Measurements of the top-quark mass in fixed schemes and with alternative methods using the ATLAS and CMS detectors at the LHC

TL;DR

This paper reviews top-quark mass measurements in well-defined schemes using ATLAS and CMS data from the LHC at 7 and 8 TeV, employing advanced QCD calculations to improve precision.

Contribution

It introduces new measurements of the top-quark mass in fixed schemes using innovative methods and theoretical calculations with ATLAS and CMS data.

Findings

Top-quark mass measured with high precision in pole-mass scheme

Use of advanced QCD calculations for mass extraction

Comparison of results from different methods and datasets

Abstract

Selected topics of the top-quark mass measurements in well-defined schemes are presented. The measurements have been performed using data recorded with the ATLAS and CMS detectors at the LHC at proton-proton centre-of-mass energies of 7 and 8 TeV. Precision theoretical QCD calculations for both inclusive top-antitop quark pair production and top-antitop quark pair production with an additional jet to extract the top quark mass in the pole-mass scheme have been used.

Figures

Tables

Table 1. Table 1: Top-quark pole mass measured by CMS at NNLO+NNLL extracted by confronting the measured t ​ t ¯ 𝑡 ¯ 𝑡 t\overline{t} production cross section at 7 and 8 TeV  [ 20 , 21 , 22 ] . The obtained combined m t p ​ o ​ l ​ e superscript subscript 𝑚 𝑡 𝑝 𝑜 𝑙 𝑒 m_{t}^{pole} results are also listed ( s = 𝑠 absent \sqrt{s}= 7 + s = 𝑠 absent \sqrt{s}= 8 TeV).

PDF	$m_t^{pole}$ ($\sqrt{s}=$ 7 TeV) [GeV]	$m_t^{pole}$ ($\sqrt{s}=$ 8 TeV) [GeV]	$m_t^{pole}$ ($\sqrt{s}=$ 7 + $\sqrt{s}=$ 8 TeV) [GeV]
NNPDF3.0 [23]	173.4 ${\pm }_{2.0}^{2.0}$	173.9 ${\pm }_{2.0}^{1.9}$	173.6 ${\pm }_{1.8}^{+1.7}$
MMHT2014 [25]	173.7 ${\pm }_{2.1}^{2.0}$	174.2 ${\pm }_{2.2}^{1.9}$	173.9 ${\pm }_{1.9}^{+1.8}$
CT14 [24]	173.9 ${\pm }_{2.4}^{2.3}$	174.3 ${\pm }_{2.4}^{2.2}$	174.1${\pm }_{2.2}^{+2.1}$

Table 2. Table 2: Measurements performed by ATLAS of m t p ​ o ​ l ​ e superscript subscript 𝑚 𝑡 𝑝 𝑜 𝑙 𝑒 m_{t}^{pole} at NNLO+NNLL extracted by confronting the measured production cross section σ t ​ t ¯ subscript 𝜎 𝑡 ¯ 𝑡 \sigma_{t\overline{t}} with predictions employing different PDF sets.

PDF	ATLAS $m_t^{pole}$ $\sqrt{s}=7$ TeV [GeV]	ATLAS $m_t^{pole}$ $\sqrt{s}=8$ TeV [GeV]
C10 NNLOCT10 NLO [34]	171.4 $\pm$ 2.6	174.1 $\pm$ 2.6
MSTW 68 % NNLO [35]	171.2 $\pm$ 2.4	174.0 $\pm$ 2.5
NNPDF2.3 5f FFN [36]	${171.3}_{-2.3}^{+2.2}$	174.2 $\pm$ 2.4

Full text

1 INTRODUCTION

The top quark is by far the heaviest known fermion and the heaviest known fundamental particle. It plays an important role in the Standard Model (SM). Precise measurements of the top-quark mass ($m_{t}$) provide a key input to consistency tests of the SM. The mass of the Higgs boson and the top quark are also important parameters in the determination of the vacuum stability [1, 2].

Nowadays, the most precise determinations of $m_{t}$ have been achieved experimentally from kinematical reconstruction of the measured top-quark decay products, e.g. measuring the semi-leptonic decay channel of top-antitop quark pairs ($t\overline{t}$), where one top quark decays into a b quark, a charged lepton and its neutrino and the other top quark decays into a b quark and two u/d/c/s quarks, yielding a value of $m_{t}=$ 172.35 $\pm$ 0.51 GeV [3]. These $m_{t}$ determinations, however, have not been linked so far in an unambiguous manner to a Lagrangian top-quark mass in a specific renormalization scheme as employed in perturbative calculations in quantum chromodynamics (QCD), electroweak fits, or any theoretical prediction in general [4, 5, 6]. The values of $m_{t}$ extracted using these schemes are usually identified with the top-quark pole mass, $m_{t}^{pole}$. Present studies estimate differences between the two top-quark mass definitions, $m_{t}$ and a theoretically well defined short-distance mass definition at a low scale (e.g. $m_{t}^{pole}$), of about 1 GeV.

