Top Quark Mass Measurements Using Neural Networks

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Top Quark Mass Measurements Using Neural Networks

• Suman B. Beri, Rajwant Kaur
• Panjab University, India
• Pushpalatha Bhat
• Fermilab
• Harrison B. Prosper
• Florida State University

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Outline

• Introduction
• Neural Networks
• Event Simulation
• Preliminary Studies
• Summary

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Introduction

• Run I,
• 1995, March 2 Discovery
• mt 176 17 GeV/c2 (CDF)
• mt 199 30 GeV/c2 (DØ)
• 1999, Combined Mass
• mt 174 5 GeV/c2 (CDF DØ)
• Run II, (2001)
• mt 174 ? GeV/c2

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Why Measure The Top Mass?
Corrections to W and Z mass
According to the Standard Model quantum
corrections to the W and Z boson masses induce a
relationship
from which we can infer something about the Higgs
mass
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Measuring the Top Mass

• In Run II we expect about 100 times more data
  than was collected in Run I.
• The main task is to reduce systematic errors so
  that we can benefit from the reduction in
  statistical errors
• Goal to determine mt as accurately as possible by
  making optimal use of information
• using as many decay modes as possible
• using several methods to cross-check the results
• exploring different methods which may yield
  smaller systematic errors.

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Feed-Forward Neural Networks
x1
x2
x3
x4
Use non-linear transfer function (e.g., sigmoid)
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Training Neural Networks
Training simply means minimizing the error
function
n(xi, w) network function xi feature vector
for pattern i, where i 1,N patterns w
weights dk desired output for pattern i, where
k 1,.. M classes
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A Bit of Bayes!
P(k) Prior probability Pr(xk) Likelihood
(Probability to get x given that x belongs to
k) P(kx) Posterior probability (Probability
to belong to k given x)
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Special Case Classification
If dk 0 for class k 1 (e.g.,
background) dk 1 for class k 2 (e.g.,
signal) Then
Reduces to
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Neural Networks in Run I and II

• Run I
• Used by DØ to discriminate signal from background
• Used in the lepton jets channel for top quark
  mass measurement
• Run II
• Can they be used to measure masses?
• Test some ideas using the e-m channel

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The e-m channel
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Branching fractions
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Characteristics of e-m Events

• Signature
• Two isolated, high pT leptons
• Significant missing transverse energy
• 2 jets from b quarks
• Branching fraction
• 2.4

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Event Simulation

• Tools
• Pythia 6.143 to generate events
• SHW 2.3 to model detector (John Conway)
• MLPfit 1.4 to train networks
• Python interface to above tools
• Signal
• Top events (100 to 250 GeV in steps 10 GeV)
• Backgrounds
• Z tt- em
• WW em

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Event Variables
End-point occurs at the top mass if b quark and
the lepton are correctly paired

• Variables
• x1 f(e,b1)
• x2 f(m,b2)
• x3 f(e,b2)
• x4 f(m,b1)
• where

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Distributions Correct/Wrong Pairing
Parton-level (blue) distributions compared to
distributions at the reconstruction-level
(red). We see that these variables are
insensitive to jet energy scale uncertainties
and fragmentation Also, note the sharp
end-point when the b and lepton are correctly
paired.
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Distributions Reconstruction Level
We have not yet devised a method to pair the
lepton and b quark with high probability. For
now we take all pairings of leptons and b quarks.
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Combining Variables using NN

• Use NN to create a single mass-dependent variable
  y from the variables x1 to x4
• Training
• 500 events/top mass (100 to 250 in steps of 10)
• Target output dk top quark mass
• 200 epochs

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Neural Network Output Distributions
160 GeV 169 23
170 GeV 175 25
GeV
GeV
180 GeV 181 24
190 GeV 186 25
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Mean NN output vs Top Mass
The distortions are caused by edge effects, that
is, restriction to a finite range. Need to deal
with this.
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Some thoughts about how to proceed

• Let y be the NN output.
• Let P(ymt) denote the probability to get y given
  the true top mass mt.
• Use Bayes theorem to invert probability
• Use position of maxP(mty as top mass estimate

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Summary

• The challenge in Run II will be to reduce
  substantially the systematic uncertainties.
• We are conducting a systematic study of neural
  network based methods of mass measurement.
• This is just the beginning.
• From our success in Run I we are hopeful that our
  current efforts will be fruitful.