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A template fit technique to A template fit technique to measure the top quark measure the top quark

mass in the l+jets channelmass in the l+jets channel

Ulrich Heintz, Vivek PariharUlrich Heintz, Vivek Parihar

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OverviewOverview OBJECTIVE: develop a fast algorithm for the OBJECTIVE: develop a fast algorithm for the

measurement of the top quark mass in l + jets channel measurement of the top quark mass in l + jets channel to complement the computing intensive matrix element to complement the computing intensive matrix element technique.technique.

currently studied a template fit method using currently studied a template fit method using only ttbar only ttbar signal MC in the e + jets channelsignal MC in the e + jets channel

results shown here are based on the output of HITFIT results shown here are based on the output of HITFIT from Pieter Houben’s Monte Carlo data files (January from Pieter Houben’s Monte Carlo data files (January version)version)

event selection is that used by the Ideogram analysis event selection is that used by the Ideogram analysis by Pieter and Michele.by Pieter and Michele.

templates are constructed using the mass for each templates are constructed using the mass for each event for which HITFIT obtains the lowest (positive) event for which HITFIT obtains the lowest (positive) chi-squared.chi-squared.

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PART 1PART 1

Parametrization of Templates :Parametrization of Templates :

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mtop=155 GeV

155

TemplatesTemplates

mtop=195 GeV

mtop=170 GeV

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TemplatesTemplates

mtop=195 GeV

mtop=170 GeV

mtop=155 GeV

Each template is fitted with Landau convoluted with Gaussian + Pure Gaussian with a total of 7 parameters

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Fit ParametersFit Parameters show that parameters vary smoothly with mshow that parameters vary smoothly with m toptop

Landau * GaussLandau * Gauss

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Fit ParametersFit ParametersGaussianGaussian

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2 D Simultaneous Fit2 D Simultaneous Fit

express the 7 parameters as functions of express the 7 parameters as functions of mmtoptop

fit all templates simultaneouslyfit all templates simultaneously

Function used : Landau*Gaussian + Gaussian with total 7 internal parameters.

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2 D Simultaneous Fit2 D Simultaneous Fit resultsresults

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                     a4*a7Most Probable        a8+ a9*(mtop-175)Sigma                      a10

a0 = 8.82   ;    a1= 0.02    ;  a2 = 162.82    ;  a3 = 0.49   ; a4 = 4.69 ;   a5 = 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 = 11.619.16  ;   a6 = 0.17   ; a7 = 0.14 ;   a8 = 175.32 ;   a9 = 0.96  ;    a10 = 11.6

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2 D Simultaneous Fit2 D Simultaneous Fit superimpose template parametrizationssuperimpose template parametrizations

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PART IIPART II

Ensemble Tests :Ensemble Tests :

-> -> 1000 ensembles with 200 ttbar events each, 1000 ensembles with 200 ttbar events each,

randomly picked from therandomly picked from the data files.data files.

-> parametrized templates used to calculate the -> parametrized templates used to calculate the negative log likelihood for each ensemble of 200 events.negative log likelihood for each ensemble of 200 events.

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Ensemble testsEnsemble tests - log likelihood plot and quadratic fit for a - log likelihood plot and quadratic fit for a

sample ensemble (msample ensemble (mtoptop = 155 GeV) = 155 GeV)

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

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Ensemble testsEnsemble tests

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

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154.4 GeV (3.31) 159.9 GeV(2.986) 165 GeV (2.919)

0.2046 (1.116) 0.0394 (1.002) 0.0171 (0.974)

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169.3 (3.2) 174.2 (3.289) 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)

-0.0299 (1.377) -0.1098 (0.9465) 0.378 (1.292)

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Calibration Plots :Calibration Plots :

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ResultsResults using 200 ttbar signal events using 200 ttbar signal events

measure the top quark mass without biasmeasure the top quark mass without bias expected statistical uncertainty expected statistical uncertainty 3.2 GeV 3.2 GeV

next stepsnext steps include backgroundsinclude backgrounds apply to p17 dataapply to p17 data

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