Measurement of the Top Quark Mass at CDF

1. Measurement of the Top Quark Mass at CDF Igor Volobouev University of Chicago / LBNL

2. 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 Mt2 and log(MH) • Highly correlated with MH in the current precision SM fit CDF/D0 2 fb-1goal

3. Top Mass and Higgs Constraints • From the precision standard model fit, MH = 96+60-38 GeV • 95% CL upper bound on MH is at 200 GeV • MH < 114.4 GeV is excluded by LEP • 1 (5 GeV) change in Mt corresponds to  35% change in MH, as shown on the right • A factor of 2 improvement in Mt resolution would lower the 95% CL upper bound on MH by 35 GeV

4. 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 mH is smaller thanMZ must have heavy top to drive mH above the current experimental limit • Excellent Mt measurement is necessary for a meaningful SUSY-EW precision fit MSSM “maximal mixing scenario”

5. What is Mt? • Depends on who you are talking to… • Bare mass (lattice QCD theorist) • Pole mass (experimentalist) • MS mass (gauge theorist) • Threshold mass (LC phenomenologists) • Potential-subtracted mass • Kinetic mass • 1S mass • Hadron collider experiments measure the pole mass

6. Top Production and Decay Basics • At Tevatron, top quarks are produced predominantly in pairs (90% qq annihilation, 10% gluon fusion at 1.8 TeV) • tt (1.8 TeV) ≈ 5 pb (theory), 6.2 ± 1.2 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 Ws.

7. Tevatron Run 1 Mt Measurements • Based on about 106 pb-1 of data collected from 1992 to 1995 • Took a while to analyze, papers were written in 1999 • Best single measurement is a recent (2003) D0 re-analysis of Run 1 data: Mt = 180.1±3.6±4.0 GeV • Not yet beaten by Run 2 (but not for much longer!) 180.1 ± 5.4 GeV/c2 D0 Lepton+jets

8. Tevatron Run 2 Upgrade • New Main Injector & Recycler • Improved antiproton source • CM energy increased from 1.8 TeV to 1.96 TeV (tt cross section up by 35%) • 36x36 bunches, 396 ns between bunch crossing (was 6x6 with 3.5 s in Run 1) • Increased luminosity. Goals by the end of FY09: • 4.4 fb-1 “base” • 8.5 fb-1 “design”

9. =1 TOF =2 =3 CDF Upgrade • Improved Si coverage • |h| < 2 • up to 8 layers • New central tracker • 96 layers • Time of Flight • Expanded muon system • Forward calorimeter • Trigger and electronics h = -ln(tan(/2))

10. Run 2 Data Sample • Total current sample on tape: 300 pb-1 • “Winter 2004” analysis sample: 160-200 pb-1 • 6-9 pb-1/week • 90% efficiency “Winter 2004” sample Total Luminosity (pb-1) Commissioning Delivered On Tape Store Number

11. Top Reconstruction • tt events have been successfully reconstructed in all channels (dilepton, lepton+jets, all hadronic) • Main signatures • High pT leptons and/or jets • Missing energy due to escaping neutrinos • Two b jets in the final state • Production near threshold  spherical topology • Lepton+jets channel is the best for Mt measurement • Lepton in the final state reduces the QCD background • Manageable jet combinatorics, especially with one or two b tags • 5 kinematic constraints (momentum conservation in the transverse plane, two W masses, Mt = Mt), 3 unknowns (neutrino momentum) • Although exceptionally clean, the dilepton channel has smaller branching fraction than l+jets by factor of 6. There are 6 unknowns, so full event reconstruction is impossible.

12. Electron Identification • Good quality track with pT > 10 GeV/c • Track |z0| < 60 cm • CEM transverse energy ET > 20 GeV • ET/pT < 2.0 when pT < 50 GeV • 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

13. Muon Identification • Good quality track with pT > 20 GeV/c • Track |z0| < 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)) GeV • EHAD < 6 + max(0, 0.0280 * (p - 100)) GeV • Fractional calorimeter energy isolation < 0.1 • Track match to a muon chamber stub: 3, 5, and 6 cm for CMU, CMP, and CMX, respectively

14. Electron trigger Requires central EM cluster with ET > 18 GeV and EHAD/EEM < 0.125 A good quality track with PT > 9 GeV/c must be matched to the cluster About 96% efficient for “triggerable” electrons with ET > 20 GeV in the W → e sample. Inefficiency is dominated by tracking. Muon trigger Requires a match between a good quality track and a muon chamber stub About 95% efficient for “triggerable” muons in the Z →+- sample High PT Lepton Triggers

15. Jet Reconstruction • We are still using the Run 1 seeded cone algorithm “JetClu”: • Build pre-clusters using adjacent seed towers with ET > 1 GeV • 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”). • Stable cones are merged if they share more than 75% of one cone’s energy. Otherwise, common towers are split between the cones.

