Measurement of the Top Quark Mass with 2.7 fb -1 of CDF Run II Data using only Leptons in the Lepton+Jets Decay Channel of Top Quark Pairs.

Victoria Giakoumopoulou, Nikos Giokaris, Arkadios Manousakis-Katsikakis and Costas Vellidis (Athens University)  [Contact]

Abstract [Link to public note]

The major source of systematic uncertainty in most methods of measurement of the top quark mass is the jet energy scale. A measurement of the top quark mass using 2.7 fb ^-1 of CDF Run II Data is presented, which uses only the transverse momentum P_T of the leptons in the lepton+jets decay channel of top quark pairs and is therefore free of the uncertainties related with the jet energy. The top quark mass M _top is measured using two methods: using the full shape of the lepton P_T distribution, which is the baseline or shape analysis method, and using only the mean value of the lepton P_T , which is the cross-checking or < P_T > analysis method. M _top is measured from electrons and muons separately with either method and the results from the two lepton samples are combined in the end. The results are (172.1 ± 7.9_stat ± 3.0_syst) GeV/c ² from the shape analysis method and (174.0 ± 7.9_stat ± 3.5_syst) GeV/c ² from the < P_T > analysis method.

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Introduction

The motivation for using only lepton (electron or muon) information to measure the top quark mass arises from the relatively large uncertainties associated with the jet calibration and the elaborate effort which is necessary for the jet calibration. The transverse momentum of the muons or transverse energy of the electrons coming from top quark decays is a variable which is free of these uncertainties and easy to implement. It is common to the semi-leptonic (or lepton+jets) and all-leptonic (or dilepton) decay channels of top quark pairs and therefore allows for measurements of M _top in the two channels using the same method. It can be precisely calibrated using dilepton data from Z boson decays, where the kinematics is simple and the lepton P_T is well constrained by the precisely known Z boson mass. In addition, from a theoretical point of view, a measurement of M _top from the lepton P_T is ultimately free of the limit of &Lambda _QCD ~ 300 MeV/c ² in the precision of any measurement of M _top using jets, which is imposed by parton fragmentation.

In order to measure M _top from the lepton P_T one has to determine the dependence of the lepton P_T spectrum on M _top . This information is provided by the Monte Carlo. The steps of the measurement are therefore simple: i) A set of Monte Carlo samples of top quark pairs is generated with different top quark mass per sample (signal templates) ii) A model sample for the background in the appropriate decay channel is built using Monte Carlo and eventually data driven methods (background template) iii) The relation of the transverse momentum of the leptons selected from the combined signal+background samples with the top quark mass input to the signal samples is parameterized, either using only the first moment of the lepton P_T distribution (< P_T > analysis method) or using the full shape of the lepton P_T distribution (shape analysis method) and iv) Given any lepton sample, data or Monte Carlo (for cross-checking), the parameterized relation of the lepton P_T with M _top is used to determine the value of the top quark mass which the given sample corresponds to.

The Monte Carlo shows that the dependence of < P_T > on M _top is linear. This relation is solved to provide a measurement of M _top from the lepton < P_T >. This method is simple and therefore useful for cross-checking and understanding, but makes limited use of the information provided by the lepton P_T spectrum and is sensitive to the composition of the lepton sample or, equivalently, to the background normalization. The full shape of the lepton P_T distribution can be accurately parameterized by a simple &Gamma function with two free parameters, the expected number p of leptons per measurement and the expected average P_T per lepton q:

Definition of the &Gamma function which models the lepton P_T distribution.

The Monte Carlo shows that the dependence of p and q on M _top is again linear. The alternative shape analysis method is therefore based on maximum likelihood fitting, where an unbinned likelihood is constructed from the shape functions of the signal (p and q linearly dependent on M _top) and the background (p and q constant) and a gaussian constraint is imposed on the expected number of background leptons. The likelihood is then maximized in M _top pluging the P_T values of the fit sample in the shape functions and letting also the expected numbers of signal and background leptons to vary. This method makes full use of the information provided by the lepton P_T spectrum and is also independent of the background normalization.