In addition to direct $m_{t}$ measurements as mentioned above, the mass dependence of the QCD prediction for the cross section ($\sigma_{t\overline{t}}$) can be used to determine $m_{t}$ by comparing the measured to the predicted $\sigma_{t\overline{t}}$ [7, 8, 9, 10, 11, 12]. Although the sensitivity of $\sigma_{t\overline{t}}$ to $m_{t}$ might not be strong enough to make this approach competitive in precision, it yields results affected by different sources of systematic uncertainties compared to the direct $m_{t}$ measurements and allows for extractions of $m_{t}$ in theoretically well-defined mass schemes. The values extracted using these methods are usually identified with the top-quark pole mass.

This distinction of the theoretical description of the measured parameter, e.g. either the parameter in the underlying Monte Carlo (MC) generator, $m_{t}^{MC}$ (or simply $m_{t}$), the mass term in the top-quark propagator, $m_{t}^{pole}$, or the mass in a well defined low-scale short distance scheme [4, 13], is recently gaining in importance.

In the following, selected $m_{t}^{pole}$ measurements performed by the ATLAS [14] and CMS [15] experiments at LHC [16] using data at proton-proton (pp) centre-of-mass energies of 7 and 8 TeV, are presented.

2 TOP-QUARK POLE MASS MEASUREMENTS

In contrast to the standard kinematical reconstruction of the measured top-quark decay product methods mentioned above, cross-section-like observables can be used to compare QCD predictions depending on $m_{t}^{pole}$, with unfolded data. The unfolding removes detector effects, and, in addition these measurements benefit from the larger independence from the mass definition in the used MC generators. For the total cross-section measurements, however, a 5% uncertainty translates into a 1% uncertainty in the top-quark mass [17] and the difference from going from next-to-leading order (NLO) to next-to-next-to-leading order (NNLO) predictions is even larger ($\sim$ 10%). Experimentally the challenges lie in the unfolding of the data and in the absolute normalization. Furthermore measurements of $m_{t}^{pole}$ involving new shape-like observables as proposed in [18] can help reduce both theoretical and experimental uncertainties.

2.1 Measurements of Top-Quark Pole Mass in $t\overline{t}$ Di-Lepton Events

The measurements of the $t\overline{t}$ production cross-section, $\sigma_{t\overline{t}}$, together with the NNLO prediction in QCD including the resummation of next-to-next-to-leading-logarithmic (NNLL) soft gluon terms [19], are used to determine the top-quark pole mass. Most of such measurements are performed in the electron-muon ($e$ - $\mu$) channel, where each W boson from the top quark decays into a lepton and a neutrino. Events are required to contain an oppositely charged $e$ - $\mu$ pair. The restriction to the di-lepton channel allows obtaining a particular clean $t\overline{t}$ event sample. The value of $m_{t}^{pole}$ is determined from the $\sigma_{t\overline{t}}$ measurements in pp collisions at centre-of-mass energies of $\sqrt{s}=7$ TeV and $\sqrt{s}=8$ TeV with the CMS and ATLAS detector at LHC. Both experiments assume a top-quark mass of $m_{t}^{MC}=172.5$ GeV in simulations to extract the reconstruction efficiency.

2.1.1 CMS Top-Quark Pole Mass Measurements

Compared to previous $m_{t}^{pole}$ measurements at 7 TeV [20] and at 8 TeV [21] the latest CMS results [22] include the full CMS data samples with integrated luminosities of 5.0 $fb^{-1}$ (7 TeV) and 19.7 $fb^{-1}$ (8 TeV). The value of $m_{t}^{pole}$ at NNLO+NNLL is extracted by confronting the measured cross section $\sigma_{t\overline{t}}$ at 7 and 8 TeV with predictions employing different parton density function (PDF) sets: NNPDF3.0 [23], CT14 [24], and MMHT2014 [25]. The obtained $m_{t}^{pole}$ values are listed in Table 1. The contributions from uncertainties on the CT14 PDF set are scaled to 68% confidence level.

A weighted average is calculated, taking into account all systematic uncertainty correlations between the measured cross sections at 7 and 8 TeV and assuming 100% correlated uncertainties for the theory predictions at the two energies. The combined $m_{t}^{pole}$ results are listed in Table 1 and are in good agreement with each other and the world average value [26].

Figure 1 shows the combined likelihood of the measured and predicted dependence of the $t\overline{t}$ production cross section on $m_{t}^{pole}$ for 7 (left plot) and 8 TeV (right plot).

