Measurement of the Top Quark Mass at CDF

1
Measurement of the Top Quark Mass at CDF

• Igor Volobouev
• Lawrence Berkeley National Laboratory

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

• Old Standard Model fit
• Mt 174.3 5.1 GeV/c2 MH 9660 GeV/c2
• New world average (hep-ex 0404010)
• Mt 178.0 4.3 GeV/c2 MH 11362 GeV/c2
• 95 CL upper bound on MH is now at 237 GeV/c2

-38
-42
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. Mt lt 160 GeV/c2 would kill
  MSSM!
• Excellent Mt measurement is necessary for a
  meaningful SUSY-EW precision fit

MSSM mmax scenario
h
5
What is Mt?

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

6
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
• Top was very new
• Background
• Combinatorics
• Jet energy calibration
• Best single measurement is the recent (published
  in June 2004!) D0 re-analysis of Run 1 data
• Mt 180.13.64.0 GeV/c2

7
Run 2 Tevatron

• 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

8
CDF II Detector
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

9
Run 2 Data Sample

• Total current sample on tape ?470 pb-1
• Winter 2004 analysis sample 160-200 pb-1
• 8-13 pb-1/week
• ?85 efficiency

600
Delivered
On Tape
400
Total Luminosity (pb-1)
Winter 2004 sample
200
0
1000
2000
3000
Store Number
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Top Production and Decay Basics

• At Tevatron, top quarks are produced
  predominantly in pairs (85 qq annihilation, 15
  gluon fusion at 1.96 TeV)
• ?tt (1.96 TeV) 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.

11
Top Reconstruction

• 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 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)
• 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 (S/B 10/1), the
  dilepton channel has smaller branching fraction
  than ljets by factor of 6. There are 6 unknowns,
  so full event reconstruction is impossible.

12
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

13
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.

14
Jet Energy Calibration

• Extremely important for the top mass
  measurement
• Electromagnetic calorimeter is calibrated
  using Z ? ee-
• Central part of the hadronic calorimeter is
  calibrated by
• Referencing MIP response to the test beam data
• Photon-jet pT balancing
• Jet response in the wall/plug regions is studied
  using dijet balance. Jets outside the 0.2 lt h
  lt 0.6 region are scaled to jets inside.

15
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 is 55
• tt tag fake rate ? 0.5

16
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.

17
Mass Templates

• Top mass templates are obtained from MC and
  parameterized by continuous functions

18
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 c2 lt
  9
• Mtop 174.9 7.1 (stat.) 6.5 (syst.) GeV/c2

-7.7
19
Systematic Errors
20
Mass Reconstruction Run 2

• Two other methods have emerged in the leptonjets
  channel
• Multivariate Template Method (MTM) a new
  template technique aimed at the improvement of
  the systematic error as the integrated luminosity
  increases.
• Dynamical Likelihood Method (DLM) a slight
  variation on the original matrix element method
  proposed by Kunitaka Kondo in 1988.
• D0 has reanalyzed Run 1 data using a matrix
  element approach. Promising for Run 2.

21
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.

22
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 ? wiTi(m, ) to represent the signal
  template. Weights are different for each event.
• Uniform treatment of events with any number of b
  tags

23
Preparing Template Mixture
Best Permutation c2

• How to assign wi? 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
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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

1 b tag
2 b tags
26
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.

27
Signal / Background Separation

• Statistical divergence measures are used to study
  how useful a variable may be in separating
  signal from background

KS is the Kolmogorov-Smirnov distance
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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

Smoothed Likelihoods
29
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

30
Applying MTM to the Data
Pull Parameters
31
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

32
Dynamical Likelihood Method
For event number i, likelihood of mt is
Bayesian transfer function probability for
parton momenta x when y are observed
Integral over parton momenta
Sum over jet assignments/n solutions
Probability of the tt transverse momentum pt
Production and decay matrix element function of
x and mt
Parton distribution function
Event sample likelihood is
33
Calorimeter Transfer Functions

• Obtained from MC
• Expressed as functions of
• 9 bins in ET, 3 in h
• Checked using different generators (HERWIG and
  PYTHIA) and by reconstructing the W mass

34
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

35
Properties of the DLM Estimator

• Tested on pseudo experiments (19 background)
• After mapping the estimator is unbiased and pull
  distributions are unit Gaussians

36
DLM Data Likelihood
Mt 177.8 4.5 6.2 GeV/c2
-5.0
37
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

Mt 175 17 8 GeV/c2
38
Summary of Top Mass Results

• Four preliminary CDF Run 2 measurements, three of
  them are in the ljets 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
• BLUE can be used if the errors are symmetrized
• For now, quote DLM as the CDF Run 2 result (best
  expected error)

39
Why Run 2 isnt Better Than Run 1 Yet

• Systematics calorimeter response studies take
  time
• Run 1 was lucky. Expected statistical errors for
  the Run 1 leptonjets Mt measurements

Pseudo Experiments
D0
Statistical Error (GeV/c2)
40
Future Plans for Mt at CDF

• Expect a significant improvement in the
  systematic error in the next pass of top mass
  measurements (aim for leptonjets 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
• Verify background modeling
• 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

41
Towards 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

42
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 GeV/c2.
• 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!

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• Backup Slides

44
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

45
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

46
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
  event-by-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

47
MTM Likelihood
48
MTM Reconstructed Mt and JES
49
MTM Systematic Errors
50
Expected Statistical Errors
Pseudo Experiments
Error (GeV/c2)
MTM
Run 1 Method
51
DLM Likelihood Examples
Signal likelihoods, generator-level input
Blue all added up Red right perm. Black
wrong perm.
52
DLM Systematic Errors
Sources ? Mtop(GeV/c2)
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