Jet Finding Algorithmと
Jet Energy Calibration
の課題研究
田中 礼三郎 (岡山大学)
アトラス日本夏の学校＠CERN
２００３年８月２２日
内容
1.
2.
3.
TevatronとLHC
Wボソン，トップクォークの質量測定
Jet Finding Algorithm
Cone, kT algorithm
4.
Jet Energy Correction
LEP, HERA, Tevatron, LHC
5.
纏め
１．TevatronとLHC
Tevatron collider in Run II

The Tevatron is a protonantiproton collider with 980
GeV/beam
s  1.96TeV in RunII (1.8TeV RunI)

36 p and p bunches 396 ns
between bunch crossing

Increased from 6x6 bunches
with 3.5ms in Run I

Increased instantaneous
luminosity:


Run II goal 30 x 1031 cm–2 s-1
Current: 3～4.5 x 1031 cm–2 s-1
Run II Data Taking Status



Lint~300 pb-1 delivered by the Tevatron
Good quality data since Spring 2002
Data collection efficiency 85～90%
Next Year projection:
additional 310～380pb-1
delivered
Tevatron Collaborations
12 countries, 62 institutions
767 physicist
19 countries
83 institutions, 664 physicists
The
CDFII Detector
RETAINED FROM CDF in RUN I
Solenoidal magnet (1.4 Tesla)
Central calorimeters
Central muon detectors
NEW FOR CDF in RUN II
Tracking system
 Silicon vertex detector (SVXII)
 Intermediate silicon layers (ISL)
 Central outer tracker (COT)
Scintillating tile end plug calorimeter
Intermediate muon detectors
Scintillator time of flight system
Front-end electronics (132 ns)
Trigger system (pipelined)
DAQ system
All detectors inside the solenoid are new
Others are from Run 1 with enhancements
wire drift chamber (96 layers) m
TOF System
2.0
A new scintillating tile plug
calorimeter covering
|η| out to 3.6.
END PLUG HADRON CALORIMETER
•
END WALL
HADRON
CAL.
SOLENOID
1.5
1.0
END PLUG EM CALORIMETER
A new 3d tracking
system and vertex detector
covering |η|out to 2.0.
n = 1.0
COT
.5
30
n = 2.0
n = 3.0
3
0
0
0
.5
1.0
Inner silicon
6 layers
1.5
2.0
2.5
3.0
Intermediate silicon
1 or 2 layers
0
m
D0
Silicon Microstrip
Tracker (SMT)
ATLAS (A Toroidal LHC ApparatuS)

Liq.Ar EM calorimeter
good e/g id, energy, ETmiss

muon spectrometer
air-core troidal magnet
Bdl = 2~6Tm (4~8Tm)

inner tracking system
pixel, silicon strip, TRT
2T solenoid magnet
good e/g id, t/b-tag
ATLAS detector
tracker
|h| < 2.5
calorimeter |h| < 4.9
CMS (Compact Muon Solenoid)



4T solenoid
Compact muon spectrometer
EM calorimeter PbWO4 for Hgg
ABC at hadron collider



We never know total longitudinal momentum in any event.
Total transverse momentum of all particles is zero.
transverse momentum
pT = |p| sinq
transverse energy
ET = E sinq
pseudo-rapidity
h = -ln tan(q/2)
missing transverse energy ETmiss = En
Distance in pseudorapidity-azimuthal angle space
（used in jet cone algorithm)

DR=(D h)2 +(D)2
Existence of minimum bias events.
LHC: inelastic, non-diffractive cross section: s70mb
 23 pile up/crossing@1034
Tevatron RUN-II:  6 pile-up/crossing (Poisson)
Troid +
2T solenoid
4T solenoid
Challenge for tracking
HZZ4m
Jet Energy Flow
Particle
type
g
e
m
Jet
Et
miss
Tracking
ECAL
HCAL
Muon
μのエネルギーロス
b-tag

