13.47 ± 0.40
13.93 ± 0.78
41 / 43
Gaussian Fit Masses - mtrue
(s) MC Signal
MC signal
Data - BG
mean [GeV]
84.59 ± 0.23
84.28 ± 0.44
(t) Data - BG
width [GeV]
9.82 ± 0.10
10.76 ± 0.29
42 / 43
mtrue
(u) MC Signal
MC signal
Data - BG
mean [GeV]
85.93 ± 0.30
85.97 ± 0.57
(v) Data - BG
width [GeV]
11.73 ± 0.18
12.12 ± 0.43
43 / 43