Measurement of the Top Quark Mass at CDF

Measurement of the Top Quark Mass at CDF Igor Volobouev Lawrence Berkeley National Laboratory TRIUMF Seminar, 2004 -07 -19, p. 1

Top Mass in the Standard Model • • Fundamental parameter Enters into a variety of electroweak calculations at one loop level Example: W mass receives quantum corrections proportional to Mt 2 and log(MH) Highly correlated with MH in the current precision SM fit Igor Volobouev CDF/D 0 2 fb-1 goal TRIUMF Seminar, 2004 -07 -19, p. 2

Top Mass and Higgs Constraints • • • Old Standard Model fit: Mt = 174. 3 ± 5. 1 Ge. V/c 2 2 MH = 96+60 -38 Ge. V/c New world average (hepex 0404010): Mt = 178. 0 ± 4. 3 Ge. V/c 2 2 MH = 113+62 Ge. V/c -42 95% CL upper bound on MH is now at 237 Ge. V/c 2 Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 3

Top Mass Beyond the SM • • Heavy top is important because of its large Yukawa coupling. SM: Yt = Mt 2/ 1 Consistent with strong dynamical EWSB (topcolor) MSSM: “bare” lightest m. H is smaller than MZ �must have heavy top to drive m. H above the current experimental limit. Mt < 160 Ge. V/c 2 would kill MSSM! Excellent Mt measurement is necessary for a meaningful SUSY-EW precision fit Igor Volobouev MSSM mmax scenario h TRIUMF Seminar, 2004 -07 -19, p. 4

What is Mt? • Depends on who you are talking to… Ø Pole mass (experimentalist) Ø Bare mass (lattice QCD theorist) Ø MS mass (gauge theorist) Ø Threshold mass (LC phenomenologists) – Potential-subtracted mass – Kinetic mass – 1 S mass • Hadron collider experiments measure the pole mass Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 5

Tevatron Run 1 Mt Measurements • • Based on about 106 pb-1 of data collected from 1992 to 1995 Took a while to analyze, final CDF papers were published in 1999 Experimental challenges: Ø Ø Top was very new Background Combinatorics Jet energy calibration Best single measurement is the recent (published in June 2004!) D 0 re-analysis of Run 1 data: Mt = 180. 1± 3. 6± 4. 0 Ge. V/c 2 Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 6

Run 2 Tevatron • • • New Main Injector & Recycler Improved antiproton source CM energy increased from 1. 8 Te. V to 1. 96 Te. V (tt cross section up by 35%) 36 x 36 bunches, 396 ns between bunch crossing (was 6 x 6 with 3. 5 s in Run 1) Increased luminosity. Goals by the end of FY 09: 4. 4 fb-1 “base” Ø 8. 5 fb-1 “design” Ø Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 7

CDF II Detector • • • Improved Si coverage Ø | | < 2 Ø up to 8 layers TOF New central tracker Ø 96 layers Time of Flight Expanded muon system Forward calorimeter Trigger and electronics Igor Volobouev = -ln(tan( /2)) 1 = =2 =3 TRIUMF Seminar, 2004 -07 -19, p. 8

• • Total current sample on tape: 470 pb-1 “Winter 2004” analysis sample: 160 -200 pb-1 8 -13 pb-1/week 85% efficiency Igor Volobouev Total Luminosity (pb-1) Run 2 Data Sample 600 Delivered On Tape 400 “Winter 2004” sample 200 0 1000 2000 3000 Store Number TRIUMF Seminar, 2004 -07 -19, p. 9

Top Production and Decay Basics • • At Tevatron, top quarks are produced predominantly in pairs (85% qq annihilation, 15% gluon fusion at 1. 96 Te. V) tt (1. 96 Te. V) ≈ 6. 7 pb (theory), 5. 6 ± 1. 4 pb (experiment) Single top production cross section is about 40% of tt. Single top has not been observed yet. Top quark decays into Wb in 99. 9% of the cases (SM). Observed tt final states are classified according to subsequent decays of the W. Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 10

