Experimental aspects of top quark physics Lecture #2 Regina Demina University of Rochester Topical Seminar on Frontier of Particle Physics Beijing, China 08/15/05

Regina Demina, Lecture #22Outline Invariant mass Template method to measure top mass Matrix element method –Jet energy scale calibration on W-boson Combined result –Constraint on Higgs mass Control questions

08/15/05Regina Demina, Lecture #23 Invariant mass Top quark decays so fast there is no time to put it on a bathroom scale We measure its mass through energy and momentum of its products: t  bW, W  qq’ E(t)=E(b)+E(q)+E(q’) P(t)=P(b)+p(q)+p(q’) M 2 (t) = E 2 (t)-p 2 (t) M, E, p in GeV

08/15/05Regina Demina, Lecture #24 Challenges of M top Measurement Lepton+Jets Channel Observed Final state Complicated final state to reconstruct M top  Leading 4 jets combinations 12 possible jet-parton assignments 6 with 1 b-tag (b-tag helps) 2 with 2 b-tags  Poor jet energy scale and resolution Hard to find the correct combination Good b-tagging and jet energy scale and resolution and good algorithm to reconstruct M top

08/15/05Regina Demina, Lecture #25 Wbb MC Data tt MC Datasets Result Likelihood fit: Best signal + bkgd templates to fit data with constraint on background normalization Likelihood fit Mass fitter Signals/background templates Data  2 mass fitter: Finds top mass that fits event best One number per event Additional selection cut on resulting  2 Template method

08/15/05Regina Demina, Lecture #26 1.Try all jet-parton assignments with kinematic constraints, but assign b-tagged jets to b-partons 2.Select the rec. mass Mt from the choice of lowest  2 3.Badly reconstructed Mt (  2 > 9 ) is removed Top mass is free parameter All jets are allowed to be float according to their resolutions to satisfy that M(W+)=M(W-)=80.4 GeV, M(t)=M(t) Mass Fitter (event by event)

08/15/05Regina Demina, Lecture #27 More correct combination with b-tag M t (GeV/c 2 ) Bkgd is large in the 0-tag Templates for different number of tags

08/15/05Regina Demina, Lecture #28  Samples: Herwig with Mtop = [130 to 230] GeV  Get analytical functions (2 Gaussian + gamma) of reconstructed mass, M t as a function of true mass, M top  Fit parameters: linear depend. on M top Smooth PDFs (M t | true Mtop) M t (GeV/c 2 ) Signal templates for different masses

08/15/05Regina Demina, Lecture #29 Comb. –Log Likelihood Expected error Result on Mtop

08/15/05Regina Demina, Lecture #210 Top mass using matrix element method in Run I Method developed by DØ (F. Canelli, J. Estrada, G. Gutierrez) in Run I Systematic error dominated by JES 3.3 GeV/c 2 With more statistics it is possible to use additional constraint on JES based on hadronic W mass in top events – in situ calibration Single most precise measurement of top mass in Run I M t =180.1±3.6(stat) ±4.0(syst) GeV/c 2

08/15/05Regina Demina, Lecture #211 Matrix element method Goal: measure top quark mass Observables: measured momenta of jets and leptons Question: for an observed set of kinematic variables x what is the most probable top mass Method: start with an observed set of events of given kinematics and find maximum of the likelihood, which provides the best measurement of top quark mass Our sample is a mixture of signal and background

08/15/05Regina Demina, Lecture #212 Matrix Element Method Normalization depends on m t Includes acceptance effects probability to observe a set of kinematic variables x for a given top mass Integrate over unknown q 1,q 2, y f(q) is the probability distribution than a parton will have a momentum q d n σ is the differential cross section Contains matrix element squared t t W(x,y) is the probability that a parton level set of variables y will be measured as a set of variables x b q’ q

08/15/05Regina Demina, Lecture #213 Transfer functions (parton  jet) Partons (quarks produced as a result of hard collision) realize themselves as jets seen by detectors –Due to strong interaction partons turn into parton jets –Each quark hardonizes into particles (mostly  and K’s) –Energy of these particles is absorbed by calorimeter –Clustered into calorimeter jet using cone algorithm Jet energy is not exactly equal to parton energy –Particles can get out of cone –Some energy due to underlying event (and detector noise) can get added –Detector response has its resolution Transfer functions W(x,y) are used to relate parton energy y to observed jet energy x

08/15/05Regina Demina, Lecture #214 Top ID in “lepton+jets” channel 2 b-jets Lepton: electron or muon Neutrino (from energy imbalance) 2 q’s – transform to jets of particles Note that these two jets come from a decay of a particle with well measured mass – W-boson – built-in thermometer for jet energies

08/15/05Regina Demina, Lecture #215 All jets are corrected by standard DØ Jet energy scale (p T,  ) Overall JES is a free parameter in the fit – it is constrained in situ by mass of W decaying hadronically JES enters into transfer functions: JES in Matrix Element