16. Jet Energy Calibration • Electromagnetic calorimeter is calibrated using Z → e+e- • Hadronic calorimeter is calibrated by monitoring MIP response from muons and referencing to test beam data • Jet response is studied using photon-jet and dijet balance

17. B Tagging with Silicon • At least two well-reconstructed tracks with  3 silicon hits • Secondary vertex LXY significance at least +3 (typical   150m) • Efficiency to tag a tt event: 55  1  5% • tt tag fake rate:  1%

18. Mass Reconstruction – Run 1 • 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). 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. • Templates are continuously parameterized as a function of Mt. • Value of Mt is found for which likelihood of the data sample is maximized using parameterized templates as prob. density

19. Mass Reconstruction – Run 2 • Three new methods have emerged in the l+jets channel: • Dynamic Likelihood Method (DLM): likelihood is determined for each Mt in each event using production and decay differential cross sections. Probabilities for all jet permutations are added when likelihood is constructed. Uses Bayesian transfer functions. • D0 method: similar to DLM in spirit. Jet pTs are allowed to vary so that calorimeter transfer functions can be included. No W mass constraints and no requirement Mt = Mt, so 2C fit becomes 5D integral. • Multivariate template method (MTM): aims at reduction of systematic error by tying the calorimeter jet energy scale to MW in each event. Statistical error is reduced by using other variables besides reconstructed mass to make templates, and by using the probability to pick the correct jet permutation for event reweighting.

20. MTM Kinematic Fit • Specialized kinematic fit is used to impose constraints on tt decay products • Jet energy scale constrained by a Gaussian prior is used as a variable in the W → qq fit. All jets in the event are rescaled according to the fitted scale, including b and b. This should reduce Mt systematic error due to jet energy scale (but the statistical uncertainty increases). • W mass Breit-Wigners are integrated correctly

21. Closer Look at the Mass Template • Template with correct leading jets and correct assignment of jets to partons has much better resolution – any improvement in combinatoric suppression is very useful • Fisher information ~ 1/2. Try the following simplified model: • There is no background • All mass templates have the same mean • Template widths and fractions as in the figure on the right Scenario 1: • Discard all events with wrong best permutation, and use only the correct permutation template Scenario 2: • Combine all templates using constant weights, and use all events In the scenario 1 we have more information about Mt in the event sample by factor of 2. • We will assign signal template fractions on event-by-event basis. Mt resolution obtained from the kinematic fit is used to scale the width of correct permutation template in every event.

22. Templates for Different Mt

23. Preparing Template Mixture • Use ∑ piTi(m, …) to represent the signal template. All mass dependence is in Ti while all template fractions pi are mass-independent. pi values can depend on 2, number of b tags in the event, etc., but not on any quantity highly correlated with the mass. • Uniform treatment of events with any number of b tags • How to assign pi? By itself, 2 of the best permutation provides little separation power between templates • Must use a more advanced model

24. Permutation “Diffusion” Blue dots: permutation 0 is correct Red dots: permutation 1 is correct

25. Correct Permutation Probability • In addition to using 2 values from all permutations, we update pcp using information from the tt production and decay dynamics: • cos(l,b) in the rest frame of the W which decays into l • tt spin correlation term

26. Multivariate Templates • Kernel density estimation method is used to create multivariate signal and background templates

27. Likelihood

28. Likelihood Continuity • Expectation from physics: for each event, likelihood dependence on Mt should be continuous and smooth • Nonparametric KDE templates do not guarantee likelihood continuity because each template is generated using an independent set of MC events and because of finite statistics • Ergo, increase MC statistics and/or smooth likelihood curves

29. Local Regression: LOESS • Smoothing likelihoods: for each event, we perform local regression in which Mt is the predictor and log(L) is the response • Quadratic polynomial is fitted to the likelihood points in a moving fashion. For each Mt coordinate, weights of points used in the fit decrease as distance to Mt increases • Concrete realization: LOESS (free code available from Netlib)

30. Applying MTM to the Data

31. Background Fraction • Background fraction floats freely in our current fitting procedure • The fraction is correlated with the mass but the mutual dependence is not trivial • Our method can be used for simultaneous measurement of Mt and the tt production cross section

32. Systematic Errors • CDF analyses assign systematic uncertainty on Mt for • Jet energy reconstruction • ISR modeling • FSR modeling • MC generators (basically, difference in jet fragmentation for HERWIG/Pythia) • Parton distribution functions • Background shape • Uncertainty in b tagging efficiency • At this time, jet energy uncertainty completely dominates all other systematic errors. Run 1 method used on Run 2 data quotes 6.2 GeV systematic error due to jets (next highest error is 2.2 GeV due to FSR). Run 1 jet systematics was 4.4 GeV. • We expect significant improvements in jet energy uncertainty by Summer 2004. Run 1 method should be able to achieve jet Mt < 5 GeV. MTM should work better than Run 1 method by at least 15%.

33. Future Plans • Balance statistical and systematic uncertainties • Add soft lepton tagger • Include l+jets events without b tags • Verify background modeling • Separate (statistically) light quark jets from gluon jets. Develop separate jet energy calibration constants for quarks and gluons. • Switch to a better clustering algorithm

34. Toward Ultimate Mt Measurement • Tevatron/LHC: with current methods, the jet energy systematic error will eventually limit the Mt precision at 1-2 GeV • A new method will be needed for hadron collider experiments to take advantage of very high luminosities • Measure Mt/MW rather than Mt ? • Emphasize angular distributions over energies? • Be careful about potential non-SM contributions! • Threshold scan at a high energy e+e-linear collider can be used to measure Mt up to 100 MeV

35. Summary • Precision top mass measurements are necessary for checking the consistency of the Standard Model. Mt and MH are highly correlated. • 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. • Multivariate template method is a new powerful analysis tool aimed at reducing both statistical and systematic uncertainties on Mt. MTM and DLM results from CDF will be presented at the April APS meeting. Come to Denver to see us!