Top Reconstruction • Main signatures High p. T leptons and/or jets Ø Missing energy due to escaping neutrinos Ø Two b jets in the final state Ø Production near threshold → spherical topology Ø • Lepton+jets channel is the best for initial top mass and cross section measurements Lepton in the final state reduces the QCD background (S/B ~ 2/1 vs. 1/10 in the all hadronic channel) Ø Manageable jet combinatorics, especially with one or two b tags Ø 5 kinematic constraints (momentum conservation in the transverse plane, two W masses, Mt = Mt), 3 unknowns (neutrino momentum) Ø Although exceptionally clean (S/B ~ 10/1), the dilepton channel has smaller branching fraction than l+jets by factor of 6. There are 6 unknowns, so full event reconstruction is impossible. Ø Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 11

High PT Lepton Triggers • Electron trigger Requires central EM cluster with ET > 18 Ge. V and EHAD/EEM < 0. 125 Ø A good quality track with PT > 9 Ge. V/c must be matched to the cluster Ø About 96% efficient for “triggerable” electrons with ET > 20 Ge. V in the W → e sample. Inefficiency is dominated by tracking. Ø Igor Volobouev • Muon trigger Requires a match between a good quality track and a muon chamber stub Ø About 95% efficient for “triggerable” muons in the Z → + - sample Ø TRIUMF Seminar, 2004 -07 -19, p. 12

Jet Reconstruction • We are still using the Run 1 seeded cone algorithm “Jet. Clu”: Build pre-clusters using adjacent seed towers with ET > 1 Ge. V Find pre-cluster centroids in the space For each pre-cluster, add all towers within the cone of R = 0. 4 in the space and recalculate the centroid. Iterate this step until the cone center stabilizes. Seeds are not allowed to leave the cones (“ratcheting”). Ø Stable cones are merged if they share more than 75% of one cone’s energy. Otherwise, common towers are split between the cones. Ø Ø Ø Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 13

Jet Energy Calibration • • • Extremely important for the top mass measurement Electromagnetic calorimeter is calibrated using Z → e+e. Central part of the hadronic calorimeter is calibrated by Referencing MIP response to the test beam data Ø Photon-jet p. T balancing Ø • Jet response in the wall/plug regions is studied using dijet balance. Jets outside the 0. 2 < | | < 0. 6 region are scaled to jets inside. Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 14

B Tagging with Silicon • • At least two wellreconstructed tracks with 3 silicon hits Secondary vertex LXY significance at least +3 (typical 150 m) Efficiency to tag a tt event is 55% tt tag fake rate: 0. 5% Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 15

Mass Reconstruction by Run 1 Method • Simplified 2 expression is constructed using transverse momenta of the jets and tt recoil, as well as kinematic constraints: • Solution with best 2 value is found (up to 24 solutions possible due to jet/neutrino combinatorics, less if there is one or more b tags). This solution is used as the reconstructed top mass in the event. MC samples generated with different Mt are used to populate mass templates. Background templates are added later. Value of Mt is found for which likelihood of the data sample is maximized using templates as probability density. • • Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 16

Mass Templates • Igor Volobouev Top mass templates are obtained from MC and parameterized by continuous functions TRIUMF Seminar, 2004 -07 -19, p. 17

Run 1 Method Result • • Background is constrained in the fit to its expected value using the cross section measurement From 28 events with at least one b tag and 2 < 9: 2 Mtop = 174. 9 +7. 1 (stat. ) ± 6. 5 (syst. ) Ge. V/c -7. 7 Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 18

Systematic Errors Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 19

Mass Reconstruction – Run 2 • Two other methods have emerged in the lepton+jets channel: Multivariate Template Method (MTM): a new template technique aimed at the improvement of the systematic error as the integrated luminosity increases. Ø Dynamical Likelihood Method (DLM): a slight variation on the original matrix element method proposed by Kunitaka Kondo in 1988. Ø • D 0 has reanalyzed Run 1 data using a matrix element approach. Promising for Run 2. Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 20

MTM Kinematic Fit • • • Idea: calibrate jet energy in-sample using W mass as a reference. Jet energy scale factor is included into the W mass kinematic fit with a Gaussian constraint. The constraint is a tunable parameter. All jets in the event are multiplied by the jet energy scale value obtained in the W mass fit. Fitted scale is different from one jet permutation to another. For the correct permutation, scale shifts due to the W mass constraint compensate on average systematic shifts. Statistical error is increased. Global energy scale fit in the top events is possible but difficult due to background and combinatorics. Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 21

