Weighing Truth in CDF

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Weighing Truth in CDF

• Erik Brubaker
• October 25, 2004
• UC HEP Seminar

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The Top Quark

• Feels strong, electroweak, gravitational forces.
• Short-liveddoesnt hadronize (t410-25 s).
• Especially interesting due to its mass
• Most massive particle at 180 GeV/c2.
• More massive than b quark by factor of 35.
• SM Yukawa coupling 1 Special role??

Mass (GeV/c2)
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Why measure the top quark mass?

• Fundamental dimensionless parameter of SM close
  to 1.
• Related to other SM parameters and observables
  through loop diagrams.
• Global fit (LEPEWWG) provides consistency check
  and predicts mass of putative Higgs particle.
• Mt (and MW) particularly poorly known in terms of
  effect on MH prediction.

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Obligatory accelerator slide

• Tevatron run II vs 1.96 TeV
• Peak luminosity broke 1032!
• Currently in shutdown

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Obligatory detector slide

• Collider Detector at Fermilab
• Standard onion-like general-purpose particle
  physics detector
• Tracking system
• Calorimeters
• Muon system

Silicon detector ? b tagging
Excellent lepton ID and triggering
Coarse segmentation,non-linear response
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Top phenomenology

• Mass analyses use t-tbar pair events.
• s 6.7 (5.7) pb_at_ Mt 175 (180) GeV/c2.
• 85 quark annihilation,15 gluon fusion.
• Top always decays to W boson and b quark.
• Events classified by decay of W to leptons or
  quarks
• Identifying b quark improves S/B ratio

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Whats the big deal?
Events are complicated!

• Experimental observations are not as pretty as
  Feynman diagrams!
• Additional jets from ISR, FSR.
• Which jets go with which quarks?
• Dileptons 2 neutrinos, 1 ET measurement.

/
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Whats the big deal, part II
Measurements are not perfect!

• Missing transverse energy ? Neutrino, but pzn not
  measured.
• Jet energies poorly measured.
• Large resolution ? statistical error.
• Fragmentation calorimeter non-linearity
• Particles leave jet cone
• Underlying event
• Uncertain scale ? sytematic error.
• No nice resonance for in situ calibration
• Z?bb??

80/vpT
O(5)
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Whats the big deal, part III
Tagged lepton jets channel
Background contamination!

• Top events trade-off between sample size and
  purity.
• Presence of background events dilutes mass
  information from signal events.
• Effects of background must be treated properly to
  avoid bias.

Dilepton channel
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How to Weigh Truth
TEMPLATES
DIRECT PROBABILITY

• Pick a test statistic
• Create templates using events simulated with
  different Mtop values ( background)
• Perform maximum likelihood fit to extract
  measured mass

• Build likelihood directly from PDFs, matrix
  element(s), and transfer functions that connect
  quarks and jets.
• Integrate over unmeasured quantities (e.g. quark
  energies).

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Template Analysis Overview
c2 mass fitterFinds best top mass and
jet-parton assignmentOne number per
eventAdditional selection cut on resulting c2
Massfitter
Templates
Likelihoodfit
Result
Likelihood fitBest signal bkgd templates to
fit dataCompare to paramizn, not
directlyConstraint on background normalization
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Event-by-event Mass Fitter

• Distill all event information into one number
  (called reconstructed mass).
• Select most probable jet-parton assgnmt based on
  c2, after requiring b-tagged jets assigned to b
  partons.

Reconstructedtop mass isfree parameter
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Signal templates
Selected templates (GeV)
140
150
160
ParameterizationBuild signal p.d.f. as a
functionof generated mass.
190
180
170
200
210
220
Reconstructed Mass
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Background template
CDF Run II Preliminary (162 pb-1)
Constraint usedin likelihood fit.
Major contributions Wheavy flavor Wjets
(mistag) QCD
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Unbinned likelihood fit

• Free parameters are Mtop, ns, and nb.
• Profile likelihood minimize w.r.t. ns,nb, no
  integration.
• Extended maximum likelihood.
• Poisson factor in front means ns,nb are Poisson
  mean parameters.
• Inside product, likelihood sums over available
  Ns, Nb around ns, nb.
• Fluctuations of nb are a systematic effect.
  Allowing nb to float in the fit means information
  in data is used to reduce the systematic
  uncertainty.
• In principle, can do the same thing for jet
  energy scale. Work in progress!