Vertex detector

Soft lepton tagging
b-quarks have a long lifetime:
t(b) ~ 1.5ps (ct~450mm)
B-tagging using displaced vertices
identifies lepton in semi-leptonic
b(or c) decays
leptons are softer less isolated than
from W/Z decay.
CDF RUN2a: b = 60% , c = 25%, j = 0.2%
ATLAS: b = 60(50)% for low (high) lumi.
RUN2b: b = 70% , c = 10%, j = 0.02%
c = 10%, j = 1%
２．Wボソン，トップ
クォークの質量測定
MW measurement
W transverse mass
mTW  2 pTl pTn (1  cos D )
l 
n
pT   | pT  u |
major uncertainty source

E, p scale & resolution
use Ze+e-/m+m-, , J/, (2s)

Recoil modelling
ISR(QCD), spectator quarks,min. bias
exploit similar production mechanism
for W and Z

pTW
use of lepton pseudorapidity
distributions in W and Z decays

PDF (parton distribution)
estimate from Z data
MW measurement at RUN-I/LHC
Energy and momentum scale/resolution
Ze+e-, Zm+m-
, J/, (2s)
Recoil modelling
neutrino  PT imbalance
recoil from



ISR(QCD)
spectator quarks
additional minimum bias
Exploit similar production
mechanism for W and Z.
Parton distribution functions (PDF)
x-region of W production
asymmetry u(x)>d(x) 
W+(W-) boosted along p(p-bar)
use of W charge asymmetry data
to constrain PDF
such an asymmetry does not
exist at LHC(pp) !
use of lepton pseudorapidity
distributions in W and Z decays
 constraint PDF to few %
DMW < 10 MeV
W production model pTW
pTW is estimated from Z data
 d 2s 
 W 
2
2
 d s 
d s
 dpT dy 




dpTW dy  dpTZ dy  data  d 2s 
 Z 
 dpT dy theory
error DMW=20 MeV
 dominated by Z statistics
 theoretical error (5 MeV)
Top production cross section
top factory
s  2TeV s NLO  7 pb
s  14TeV s NLO  800pb


stot=70mb for LHC
109 interactions/sec@1034cm2s-1
Interesting physics
W production: ~2kHz
Top production: 10Hz
Higgs production: 0.1(0.01)Hz
for MH=100(500) GeV
s ( s)  
ij
1
 dx dx
0
1
^
^
f ( x1 ) f i ( x2 ) s ij ( s, mt )
2 i
PDF: ｆi(x1),ｆi(x2)
xi is momentum fraction of
parton i. ^
s  x1 x2 s

Tevatron
qq(90%), gg(10%) RUN-I
qq(85%), gg(15%) RUN-II

LHC
qq( 5%), gg(95%)
enhanced gluon structure
function.
LO
CDF実験 RUN1 トップクォーク質量
最大の系統誤差は，
Jet Energy Calibration
→LHCでも同じ。
Top, Higgs, SUSY…
PRD63(2001)032003
Double b-tagged
dilepton event @ CDF
69.7
First look at top mass in Run II
CDF RunII preliminary, 108 pb-1
CDF RunII preliminary, 126 pb-1
Data 22 evts
6 events
Mass in lepton+jets channel
with a b-tagged jet
2
177.5 12.7
(stat)

7.1(syst)
GeV/c
9.4
Mass in dilepton channel
2
175.0 17.4
(stat)

7.9(syst)
GeV/c
16.9
３．Jet Finding
Algorithm
Jet Finding
 Calorimeter
jet (cone)
jet is a collection of energy deposits with a
given cone R: R  Δ 2  Δη2
 cone direction maximizes the total ET of the jet
 various clustering algorithms

 correct for finite energy resolution
 subtract underlying event
 add out of cone energy
 Particle jet
a spread of particles running roughly in the
same direction as the parton after hadronization