Closer Look at the Mass Templates • • • Idea: reweight events using the probability to pick the correct jet permutation Correct permutation template has much better resolution In case of negligible background, exact knowledge of the signal subsample would improve the mass resolution by factor of 1. 7 Use ∑ wi. Ti(m, …) to represent the signal template. Weights are different for each event. Uniform treatment of events with any number of b tags Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 22

Preparing Template Mixture Best Permutation 2 • • How to assign wi? By itself, 2 of the best permutation provides little separation power between templates Must use a more advanced model Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 23

Permutation “Diffusion” Blue dots: permutation 0 is correct Red dots: permutation 1 is correct Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 24

Correct Permutation Probability 1 b tag • In addition to using 2 values from all permutations, we update pcp using information from the tt production and decay dynamics: 2 b tags cos(l, b) in the rest frame of the W which decays into l Ø tt spin correlation term Ø Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 25

Multivariate Templates • • Idea: templates can use several variables Mostly helps with S/B separation Kernel density estimation method is used to create multivariate signal and background templates Inverse of a robust covariance matrix is used as a metric. Standard plug-in algorithm determines global bandwidth. Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 26

Signal / Background Separation • Statistical divergence measures are used to study how useful a variable may be in separating signal from background Igor Volobouev KS is the Kolmogorov-Smirnov distance TRIUMF Seminar, 2004 -07 -19, p. 27

Likelihood Continuity • • • Idea: smooth event likelihoods instead of templates Expectation from physics: for each event, likelihood dependence on Mt should be continuous and smooth Run 1 method enforces continuity of the likelihood by introducing explicit dependence of the template parameters on top mass KDE templates do not guarantee likelihood continuity because each template is generated using an independent set of MC events with finite statistics We use local quadratic polynomial regression to interpolate and smooth likelihood curves Igor Volobouev Smoothed Likelihoods TRIUMF Seminar, 2004 -07 -19, p. 28

Tuning the JES Constraint • • • The total expected error is studied with pseudo experiments as a function of the jet energy scale constraint in the kinematic fit Several variable sets provide similar performance, we choose the one with the best background suppression In the future systematic error will be more important – the choice of variables will have to be adjusted accordingly Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 29

Applying MTM to the Data Pull Parameters Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 30

Background Fraction • • • Background fraction floats freely in the current MTM template fitting procedure The fraction is correlated with the mass but the mutual dependence is not trivial In the future, we plan to perform a simultaneous measurement of Mt and the tt production cross section Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 31

Dynamical Likelihood Method For event number i, likelihood of mt is Integral over parton momenta Sum over jet assignments/ solutions Production and decay matrix element – function of x and mt Bayesian transfer function: probability for parton momenta x when y are observed Probability of the tt transverse momentum pt Parton distribution function Event sample likelihood is Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 32

Calorimeter Transfer Functions • • Obtained from MC Expressed as functions of • • 9 bins in ET, 3 in Checked using different generators (HERWIG and PYTHIA) and by reconstructing the W mass Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 33

Background Treatment in DLM • • Background fraction is minimized by choosing events with exactly 4 jets Maximum likelihood mass is remapped using expected background from the cross section measurement Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 34

Properties of the DLM Estimator • • Tested on pseudo experiments (19% background) After mapping the estimator is unbiased and pull distributions are unit Gaussians Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 35

DLM Data Likelihood 2 Mt = 177. 8 +4. 5 ± 6. 2 Ge. V/c -5. 0 Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 36

Top Mass in the Dilepton Channel • • • Based on 126 pb-1 Mass templates are built by sampling the z momentum of the tt system to get the most probable mass for each event. Use jet permutation/neutrino solution with the smallest tt mass. Background is ~0. 5 events Igor Volobouev Mt = 175 ± 17 ± 8 Ge. V/c 2 TRIUMF Seminar, 2004 -07 -19, p. 37

Summary of Top Mass Results • • Four preliminary CDF Run 2 measurements, three of them are in the l+jets channel → highly correlated Combining correlated measurements with asymmetric errors is an unsolved statistical problem Can be done using a nonparametric technique but this requires too much CPU power Ø BLUE can be used if the errors are symmetrized Ø • For now, quote DLM as the CDF Run 2 result (best expected Igorerror) Volobouev TRIUMF Seminar, 2004 -07 -19, p. 38