InterestingParameter!
bkgd (mean)constraint
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Data fit
Best fit 174.9 7.1/-7.7 GeV/c2
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Systematics Summary
CDF Run II Preliminary (162 pb-1)
Systematics dominatedby jet energy scale.
CDF Run II Preliminary (162 pb-1)
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Dynamical Likelihood Method

• Maximum likelihood method, where likelihood is
  built up for each event i as below.

Transferfunctionsconnectjets topartons
Quadratic eqnsgive multiplesolns for nsum
over them.
Sum overall possiblejet-partonassnmts
PartonDistributionFunctions
Matrix elementprovides completedynamical
eventinformation
Ad hoctreatmentof ISR
Integrateover z1, z2,y (partons)
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DLM background

• More difficult to treat background than in
  template analyses.
• Ideally, need matrix element for background.

• Instead, DLM uses a mapping function background
  dilutes mass information in a known manner, so
  correct for it.

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DLM transfer functions

• Describe probability that a jet with a given
  measured ET came from a parton with particular
  ET P(yx).
• Detector response, P(xy), is process-independent.
  
• Through Bayes, P(yx) depends on P(y), therefore
  on Mtop.
• This dependence also taken out using mapping
  function.

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DLM results
Jet systematics smaller thantemplate
methods. Effect of transfer functions,integration
over partons? Use more event information?
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Summary of CDF results
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Templates subdivide sample

• Use 4 categories of events with different
  background content and reconstructed mass shape.

0-tagSB 12RMS 35
1-tag(L)SB 21RMS 30
1-tag(T)SB 61RMS 30
2-tagSB 10RMS 26
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Templates subdivide sample

• Improves statistical uncertainty w.r.t. previous
  analysis.
• Adds 0-tag events.
• Pure and well reconstructed events contribute
  more to result.
• Systematic uncertainty is not improved.
• Most systematics, including jet energy scale, are
  highly correlated between the samples.

Mtop 176.7 6.0/-5.4 (stat.) /-7.1 (syst.)
GeV/c2
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Summary of CDF results
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Multivariate template method

• Add second test statistic SpT4jdiscriminates
  signal vs background events.
• Fit jet energy scale in every event using W
  masstrades statistical error for systematic.

stat
syst
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Summary of CDF results
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Dilepton analyses

• Under-constrained kinematic system.
• Must always make extra assumptions.
• h1, h2 of neutrinos
• f1, f2 of neutrinos
• Pzttbar
• So far, all analyses in this channel use the
  template approach.

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Neutrino weighting approach

• Assume top mass, W mass, determine probability of
  event.
• Integrate over unknowns.
• Lepton-jet pairing
• Neutrino h
• Missing energy solutions
• Mt for which event is most likely ? Mreco.

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NWA results
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Summary of CDF results
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Dilepton Reconstructed Mass

• Use c2 from the lepton jets analysis, slightly
  modified.
• Assume f1, f2 of the two neutrinos (scan over
  plane).
• Weight each point inf1-f2 space byexp(-c2/2).
• All points contribute to templates and to data
  distribution.

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Dilepton reconstructed mass results

• Tighter selection than NWA gives fewer events,
  but smoother distrubution due to weighting
  solutions.
• Background peaks near signaldilutes information
  in likelihood.

Mtop 170.0 16.6(stat.) 7.4(syst.)  GeV/c2
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Summary of CDF results
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Kinematic reconstruction assuming Pztt

• Assume Pztt 0 180 GeV/c
• Scan over Pztt and parton energies, perform
  kinematic reconstruction at each point.
• Test statistic is the top mass that contains the
  most likely point in this phase space (no
  integration).

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Whats coming?
Maturing Analyses
General improvements

• Matrix element techniques
• Full background matrix element treatment
• Apply to dilepton channel
• All-hadronic channel
• Several algorithms in progress
• Large background, more jets, even harder
  combinatorics!

• Reduced jet systematics
• Improved detector simulation/calibration
• Remove doubly counted errors
• This will still limit our precision! Needs more
  work!
• Combine measurements across channels, techniques
• Hard problem. Highly correlated systematics,
  non-Gaussian stat uncertainties.

CDF topquark mass
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Backups
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Checks on final measurement
3.5-jet unconstrained
4-jet constrained
4-jet unconstrained
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Indirect fits two interpretations