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
  9660-38 GeV
• 95 CL upper bound on MH is at 200 GeV
• MH lt 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 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

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 180.13.64.0
  GeV
• Not yet beaten by Run 2 (but not for much
  longer!)

180.1 5.4 GeV/c2 D0 Leptonjets
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
CDF Upgrade
h -ln(tan(?/2))

• Improved Si coverage
• h lt 2
• up to 8 layers
• New central tracker
• 96 layers
• Time of Flight
• Expanded muon system
• Forward calorimeter
• Trigger and electronics

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, leptonjets, 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
• Leptonjets 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
  ljets by factor of 6. There are 6 unknowns, so
  full event reconstruction is impossible.

12
Electron Identification

• Good quality track with pT gt 10 GeV/c
• Track z0 lt 60 cm
• CEM transverse energy ET gt 20 GeV
• ET/pT lt 2.0 when pT lt 50 GeV
• Cluster EHAD/EEM lt 0.055 0.00045 E
• Track-to-shower match ? 3 cm
• Fractional calorimeter energy isolation lt 0.1
• Shower profile consistent with electron
• Fiducial to CES
• Conversion veto

13
Muon Identification

• Good quality track with pT gt 20 GeV/c
• Track z0 lt 60 cm
• Cosmic ray veto
• Track impact parameter lt 0.02 cm with silicon
  hits, 0.2 cm without
• EEM lt 2 max(0, 0.0115 (p - 100)) GeV
• EHAD lt 6 max(0, 0.0280 (p - 100)) GeV
• Fractional calorimeter energy isolation lt 0.1
• Track match to a muon chamber stub 3, 5, and 6
  cm for CMU, CMP, and CMX, respectively

14
High PT Lepton Triggers

• Electron trigger
• Requires central EM cluster with ET gt 18 GeV and
  EHAD/EEM lt 0.125
• A good quality track with PT gt 9 GeV/c must be
  matched to the cluster
• About 96 efficient for triggerable electrons
  with ET gt 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

15
Jet Reconstruction

• We are still using the Run 1 seeded cone
  algorithm JetClu
• Build pre-clusters using adjacent seed towers
  with ET gt 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 cones energy. Otherwise, common
  towers are split between the cones.

16
Jet Energy Calibration

• Electromagnetic calorimeter is calibrated using Z
  ? ee-
• 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 ljets
  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 lt 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 ljets 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 ee- 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!