For the lepton P_T calibration, the global scale is first calibrated using di-electron and di-muon data from Z decays. The dilepton invariant mass is recontsructed from this data and its spectrum is fit with a function to accurately determine the centroid, which is then compared with the world average of the Z boson mass. The comparison provides a global correction to the lepton P_T . For the local scale, non-linear corrections in the spectrometer are studied using di-muon data from Z decays. The inverse of P_T is binned and the di-muon invariant mass is reconstructed in each bin and tuned to the world average of the Z boson mass. This provides a local correction to the lepton P_T . Having the momentum calibrated with the di-muon sample, non-linear corrections in the calorimeter, related with the measurement of the transverse energy of the electrons, are studied using electron + 1 jet data. This sample is dominated by W boson decays associated with one jet. The transverse energy E_T of the electrons is binned and the ratio E/P of the energy to the momentum of the electrons, corrected for the momentum calibration, is integrated over each bin. The fraction of integrated E/P of the data over integrated E/P of the Monte Carlo is studied as a function of E_T for each bin. Non-linear corrections to the electron E_T spectrum are derived from the slope of this fraction with respect to E_T .

The data used in the top quark mass measurement and the lepton calibrations were collected with the CDF II detector at the Tevatron collider at Fermilab.

Event Selection and Background Model

Events are selected by requiring one and only one tight central lepton (-1<&eta<1), electron or muon, with P_T > 20 GeV/c, at least four tight central jets (-2<&eta<2) with E_T > 20 GeV and high Missing E_T (MET > 20 GeV). At least one tight heavy flavor tag (b-tag) is also required for each selected event. This cut, with an efficiency of 40%, enhances the Signal-to-Background (S/B) ratio to 3.2 for the electrons and 4.5 for the muons. Good runs with the silicon detector on are required for the b-tagging. 472 electrons and 386 muons are thus selected from a data sample corresponding to an integrated luminosity of 2.7 fb ^-1.

A model for the expected background in the selected sample is built by a standard fit (Method II) also used for the official CDF measurement of the cross section for top quark pair production in the lepton+jets decay channel. Background contributions from W boson production associated with heavy flavor jets, Z boson production associated with light flavor jets, diboson production and single top production are modeled by the Monte Carlo (MC). The shape of the background contribution from W boson production associated with light flavor jets is modeled by the MC and its magnitude is etimated from the negative b-tag rate (mistags). The shape of the background contribution from fake leptons is determined from the data by inverting one of the cuts required for the definition of a tight lepton. Finally, the magnitude of the fakes background is estimated by a fit to the MET spectrum of the data, varying the amount of fakes and keeping all of the other background components fixed. The fit gives 112 ± 29 expected background electrons and 71 ± 9 expected background muons in the data sample of 2.7 fb ^-1. The expected fake electrons are 40 ± 10 and the expected fake muons are 0 ± 1.

The procedure for building the background model in the 4 or more jets multiplicity bin is repeated in the 1 and 2 jets bins, where the signal from top quarks is negligible and the model histograms can be tested against real data (control regions). The figures below show the background models in the signal region and the comparison of the corresponding models with the data in the control regions. The bin-by-bin ratios of the data histograms to the model histograms in the control regions are flat and consistent with unity, providing thus confidence for the expected background models in the signal region.

Background models (left plot) and their validation in the control regions (right two plots).

The Pythia generator is used for the MC signal samples and diboson background samples. The Alpgen+Pythia generator (Pythia here for parton showering only) is used for the MC W and Z background samples. The MadEvent+Pythia generator is used for the single top background.

Sensitivity of the Lepton Transverse Momentum to the Top Quark Mass

The figures below show the dependence of the lepton P_T on M _top . It is linear, within MC statistics, in all cases. The mean value < P_T > of the signal distribution has a slope of 17% with respect to M _top , which is reduced down to 13% for the signal+background distribution. From the shape parameters p and q, the expected number of leptons per measurement p shows a very weak, but still significant, dependence on M _top with a slope of -0.5%, whereas the expected average P_T per lepton q is much more sensitive to M _top with a slope of 10%.

From left to right: the dependence of the lepton < P_T > on M _top for electrons (signal only and signal+background) and muons (signal only and signal+background).

The dependence of the shape parameters of the lepton P_T distribution on M _top .

