Measurement of the Top Quark Mass at CDF

Measurement of the Top Quark Mass at CDF Igor Volobouev University of Chicago / LBNL SMU Physics Seminar, 02/09/04, 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 SMU Physics Seminar, 02/09/04, p. 2

Top Mass and Higgs Constraints • • • From the precision standard model fit, MH = 96+60 -38 Ge. V 95% CL upper bound on MH is at 200 Ge. V MH < 114. 4 Ge. V is excluded by LEP 1 (5 Ge. V) 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 Ge. V Igor Volobouev SMU Physics Seminar, 02/09/04, 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 Excellent Mt measurement is necessary for a meaningful SUSY-EW precision fit Igor Volobouev MSSM “maximal mixing scenario” SMU Physics Seminar, 02/09/04, p. 4

What is Mt? • Depends on who you are talking to… Ø Bare mass (lattice QCD theorist) Ø Pole mass (experimentalist) 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 SMU Physics Seminar, 02/09/04, p. 5

Top Production and Decay Basics • • At Tevatron, top quarks are produced predominantly in pairs (90% qq annihilation, 10% gluon fusion at 1. 8 Te. V) tt (1. 8 Te. V) ≈ 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. Igor Volobouev SMU Physics Seminar, 02/09/04, p. 6

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) D 0 reanalysis of Run 1 data: Mt = 180. 1± 3. 6± 4. 0 Ge. V Not yet beaten by Run 2 (but not for much longer!) Igor Volobouev 180. 1 ± 5. 4 Ge. V/c 2 D 0 Lepton+jets SMU Physics Seminar, 02/09/04, p. 7

Tevatron Run 2 Upgrade • • • 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 SMU Physics Seminar, 02/09/04, p. 8

CDF Upgrade • • • Improved Si coverage Ø | | < 2 TOF Ø up to 8 layers 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 SMU Physics Seminar, 02/09/04, p. 9

• • Total current sample on tape: 300 pb-1 “Winter 2004” analysis sample: 160 -200 pb-1 6 -9 pb-1/week 90% efficiency Total Luminosity (pb-1) Run 2 Data Sample “Winter 2004” sample Commissioning Delivered On Tape Store Number Igor Volobouev SMU Physics Seminar, 02/09/04, p. 10

Top Reconstruction • • tt events have been successfully reconstructed in all channels (dilepton, lepton+jets, all hadronic) 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 Mt measurement Lepton in the final state reduces the QCD background 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, 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 SMU Physics Seminar, 02/09/04, p. 11

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 SMU Physics Seminar, 02/09/04, p. 12

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 SMU Physics Seminar, 02/09/04, p. 13

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 SMU Physics Seminar, 02/09/04, p. 14

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 Ø Find pre-cluster centroids in the space Ø 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 Igor Volobouev SMU Physics Seminar, 02/09/04, p. 15

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 Igor Volobouev SMU Physics Seminar, 02/09/04, p. 16

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: 55 1 5% tt tag fake rate: 1% Igor Volobouev SMU Physics Seminar, 02/09/04, p. 17

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 • • • Igor Volobouev SMU Physics Seminar, 02/09/04, p. 18

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. Ø D 0 method: similar to DLM in spirit. Jet p. Ts are allowed to vary so that calorimeter transfer functions can be included. No W mass constraints and no requirement Mt = Mt, so 2 C fit becomes 5 D integral. Ø 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. Ø Igor Volobouev SMU Physics Seminar, 02/09/04, p. 19

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 Igor Volobouev SMU Physics Seminar, 02/09/04, p. 20

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: Ø Ø Ø There is no background All mass templates have the same mean Template widths and fractions as in the figure on the right Scenario 1: Ø Discard all events with wrong best permutation, and use only the correct permutation template Scenario 2: Ø • 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 assignal 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. Igor Volobouev SMU Physics Seminar, 02/09/04, p. 21

Templates for Different Mt Igor Volobouev SMU Physics Seminar, 02/09/04, p. 22

Preparing Template Mixture • • Use ∑ pi. Ti(m, …) to represent the signal template. All mass dependence is in Ti while all template fractions pi are massindependent. 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 Igor Volobouev SMU Physics Seminar, 02/09/04, p. 23

Permutation “Diffusion” Blue dots: permutation 0 is correct Red dots: permutation 1 is correct Igor Volobouev SMU Physics Seminar, 02/09/04, p. 24

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 Ø tt spin correlation term Ø Igor Volobouev SMU Physics Seminar, 02/09/04, p. 25

Multivariate Templates • Kernel density estimation method is used to create multivariate signal and background templates Igor Volobouev SMU Physics Seminar, 02/09/04, p. 26

Likelihood Igor Volobouev SMU Physics Seminar, 02/09/04, p. 27

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 Igor Volobouev SMU Physics Seminar, 02/09/04, p. 28

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) Igor Volobouev SMU Physics Seminar, 02/09/04, p. 29

Applying MTM to the Data Igor Volobouev SMU Physics Seminar, 02/09/04, p. 30

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 Igor Volobouev SMU Physics Seminar, 02/09/04, p. 31

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) Ø Parton distribution functions Ø Background shape Ø Uncertainty in b tagging efficiency Ø Ø • • At this time, jet energy uncertainty completely dominates all other systematic errors. Run 1 method used on Run 2 data quotes 6. 2 Ge. V systematic error due to jets (next highest error is 2. 2 Ge. V due to FSR). Run 1 jet systematics was 4. 4 Ge. V. We expect significant improvements in jet energy uncertainty by Summer 2004. Run 1 method should be able to achieve jet Mt < 5 Ge. V. MTM should work better than Run 1 method by at least 15%. Igor Volobouev SMU Physics Seminar, 02/09/04, p. 32

Future Plans • • • Balance statistical and systematic uncertainties Add soft lepton tagger Include l+jets events without b tags Ø 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 Igor Volobouev SMU Physics Seminar, 02/09/04, p. 33

Toward 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 SMU Physics Seminar, 02/09/04, p. 34

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! Igor Volobouev SMU Physics Seminar, 02/09/04, p. 35