Why Run 2 isn’t Better Than Run 1 Yet CDF Statistical Error (Ge. V/c 2) Igor Volobouev Pseudo Experiments Systematics: calorimeter response studies take time Run 1 was lucky. Expected statistical errors for the Run 1 lepton+jets Mt measurements: Pseudo Experiments • • D 0 Statistical Error (Ge. V/c 2) TRIUMF Seminar, 2004 -07 -19, p. 39

Future Plans for Mt at CDF • • • Expect a significant improvement in the systematic error in the next pass of top mass measurements (aim for lepton+jets publications by the end of 2004) Fully explore the dilepton and all hadronic channels Add other b taggers and events without tags Measure efficiency and fake rates Ø Verify background modeling Ø • • • Improve jet energy resolution by taking jet fragmentation into account Separate (statistically) light quark jets from gluon jets. Develop separate jet energy calibration constants for quarks and gluons. Switch to a better clustering algorithm Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 40

Towards Ultimate Mt Measurement • • Tevatron/LHC: with current methods, the jet energy systematic error will eventually limit the Mt precision at 1 -2 Ge. V A new method will be needed for hadron collider experiments to take advantage of very high luminosities Measure Mt/MW rather than Mt? Ø Emphasize angular distributions over energies? Ø Be careful about potential non-SM contributions! Ø • Threshold scan at a high energy e+e- linear collider can be used to measure Mt up to 100 Me. V Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 41

Conclusions • • Precision top mass measurements are necessary for checking the consistency of the Standard Model. Mt and MH are highly correlated. Up to now all measurements are consistent with the Standard Model top with Mt 178 Ge. V/c 2. Tevatron has already accumulated enough Run 2 data for a significantly better Mt measurement than Run 1 result. Improvements in calibration and simulation are on the way. MTM and DLM are powerful Run 2 analysis tools aimed at reducing both statistical and systematic uncertainties on Mt. Read PRD at the end of the year! Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 42

Backup Slides Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 43

Electron Identification • • • Good quality track with p. T > 10 Ge. V/c Track |z 0| < 60 cm CEM transverse energy ET > 20 Ge. V ET/p. T < 2. 0 when p. T < 50 Ge. V Cluster EHAD/EEM < 0. 055 + 0. 00045 * E Track-to-shower match 3 cm Fractional calorimeter energy isolation < 0. 1 Shower profile consistent with electron Fiducial to CES Conversion veto Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 44

Muon Identification • • Good quality track with p. T > 20 Ge. V/c Track |z 0| < 60 cm Cosmic ray veto Track impact parameter < 0. 02 cm with silicon hits, 0. 2 cm without EEM < 2 + max(0, 0. 0115 * (p - 100)) Ge. V EHAD < 6 + max(0, 0. 0280 * (p - 100)) Ge. V Fractional calorimeter energy isolation < 0. 1 Track match to a muon chamber stub: 3, 5, and 6 cm for CMU, CMP, and CMX, respectively Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 45

MTM Basic Ideas • • Reduce systematics by calibrating jet energy scale in the sample of top candidates. Reduce statistical uncertainty by estimating the probability to pick correct jet permutation on eventby-event basis. Reweight events according to this probability. Improve signal/background separation by utilizing other kinematic variables in addition to the reconstructed top mass. Avoid hard cuts. Introduce fewer assumptions into the analysis by using nonparametric statistical techniques Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 46

MTM Likelihood Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 47

MTM Reconstructed Mt and JES Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 48

MTM Systematic Errors Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 49

Pseudo Experiments Expected Statistical Errors Error (Ge. V/c 2) Run 1 Method Igor Volobouev MTM TRIUMF Seminar, 2004 -07 -19, p. 50

DLM Likelihood Examples Signal likelihoods, generator-level input Blue : all added up Red : right perm. Black : wrong perm. Igor Volobouev TRIUMF Seminar, 2004 -07 -19, p. 51

DLM Systematic Errors Igor Volobouev Sources Δ Mtop(Ge. V/c 2) Jet Energy Scale 5. 3 ISR 0. 5 FSR 0. 5 PDF 2. 0 Generator 0. 6 Spin correlation 0. 4 NLO effect 0. 4 Bkg fraction(± 5%) 0. 5 Bkg Modeling 0. 5 MC Modeling(jet, UE) 0. 6 Transfer function 2. 0 Total 6. 2 TRIUMF Seminar, 2004 -07 -19, p. 52