Systematic Uncertainties

• The systematic uncertainty due to the finite MC statistics is estimated by varying the < P_T > or shape parameters, according to the M _top measurement method, by ± 1 &sigma about their central values determined from the fits to the MC templates, taking into account the total anti-correlation of intercept and slope with respect to M _top (see above figures of sensitivity to M _top).
• The systematic uncertainty due to the global P_T scale calibration is estimated by varying the global P_T scale correction coefficient by ± 1 &sigma about its central values determined from the fits to the dilepton data and MC.
• The systematic uncertainty due to the local P_T scale calibration is estimated by varying the local P_T scale correction coefficients by ± 1 &sigma about their central values determined from the fits to the di-muon data (for the muons) and the e+1jet data (for the electrons), taking into account the total anti-correlation of intercept and slope with respect to P_T (see the Introduction).
• The systematic uncertainty due to the generator is estimated by comparing two different generators for the signal, Pythia and Herwig, adding in both cases the same backgrounds.
• The systematic uncertainty due to the initial/final state radiation (IFSR) of gluons is estimated by varying the radiation strength in Pythia by an amount appropriately tuned to various data sets.
• For the parton distribution functions (PDF) the Pythia MC is re-weighted from the LO default set CTEQ5L to the NLO set CTEQ6M and the LO 5% fraction of top pair events that Pythia produces via gluon fusion is also re-weighted to the NLO fraction of 10%. The uncertainty associated with that re-weighting is estimated from the mass shifts of the 20 CTEQ6M eigenvectors from the mass measurement with the nominal CTEQ6M set and the shift of the average of 6 &alpha_S values from the world average of &alpha_S(M_Z), all added in quadrature.
• The uncertainty due to the choice of the Q² scale in the W+jets MC background samples is estimated by multiplying and dividing the scale by a factor of 2.
• The uncertainty due to the jet energy scale (JES) is estimated by varying the jet energy scale by ± 1 &sigma of the combined jet energy corrections.
• The uncertainty due to pile-up is estimated by re-weighting the average number of vertices in the MC (1.5) to the average number of vertices in the data after period 8 (2.0).
• The uncertainty due to the fake electrons, which affects the shape of the background P_T distribution by changing the composition of the background sample, is estimated by varying the amount of anti-electrons (electrons selected with one cut inverted) in the background model by ± 25% (the corresponding Method II fit uncertainty).
• In the < P_T > analysis method, the uncertainty due to the overall normalization of the background is estimated by varying the total amount of background by the respective Method II fit uncertainty (± 25% for the electrons, ± 15% for the muons).
• In the < P_T > analysis method, a +(0.8 ± 0.3) GeV/c ² bias in the mass measurement from the electron sample and a +(1.4 ± 0.3) GeV/c ² bias in the mass measurement from the muon sample, detected in the mass residuals of pseudo-experiments, are corrected. The uncertainty due to this correction is ± 0.3 GeV/c ², as determined from the pseudo-experiments.

The tables below summarize the systematic uncertainties in the top quark mass measured from each sample, electrons or muons, and combined together.

Systematic errors per sample (e/&mu) in the shape analysis. Additional uncertainties of ± 3.0 GeV/c ² (electrons) and ± 0.9 GeV/c ² (muons) from the background normalization and ± 0.3 GeV/c ² (electrons) and ± 0.3 GeV/c ² (muons) from the bias correction are added in the < P_T > analysis.

Systematic errors for the combined samples in the shape analysis. Additional uncertainties of ± 1.8 GeV/c ² from the background normalization and ± 0.2 GeV/c ² from the bias correction are added in the < P_T > analysis.

Results

The tables below summarize the top quark mass measurements from the CDF Run II Data of 2.7 fb ^-1 and the respective corrections.

Summary of all corrections applied to the top quark mass measurements.

Summary of the top quark mass measurements before and after all corrections are applied. The errors are statistical only.

The figures below show the maximum likelihood fits to the CDF Run II Data of 2.7 fb ^-1, for the electron and muon samples separately.

Left: the fit to the electron data; right: the fit to the muon data.

Left: the log-likelihood curve of the fit to the electron data; right: the log-likelihood curve of the fit to the muon data.

The combination of the two fit results using the Best Linear Unbiased Estimator (BLUE) algorithm gives a final result of

This result is fully consistent with the corresponding result of (174.0 ± 7.9_stat ± 3.5_syst) GeV/c ² from the BLUE combination of the measurements using the < P_T > analysis method. The two results are also consistent with the world average of (172.4 ± 0.7_stat ± 1.0_syst) GeV/c ² as of July 2008.