Jet Algorithms
Fixed Cone (RunI)
kT (Ellis-Soper)
• Iterative
• Recombinant
• Fixed cone of radius R
• Distance parameter D
• Overlapping cones:
split/merge parameter
• Sensitivity to soft
radiation
• Infrared and collinear
safe in principle
kT Algorithm
d ij  min( PT2,i , PT2, j )
Ellis-Soper PRD48(1993) 3160
DRij2
D2
preclusters
KT jet
Cone jet
A cone jet is just the
highest-ET stable cone…
final jets
hep-ex/0005012
Jet Algorithms: kT
For each object and pair of objects:
dii  k 2T,i
order all dii and dij:
If dmin=dij
2
ΔR
ij
dij  min(k 2T,i ,k 2T, j ) 2
D
Soft
Collinear
 merge particles
(if DR<<1 )
Resolution
parameter
(D=1)
 theoretically favored, no split-merge
 to reduce computation time, start
with 0.2 x 0.2 pre-clusters
 x-section measurement differ from
cone-jet
If dmin=dii
 jet
(JETRAD)
DØ
Subjet multiplicity of gluon and quark jets reconstructed using the kT algorithm in pbarp collisions
Phys. Rev. D65 052008 (2002) hep-ex/0108054
The inclusive jet cross section in pbarp collisions at sqrt(s)=1.8 TeV using the kT algorithm
Phys. Lett. B {525}, 211 (2002) hep-ex/0109041
Inclusive Jet Cross Section


First analysis you do…count jets in pT bins
Central region has large cross section, well-controlled
systematic uncertainties
d s
N

 Csmear
dET dh   L  DpT  Dh
2
versus
pT
Results for kT and cone
D0
Each distribution is
compared to its
own prediction
Uncertainties highlycorrelated from
one bin to the next
 normalization not well-determined, but shape is
Important deviation from cone and from predictions at low-pT
Jet Finding Algorithmの歴史

UA2: fixed size cones, R=1.3
± 30 % cross section uncertainty

TeVatron Run 1: cones R=0.7, merge/split
factor of 2 or more improvement in precision

End of Run 1: DØ looks at kT algorithm, similar
to ones used by HERA experiments

CDF/DØ attempt to improve both algorithms and
achieve consistency
４．Jet Energy
Correction
① LEP
Energy Flow
Total energy
in the Jets



ETOT=pe+ pm + pcharged hadron + Eg + Eneutral hadron
[ tracks only]
[calorimeter only]
to improve the energy flow
resolution, the neutral particle
id such as g(0), neutron, K0L is
most important,
this is achieved with fine
granular and hermetic
calorimeter design.
e/ ratio can be corrected to
unity with software correction
(i.e. don't need to construct
Scinti:Pb=1:4 calorimetre for
hardware compensation).
s Energy Flow  0.59 E (GeV )
(1.2 E (GeV )
if ETOT  EECAL  EHCAL )
E-flow algorithm
M-N. Minard
http://3w.hep.caltech.edu/calor02/
- Good track resolution
- Calorimeter segmentation is used
to identify differents contribution:
* Charged tracks & identified lepton
* g ( and 0)
* hadronic neutral
* Residual from g, charged hadron
Energy resolution from Z->qqg events
s(E)/E = (0.59+-0.03)/E + (0.6+-0.3) GeV
Expected resolution at high energy is derived
Jet reconstruction
Algorithm used Durham:
- E-flow object with
yij = 2 min(Ei2,Ej2)(1-cosqij)/Ecm2 < ycut
associated in the same jet
- WW-> q1q2q ’1q ’2 forced into 4 jets
Jet performances studied from Z data
- Energy response and resolution
d(Ejet)/Ejet = 0.67/Ejet
(10% at 45 GeV- perfect detector:6-7%)
- Angular resolution
0.9° with Eflow
charged track only : 1.6°, calorimeters : 1.4°
② HERA
H1/ZEUS Jet Algorithm
hep-ph/0211298
③ Tevatron
Jet Energy Correction

Relative correction
 検出器の相対的な補正

Absolute correction
 検出器の絶対的な補正

Underlying event subtraction
 ミニマムバイアス，マルチプル散乱

Out-of-cone addition
 コーン外側のエネルギー補正
Physics effects & Detector response
Phycics effects




Natural W width
Underlying event
fluctuation
Final State Radiation
(FSR)
Initial State gluon
Radiation (ISR)
"Halloween" Photon + Jet Event (seen October 24,1994)
This event has a 311 GeV photon opposite a 295 GeV jet.
The photon + jet mass is at least 0.76 TeV, not bad for a 1.8 TeV
pbar-p collision!
Energy Flowとγ＋Jetによる補正
Jet Energy Scale
jet
g
 correct Jet Energy to the particle level
ptcl
E jet