08/15/05Regina Demina, Lecture #216 Signal Integration Set of observables – momenta of jets and leptons: x Integrate over unknown –Kinematic variables of initial (q 1,q 2 ) and final state partons (y: 6 x3 p) = 20 variables –Integral contains 15 (14)  -functions for e(  )+jets total energy-momentum conservation: 4 angles are considered to be measured perfectly: 2x4 jet +2 lepton Electron momentum is also considered perfectly measured, not true for muon momentum: 1(0) –5(6) dimensional integration is carried out by Vegas –The correspondence between parton level variables and jets is established by transfer functions W(x,y) derived on MC for light jets (from hadronic W decay) for b-jets with b-hadron decaying semi-muonically for other b-jets Approximations –LO matrix element –qq  tt process only (no gluon fusion – 15%)

08/15/05Regina Demina, Lecture #217 Background integration W+jets is the dominant background process Kinematics of W+jets is used as a representation for overall background (admixture of multijet background is a source of systematic uncertainty) –Contribution of a large number of diagrams makes analytical calculation prohibitively complex –Use Vecbos Evaluate ME wjjjj in N points selected according to the transfer functions over phase space P bkg - average over points

08/15/05Regina Demina, Lecture #218 Sample composition Lepton+jets sample –Isolated e (P T >20GeV/c, |  |<1.1) –Isolated  (P T >20GeV/c, |  |<2.0) –Missing E T >20 GeV –Exactly four jets P T >20GeV/c, |  |<2.5 (jet energies corrected to particle level) Use “low-bias” discriminant to fit sample composition –Used for ensemble testing and normalization of the background probability. –Final fraction of ttbar events is fit together with mass e+jets  +jets # of events7080 Signal fraction45±12%29±10%

08/15/05Regina Demina, Lecture #219 Calibration on Full MC lepton+jets

08/15/05Regina Demina, Lecture #220 calibrated expected: 36.4% DØ RunII Preliminary M t =169.5±4.4 GeV/c 2 JES=1.034±0.034

08/15/05Regina Demina, Lecture #221 Systematics summary Source of uncertaintyEffect on top mass (GeV/c 2 ) B-jet energy scale Signal modeling (gluons rad)0.34 Background modeling0.32 Signal fraction QCD contribution0.67 MC calibration0.38 trigger0.08 PDF’s0.07 Total

08/15/05Regina Demina, Lecture #222 B-jet energy scale ● Relative data/MC b/light jet energy scale ratio fragmentation: GeV/c 2  different amounts of  0, different  + momentum spectrum  fragmentation uncertainties lead to uncertainty in b/light JES ratio compare MC samples with different fragmentation models: Peterson fragmentation with e b = Bowler fragmentation with r t =0.69 calorimeter response: GeV/c 2 uncertainties in the h/e response ratio + charged hadron energy fraction of b jets > that of light jets  corresponding uncertainty in the b/light JES ratio Difference in p T spectrum of b-jets and jets from W-decay: 0.7 GeV/c 2

08/15/05Regina Demina, Lecture #223 Gluon radiation  Extra jets from initial/final state gluons  80% of the time, leading 4 jets correspond to 4 partons (qqbb) Final effect on top mass 0.34 GeV/c 2 q q e

08/15/05Regina Demina, Lecture #224 Result and cross checks Run II top quark mass based on lepton+jets sample: M t =169.5 ±4.4(stat+JES) (syst) GeV/c 2 JES contribution to (stat+JES) 3.3 GeV/c 2 Break down by lepton flavor –M t (e+jets)=168.8 ±6.0(stat+JES) GeV/c 2 –M t (  +jets)=172.3 ±9.6(stat+JES)GeV/c 2 Cross check W-mass

08/15/05Regina Demina, Lecture #225 Summary of DØ M t measurements Statistical uncertainties are partially correlated for all l+jets Run II results DØ Run II preliminary

08/15/05Regina Demina, Lecture #226 Combination of Tevatron results JES is treated as a part of systematic uncertainty, taken out of stat error

08/15/05Regina Demina, Lecture #227Combination M t =172.7±2.9 GeV/c 2 Stat uncertainty: 1.7GeV/c 2 Syst uncertainty: 2.4GeV/c 2 hep-ex/ Top quark Yukawa coupling to Higgs boson g t =M t √2/vev=0.993±0.017

08/15/05Regina Demina, Lecture #228 Top Quark Mass: Motivation Fundamental parameter of the Standard Model. Important ingredient for EW precision analyses at the quantum level: which were initially used to indirectly determine m t. After the top quark discovery, use precision measurements of M W and m t to constrain M H. WW t b WW H  M W  m t 2  M W  ln(M H ) CDF&D0 RUNII

08/15/05Regina Demina, Lecture #229 What does it do to Higgs? M H = GeV/c 2 M H <186 GeV/c M H,GeV/c 2 M t,GeV/c 2 M W,GeV/c 2 68% CL

08/15/05Regina Demina, Lecture #230 Projection for uncertainty on top quark mass Assumptions: only lepton+jets channel considered statistical uncertainty normalized at L=318 pb -1 to performance of current analyses. dominant JES systematic is handled ONLY via in-situ calibration making use of MW in ttbar events. remaining systematic uncertainties: include b-JES, signal and background modeling, etc (fully correlated between experiments) Normalized to 1.7 GeV at L=318 pb-1. Since most of these systematic uncertainties are of theoretical nature, assume that we can use the large data sets to constrain some of the model parameters and ultimately reduce it to 1 GeV after 8 fb -1.

08/15/05Regina Demina, Lecture #231 High statistics (LHC) approach In 100fb -1 about 1000 signal events is expected No jes systematics !!!