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



                           SMU Physics Seminar, 02/09/04, p. 1
CDF              Top Mass in the Standard Model

 •   Fundamental parameter
 •   Enters into a variety of
     electroweak calculations
     at one loop level
 •   Example: W mass
     receives quantum              CDF/D0
                                   2 fb-1goal
     corrections proportional
     to Mt2 and log(MH)
 •   Highly correlated with
     MH in the current
     precision SM fit

Igor Volobouev                           SMU Physics Seminar, 02/09/04, p. 2
CDF              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

Igor Volobouev                        SMU Physics Seminar, 02/09/04, p. 3
CDF              Top Mass Beyond the SM
•   Heavy top is important           MSSM “maximal mixing scenario”
    because of its large Yukawa
    coupling. SM: Yt = Mt2/  1
•   Consistent with strong
    dynamical EWSB (topcolor)
•   MSSM: “bare” lightest mH is
    smaller than MZ must have
    heavy top to drive mH above
    the current experimental limit
•   Excellent Mt measurement is
    necessary for a meaningful
    SUSY-EW precision fit

Igor Volobouev                               SMU Physics Seminar, 02/09/04, p. 4
CDF                            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
Igor Volobouev                               SMU Physics Seminar, 02/09/04, p. 5
CDF              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)                               e-e(1/81)

•   Single top production cross                             mu-mu (1/81)

    section is about 40% of tt .                           tau-tau (1/81)

    Single top has not been                                 e -mu (2/81)

    observed yet.                                           e -tau(2/81)

•   Top quark decays into Wb in                             mu-tau (2/81)

     99.9% of the cases (SM).                              e+jets (12/81)

    Observed tt final states are                            mu+jets(12/81)
    classified according to                                 tau+jets(12/81)
    subsequent decays of the Ws.                            jets (36/81)



Igor Volobouev                        SMU Physics Seminar, 02/09/04, p. 6
CDF              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         180.1 ± 5.4 GeV/c2 D0 Lepton+jets
    (but not for much longer!)

Igor Volobouev                        SMU Physics Seminar, 02/09/04, p. 7
CDF                   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”

Igor Volobouev                        SMU Physics Seminar, 02/09/04, p. 8
CDF                        CDF Upgrade

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

    Igor Volobouev                         SMU Physics Seminar, 02/09/04, p. 9
CDF              Run 2 Data Sample

•   Total current




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

Igor Volobouev                                               SMU Physics Seminar, 02/09/04, p. 10
CDF                        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.
Igor Volobouev                                                SMU Physics Seminar, 02/09/04, p. 11
CDF              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
Igor Volobouev                            SMU Physics Seminar, 02/09/04, p. 12
CDF              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
Igor Volobouev                           SMU Physics Seminar, 02/09/04, p. 13
CDF               High PT Lepton Triggers
 •   Electron trigger                •   Muon trigger
        Requires central EM                Requires a match
         cluster with ET > 18 GeV            between a good quality
         and EHAD/EEM < 0.125                track and a muon
        A good quality track with           chamber stub
         PT > 9 GeV/c must be               About 95% efficient for
         matched to the cluster              “triggerable” muons in
        About 96% efficient for             the Z →+- sample
         “triggerable” electrons
         with ET > 20 GeV in the
         W → e sample.
         Inefficiency is dominated
         by tracking.

Igor Volobouev                                    SMU Physics Seminar, 02/09/04, p. 14
CDF                         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.




Igor Volobouev                                             SMU Physics Seminar, 02/09/04, p. 15
CDF              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
CDF              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%
Igor Volobouev                   SMU Physics Seminar, 02/09/04, p. 17
CDF              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
CDF              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.
Igor Volobouev                                       SMU Physics Seminar, 02/09/04, p. 19
CDF              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
CDF          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.

Igor Volobouev                                       SMU Physics Seminar, 02/09/04, p. 21
CDF              Templates for Different Mt




Igor Volobouev                     SMU Physics Seminar, 02/09/04, p. 22
CDF              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



Igor Volobouev                             SMU Physics Seminar, 02/09/04, p. 23
CDF                 Permutation “Diffusion”




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

Igor Volobouev                                   SMU Physics Seminar, 02/09/04, p. 25
CDF              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
CDF              Likelihood




Igor Volobouev                SMU Physics Seminar, 02/09/04, p. 27
CDF                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
CDF              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
CDF              Applying MTM to the Data




Igor Volobouev                    SMU Physics Seminar, 02/09/04, p. 30
CDF                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
CDF                          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%.
Igor Volobouev                                              SMU Physics Seminar, 02/09/04, p. 32
CDF                       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

Igor Volobouev                          SMU Physics Seminar, 02/09/04, p. 33
CDF          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

Igor Volobouev                                    SMU Physics Seminar, 02/09/04, p. 34
CDF                      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

								
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