Top-quark mass measurements using the ATLAS detector at the LHC

The most recent results of the top-quark mass measurements with the ATLAS detector using data collected from proton-proton collisions at the Large Hadron Collider are presented. Although several decay modes of the top-quark pairs have been used in ATLAS for top-quark mass measurements, only the latest results are presented (single lepton and dilepton channels). The top-quark pole mass from the $t\overline{t}$ cross-section measurement in the dilepton channel and the top-antitop mass difference measurement in the single-lepton channel are also shown. The systematic uncertainties associated to these measurements are discussed in some detail.


Introduction
The top quark is the heaviest elementary particle in the Standard Model and its mass is a fundamental parameter in quantum chromodynamics. Its value must be determined experimentally and its precise measurement has a large impact in the computation of electroweak corrections.
The ATLAS detector [1] is a general purpose detector located at the Large Hadron Collider (LHC) [2]. Over the last years, the ATLAS Collaboration has measured the top-quark mass with increasing precision, with the following most recent analyses: • Top-quark mass measurement in the tt single lepton channel [3]; • Top-quark mass measurement in the tt dilepton channel [4]; • Top-quark pole mass from the tt cross-section measurement in the dilepton channel [5]; • Top-antitop mass difference in the tt single lepton channel [6].
Almost all the analyses use the template method to extract the variable of interest from data, where the templates are built with the help of Monte-Carlo simulations.

Top-quark mass measurement in the tt single lepton channel
The analysis [3] is performed using data at a centreof-mass energy of √ s = 7 TeV, which amounts to an integrated luminosity of 4.7 fb −1 .
A three-dimensional template technique is used, where the m reco top , the jet scale factor (JSF) and the b-jet scale factor (bJSF) are measured simultaneously by fitting the distribution of three observables reconstructed using a kinematic likelihood fit: the top-quark mass, the W-boson mass and the ratio between the average transverse momentum of the b-tagged jets and the average transverse momentum of the two jets of the W-boson hadronic decay, R reco b (see Figure 1). The reconstructed top-quark mass is expected to be sensitive to the top-quark mass, the JSF and the bJSF, while the reconstructed W-boson mass is expected to only depend on the JSF. Finally, the reconstructed R lb is expected to depend on the bJSF and the top-quark mass.
Applying the three-dimensional template technique to data, the top-quark mass is measured to be: m top = 172.31 ± 0.75(stat) ± 1.35(syst) GeV, (1) where the statistical uncertainty also include the uncertainty from the JSF and bJSF measurements.  By comparing a two-dimensional template analysis (where the b-jet energy scale is fixed) to the threedimensional template analysis (where the b-jet energy scale is allowed to vary), it is shown that the three-dimensional template technique significantly reduces the b-jet energy scale uncertainty from 0.92 GeV to 0.08 GeV and the hadronization uncertainty from 1.30 GeV to 0.27 GeV. There is a drawback, however, since the b-tagging efficiency and mistag rate uncertainty increases from 0.17 GeV to 0.81 GeV. But the overall effect is a total systematic uncertainty improvement of 33%, reducing from 2.02 GeV to the final 1.35 GeV quoted in this measurement.

Top-quark mass measurement in the tt dilepton channel
The dilepton channel does not allow a direct mass reconstruction, but has the advantage that it offers a very clean signal and a very good signal-to-background ratio. The analysis [4] is performed using 4.7 fb −1 of 7 TeV data.
The template method is used to measure the topquark mass using the m b variable, defined as the average invariant mass of the two lepton-b-jet systems in the dileptonic channel. Since the correct pairing between the two leptons and the two b-jets is not known, the values of m b for both combinations are computed and the smallest value is taken. This algorithm gives the correct pairing 77% of the times.
The m b distribution of the signal is modelled as the sum of a Gaussian function and a Landau function for the signal, while th background is modelled as a Landau function. It is to be noted that the background is very small, contributing only 3% to the total number of events. The template fit function for different input topquark masses is shown in Figure 2.
Applying the template fit to data gives the value (see Figure 3): m top = 173.09 ± 0.64(stat) ± 1.50(syst) GeV, (2) where the systematic uncertainty is dominated by the jet energy scale (0.89 GeV) and the b-jet energy scale (0.71 GeV).

Top-quark pole mass from the tt cross-section measurement in the dilepton channel
The ATLAS collaboration has performed a tt crosssection measurement in the dilepton channel using  With the top-quark mass measurements reaching precisions of the order 1 GeV, one should remember that the values of these reconstructed top-quark masses are different from the value of the top-quark pole mass. This difference has been estimated to be of the order of 1 GeV [7].
The top-quark pole mass, i.e., the mass of the top quark as a free particle, can be computed from the tt cross section. The idea is to exploit the strong dependence of the tt cross section on the top-quark pole mass. This dependence is obtained for both centre-of-mass energies using different parton density function (PDF) models, as shown in Figure 4. Notice that the measured cross section does not depend on the assumed input Monte-Carlo top-quark mass, ensuring that the method used to measure the tt cross section is independent from the value of the top-quark pole mass. This requirement is important in order to extract the top-quark pole mass from the measured value of the tt cross section.
The dependence of the tt cross section on the topquark pole mass is parametrized as:  Once the parameters are computed, the pole mass is extracted by maximizing the likelihood: where L, σ tt and σ theo tt depend on m pole top . The function G (x|µ, ρ) is a Gaussian probability density in the variable x with mean µ and standard deviation ρ.
The top-quark pole mass measurements using different PDF sets and the two different cross sections are shown in Table 1. By combining both measurements, the top-quark pole mass is found to be: m pole top = 172.9 +2.5 −2.6 GeV.

Top-antitop mass difference in the tt single lepton channel
The analysis [6] is performed in the tt single-lepton channel using data at a centre-of-mass energy of √ s = 7 TeV, which amounts to an integrated luminosity of 4.7 fb −1 .
A kinematic fit is used to fully reconstruct the top quark pair in each event, where the mass values of the top quark and the antitop quark are obtained from this fit. Therefore, the difference between the top quark and antitop-quark masses can be defined as: where q is the charge of the lepton. As one of the top quarks in the tt pair decays hadronically and the other one decays leptonically, m fit b ν is the fitted mass of the leptonic decay while m fit b j j is the fitted mass of the hadronic decay.
The distribution of ∆ fit m is parametrized as the sum of two Gaussians for the signal, and as a single Gaussian function for the background. The signal templates are shown in Figure 5.   Applying the template fit to data (see Figure 6), the measured mass difference between the top quark and the antitop quark is: ∆m tt = 0.67 ± 0.61(stat) ± 0.41(syst) GeV.
The systematic uncertainty is completely dominated by the b-fragmentation model. This uncertainty addresses differences in the detector response to jets originating from b andb quarks. In order to evaluate this effect, events were generated using Powheg and interfaced with Pythia. These events were then compared with the same generated events, but the b-hadron decays were simulated with EvtGen instead. Using this procedure, the b-fragmentation model uncertainty is estimated to be 0.34 GeV.