Jets

Jet Finding AlgorithmとJet Energy Calibrationの課題研究: 

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: 

内容 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 Jet Energy Correction LEP, HERA, Tevatron, LHC 纏め

１．TevatronとLHC: 

１．TevatronとLHC

Tevatron collider in Run II: 

The Tevatron is a proton-antiproton collider with 980 GeV/beam 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 Tevatron collider in Run II

Run II Data Taking Status: 

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: 

Tevatron Collaborations 19 countries 83 institutions, 664 physicists 12 countries, 62 institutions 767 physicist

The CDFII Detector: 

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

Slide8: 

All detectors inside the solenoid are new Others are from Run 1 with enhancements wire drift chamber (96 layers) TOF System A new 3d tracking system and vertex detector covering |η|out to 2.0. A new scintillating tile plug calorimeter covering |η| out to 3.6.

D0 : 

D0 Silicon Microstrip Tracker (SMT)

ATLAS (A Toroidal LHC ApparatuS): 

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): 

CMS (Compact Muon Solenoid) 4T solenoid Compact muon spectrometer EM calorimeter PbWO4 for Hgg

ABC at hadron collider: 

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)

Slide21: 

Troid + 2T solenoid 4T solenoid

Challenge for tracking: 

Challenge for tracking HZZ4m

Jet Energy Flow: 

Jet Energy Flow

Slide24: 

μのエネルギーロス　

b-tag: 

b-tag Vertex detector b-quarks have a long lifetime: t(b) ~ 1.5ps (ct~450mm) B-tagging using displaced vertices CDF RUN2a: b = 60% , c = 25%, j = 0.2% RUN2b: b = 70% , c = 10%, j = 0.02% Soft lepton tagging identifies lepton in semi-leptonic b(or c) decays leptons are softer less isolated than from W/Z decay. ATLAS: b = 60(50)% for low (high) lumi. c = 10%, j = 1%

２．Wボソン，トップクォークの質量測定: 

２．Wボソン，トップクォークの質量測定

MW measurement: 

MW measurement W transverse mass 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: 

MW measurement at RUN-I/LHC

Energy and momentum scale/resolution: 

Energy and momentum scale/resolution Ze+e-, Zm+m- , J/, (2s)

Recoil modelling: 

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): 

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: 

W production model pTW pTW is estimated from Z data error DMW=20 MeV dominated by Z statistics theoretical error (5 MeV)

Top production cross section: 

Top production cross section top factory tot=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

Slide36: 

PDF:　ｆi(x1),ｆi(x2) xi is momentum fraction of parton i. 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: 

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: 

Double b-tagged dilepton event @ CDF 69.7

First look at top mass in Run II: 

First look at top mass in Run II Mass in lepton+jets channel with a b-tagged jet Mass in dilepton channel CDF RunII preliminary, 108 pb-1 CDF RunII preliminary, 126 pb-1 6 events Data 22 evts

３．Jet Finding 　　Algorithm: 

３．Jet Finding 　　Algorithm

Jet Finding: 

Jet Finding Particle jet a spread of particles running roughly in the same direction as the parton after hadronization correct for finite energy resolution subtract underlying event add out of cone energy

Jet Algorithms: 

Jet Algorithms Fixed Cone (RunI) Iterative Fixed cone of radius R Overlapping cones: split/merge parameter Sensitivity to soft radiation kT (Ellis-Soper) Recombinant Distance parameter D Infrared and collinear safe in principle

kT Algorithm: 

kT Algorithm Ellis-Soper PRD48(1993) 3160 A cone jet is just the highest-ET stable cone… hep-ex/0005012 preclusters final jets

Jet Algorithms: kT: 

Jet Algorithms: kT 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 (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: 

Inclusive Jet Cross Section First analysis you do…count jets in pT bins Central region has large cross section, well-controlled systematic uncertainties

Results for kT and cone: 

Results for kT and cone Each distribution is compared to its own prediction Uncertainties highly- correlated from one bin to the next ® normalization not well-determined, but shape is Important deviation from cone and from predictions at low-pT D0

Jet Finding Algorithmの歴史: 

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: 

４．Jet Energy 　　 　　Correction

①　LEP: 

①　LEP

Energy Flow: 

Energy Flow Total energy in the Jets to improve the energy flow resolution, the neutral particle id such as (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). ETOT=pe+ p + pcharged hadron + E + Eneutral hadron [ tracks only] [calorimeter only]

E-flow algorithm: 

E-flow algorithm 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 - Good track resolution - Calorimeter segmentation is used to identify differents contribution: * Charged tracks & identified lepton * g ( and p0) * hadronic neutral * Residual from g, charged hadron M-N. Minard http://3w.hep.caltech.edu/calor02/

Jet reconstruction: 

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: 

②　HERA

H1/ZEUS Jet Algorithm: 

H1/ZEUS Jet Algorithm hep-ph/0211298

③　Tevatron: 

③　Tevatron

Jet Energy Correction: 

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: 

Physics effects & Detector response

Phycics effects: 

Phycics effects Natural W width Underlying event fluctuation Final State Radiation (FSR) Initial State gluon Radiation (ISR)

Slide75: 

"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: 

Energy Flowとγ＋Jetによる補正

Jet Energy Scale : 

Jet Energy Scale correct Jet Energy to the particle level Eoffset energy offset from underlying event, pile-up, noise determined from Min. Bias Events Rcalo calorimeter response using -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: +jet / Z+jet: 

Run II: +jet / Z+jet +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: 

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 (, ) wider b-jets (due to the large b-mass)

Z bb vs  + b-jet: 

Z bb vs  + b-jet high statistics, allows for a tight b-jet selection (b-tagging). expected number of tagged events: 1.2 M but: sensitive fractional imbalance I= (pT() - ET(jet))/ pT() Zbb:  + b-jet : 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: 

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  exces

④　LHC　ATLAS: 

④　LHC　ATLAS

ATLAS実験: 

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/

Slide84: 

pxmiss (pymiss) = (E1  u1 ) x(y) + (E2  u2 ) x(y) ETmiss critical for invariant  mass reconstruction : Assumptions : m = 0 the two neutrino system directions are coincident with the ones of the measured -decay products ( u1, u2 ) -decay products are not back to back E1,E2 = -decay products energies  = angle between -decay products directions E1, E2 = energies of the two neutrino systems : E1, E2 must be physical ( > 0 ) m =  2(E1+ E1 )(E2+ E2)(1 - cos)  (m)   (ETmiss) / |sin () prod1 prod2 | Z/A/H   1 2  prod1 1 prod2 2 prod1(2) = jet , lept D.Cavalli et al., Athens 2003

Slide85: 

DC1 data : bbA  , Z  No Noise added H1-Style calib in GOOD agreement with PHYS TDR !! ETmiss Resolution =  ( Ex(y)miss Rec ||< 5 - Ex(y)miss_NonInt ) SumET = ET calo cells within ||< 5 ETmiss Resolution = k   SumEt PHYS TDR Noise added : Ecell > 1.5 (Noise) Calibration : different sets of calibration constants for hadronic cluster cells, em cluster cells and cells outside clusters in different calorimeters D.Cavalli et al., Athens 2003

５．纏め: 

５．纏め

Slide87: 

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