E meas
jet  E offset
shower
R calo
R
jet
jet
 Eoffset energy offset from underlying event,
pile-up, noise
determined from Min. Bias Events
 Rcalo calorimeter response
using g-jet events: Missing ET
Projection Fraction Method
 Rshower energy contained in jet
corrections from MC - energy in
cones around the jet axis
 depending on jet algorithm!
Determination of the Absolute Jet Energy Scale in the D0
Calorimeters. NIM A424, 352 (1999), hep-ex/9805009
Run II: g+jet / Z+jet
g/Z+jet
QCD (udsg)
signal:152 M evts
bkgd: 47.1 M evts
signal: 64.8k evts
bkgd: 650 evts
QCD (cbt)
W+jet, Z+X,
nn
• g+jet: Run I method – jet calibration possible up to 250 GeV
• Z+jet: lower statistics, but clean sample, useful at low energies, x-check!
b-jet calibration
 naïve reconstruction
of Z-mass shows a
lower mass for selected
b-jets than light quark
jets.
 energy losses from
semi-leptonic b decays
(n, m)
 wider b-jets (due to
the large b-mass)
Z  bb
peak: 82.6
Z  qq
peak: 86.8
Z bb vs g + b-jet
g + b-jet :
Zbb:
 high statistics, allows for a tight b-jet selection (btagging).
 expected number of tagged events: 1.2 M
but: sensitive fractional imbalance I= (pT(g) - ET(jet))/ pT(g)
 systematics closer to physics processes (H or
Top) at high pT
 resonance mass independent of
multiple interactions.
 but: signal/noise~10-3 requires special trigger
(Silicon Track Trigger – operational end 2002)
CDF Run 1: Z bb Signal
 after cuts:
S/N=1/6 at the Z
mass peak
 select/antiselect
w.r.t. the 2
variables to
determine the
tagging probability
 3.2 s exces
④ LHC ATLAS
ATLAS実験
Jet / ET miss / Tau Combined Performance WG
Martine Bosman，Donatella Cavalli，Frank Paigeら。

Cone and KT jet algorithms がAthenaに入っている。

JetRec, TauRec, EmisRec and EflowRec in Athena。
H1の較正方法を採用している。
検出器のノイズやpile-upの効果の研究がなされている。
SUSYグループと協力。



Calibration Workshop at Ringberg Castle (Germany) 21-24th July
http://wwwatlas.mppmu.mpg.de/ringberg2002/
D.Cavalli et al., Athens 2003
ETmiss critical for invariant tt mass reconstruction :
Z/A/H   t1 t2  prod1 n1 prod2 n2

prod1(2) = jet , lept
Assumptions :
 mt = 0
 the two neutrino system directions are coincident with the ones
of the measured t-decay products ( u1, u2 )

t-decay products are not back to back
mtt =  2(E1+ En1 )(E2+ En2)(1 - cosq)

E1,E2 = t-decay products energies

q = angle between t-decay products directions

En1, En2 = energies of the two neutrino systems :
pxmiss (pymiss) = (En1  u1 ) x(y) + (En2  u2 ) x(y)

En1, En2 must be physical ( > 0 )
s (mtt)  s (ETmiss) / |sin (D) prod1 prod2 |
DC1 data : bbA tt , Z tt
No Noise added
D.Cavalli et al., Athens 2003
PHYS TDR
Noise added :
Ecell > 1.5 s(Noise)
Calibration :
different sets of
calibration constants
for hadronic cluster
cells, em cluster cells
and cells outside clusters
in different calorimeters
H1-Style calib in
GOOD agreement
with PHYS TDR !!
ETmiss Resolution = s ( Ex(y)miss Rec |h|< 5 - Ex(y)miss_NonInt )
SumET
= ET calo cells within |h|< 5
ETmiss Resolution = k   SumEt
５．纏め



LHCにおいても，Jet Energy Calibrationはとても重要。
Jet Finding algorithm – cone, kTなど。
実際のデータを用いて較正する。実験屋のアイデア次第。
 J/ΨやΥデータ，γ＋Jets，W/Z＋Jets，Z→bb

ATLAS測定器はfine granularである。
 Energy
Flowの研究をしてはどうか？
おわり