A template fit technique to measure the top quark mass in the l jets channel

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A template fit technique to measure the top quark
mass in the ljets channel

• Ulrich Heintz, Vivek Parihar

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Overview

• OBJECTIVE develop a fast algorithm for the
  measurement of the top quark mass in l jets
  channel to complement the computing intensive
  matrix element technique.
• currently studied a template fit method using
  only ttbar signal MC in the e jets channel
• results shown here are based on the output of
  HITFIT from Pieter Houbens Monte Carlo data
  files (January version)
• event selection is that used by the Ideogram
  analysis by Pieter and Michele.
• templates are constructed using the mass for each
  event for which HITFIT obtains the lowest
  (positive) chi-squared.

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PART 1

• Parametrization of Templates

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Templates
mtop170 GeV
mtop155 GeV
155
mtop195 GeV
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Templates
mtop170 GeV
mtop155 GeV
mtop195 GeV
Each template is fitted with Landau convoluted
with Gaussian Pure Gaussian with a total of 7
parameters
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Fit Parameters

• show that parameters vary smoothly with mtop
• Landau Gauss

7
Fit Parameters

• Gaussian

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2 D Simultaneous Fit

• express the 7 parameters as functions of mtop
• fit all templates simultaneously

Function used LandauGaussian Gaussian with
total 7 internal parameters.
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2 D Simultaneous Fit

• results

Landau gauss parameters Width of Landau      a0
- a1(mtop-175) Most Probable         a2
a3(mtop-175) Area                       a4(1-
a7) GSigma                   a5
a6(mtop-175)   Pure Gaussian Norm               
      a4a7 Most Probable        a8
a9(mtop-175) Sigma                      a10
a0 8.82       a1 0.02      a2 162.82     
a3 0.49   a4 4.69    a5 19.16     a6
0.17   a7 0.14    a8 175.32    a9 0.96 
    a10 11.6
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2 D Simultaneous Fit

• superimpose template parametrizations

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PART II

• Ensemble Tests
• -gt 1000 ensembles with 200 ttbar events
  each, randomly picked from the data files.
• -gt parametrized templates used to
  calculate the negative log likelihood for each
  ensemble of 200 events.

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Ensemble tests

• - log likelihood plot and quadratic fit for a
  sample ensemble (mtop 155 GeV)

The fit procedure, determines the measured top
mass by, finding the minimum of the Log
likelihood curve.
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Ensemble tests

• Distributions of Measured (fitted) Top Mass
  (upper row) and Pulls (bottom row)

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165 GeV (2.919)
159.9 GeV(2.986)
154.4 GeV (3.31)
0.0394 (1.002)
0.2046 (1.116)
0.0171 (0.974)
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174.2 (3.289)
169.3 (3.2)
179.4 (3.339)
0.2428 (1.042)
0.2527 (1.03)
0.188 (1.041)
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185.2 GeV(4.467)
190.4 GeV (3.108)
193.8 GeV (4.488)
0.378 (1.292)
-0.1098 (0.9465)
-0.0299 (1.377)
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Calibration Plots
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Results

• using 200 ttbar signal events
• measure the top quark mass without bias
• expected statistical uncertainty ? 3.2 GeV
• next steps
• include backgrounds
• apply to p17 data

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