In another measurement at $\sqrt{s}=$ 8 TeV CMS [27] uses a folding technique to map fixed order QCD calculations depending on $m_{t}^{pole}$ as implemented in the Monte Carlo for Femtobarn calculation MCFM [28], to predict the shape in $m_{lb}^{min}$. The top quark decay chain considered in this analysis is $t\to Wb$ followed by $W\to l\nu$. Neglecting both leptons and b-quark masses, at leading order the quantity $m_{lb}$ is directly related to $m_{t}$ and the mass of the W boson, $m_{W}$, as follows: $m_{lb}^{2}=\frac{m_{t}^{2}-m_{w}^{2}}{2}(1-\cos\theta_{lb})$. Here, $\theta_{lb}$ is the opening angle between the lepton and the b quark in the W-boson rest frame. The distribution of $m_{lb}$ has an end point at $max(m_{lb})\sim\sqrt{m_{t}^{2}-m_{W^{\prime}}^{2}}$, i.e. around 153 GeV for a top-quark mass of 173 GeV. In the analysis, $m_{lb}$ is reconstructed by choosing the permutation that minimizes the value of $m_{lb}$ in each event and only the b-jet candidate with the highest transverse momentum $p_{\perp}$ is considered together with both leptons ($e$ and $\mu$). Only one top quark in each event is used. In this particular definition, the combination yielding the smallest $m_{lb}$ in the event is kept, and referred to as $m_{lb}^{min}$, shown in Figure 2. The response matrices in $m_{lb}^{min}$ are obtained from fully simulated events obtained using the matrix element generator MADGRAPH 5.1.5.11 [29] with MADSPIN [30] for the decay of heavy resonances, PYTHIA 6.426 [31] for parton showering; the MC events have been passed through a full simulation of the CMS detector based on GEANT [32] (combination called MADGRAPH + PYTHIA + GEANT). By using the information on the rate of events alone a value of $m_{t}=171.4\pm 0.4_{stat}\pm 1.0_{syst}$ GeV is measured. Combining the results obtained using rate+$m_{lb}^{min}$ shape fits one is able to extract $m_{t}=173.1^{1.9}_{1.8}$ GeV. These results can be compared to the mass extraction from the same dataset via the total cross-section calculated at NNLO.

2.1.2 ATLAS Top-Quark Pole Mass Measurements

ATLAS also extracts $m_{t}^{pole}$ at NNLO+NNLL by confronting the measured production cross section $\sigma_{t\overline{t}}$ at 7 and 8 TeV with predictions employing different PDF sets [33]: CT10 NLO [34], MSTW 2008 68% CL NLO [35], and NNPDF 2.3 NLO [36]. The extraction of $m_{t}^{pole}$ is performed by maximizing a Bayesian likehood function separately for each PDF set and centre-of-mass energy to give $m_{t}^{pole}$ values shown in Table 2.

Finally $m_{t}^{pole}$ is extracted from the combined $\sqrt{s}=$ 7 and $\sqrt{s}=$ 8 TeV dataset. The resulting value using the envelope of all three considered PDF sets is $m_{t}^{pole}=172.9^{+2.5}_{-2.6}$ GeV. The results are shown in Figure 3, together with previous determinations using similar techniques from D0 [37] and CMS [38].

All extracted values are consistent with the average of measurements from kinematic reconstruction of $t\overline{t}$ events of $173.34\pm 0.76$ GeV [26], showing good compatibility of top-quark masses extracted using very different techniques and assumptions.

2.2 Measurements of Top-Quark Pole Mass in $t\overline{t}\,+$ 1-Jet Events

The normalized differential cross section for $t\overline{t}$ production in association with at least 1-jet is studied as a function of the inverse of the invariant mass of the $t\overline{t}\,+$ 1-jet system. This distribution is used by the ATLAS experiment [39] for a precise determination of $m_{t}^{pole}$. A new observable suggested in [18] is used in this measurement: ${\cal R}(m_{t}^{pole},\rho_{s})=\frac{1}{\sigma_{t\overline{t}+1jet}}\frac{d\sigma_{t\overline{t}+1jet}}{d\rho_{s}}(m_{t}^{pole},\rho_{s})$. The differential is taken in $\rho_{s}=2m_{0}/\sqrt{s_{t\overline{t}j}}$, that is the ratio of an arbitrary mass scale in the vicinity of $m_{t}$, here set to $m_{0}=170$ GeV, over the invariant $t\overline{t}+1\,$jet mass. $t\overline{t}$ events are selected at $\sqrt{s}=7$ TeV in a similar way as done for the the lepton+jets analysis [40], and an additional central jet with $p_{\perp}>50$ GeV is added. An SVD unfolding [41] with a response matrix from POWHEG+PYTHIA+GEANT4 [31, 32, 42] maps the measured $\rho_{s}$ to parton level. The unfolded distribution of ${\cal R}(m_{t}^{pole},\rho_{s})$ is shown in Figure 4 (left). The measurement of $m_{t}^{pole}=$ 173.7 $\pm 1.5_{stat}\pm 1.4_{syst}$ GeV is then obtained in a $\chi^{2}$-fit to $0.25<\rho_{s}<1$ with $\rho_{s}>0.675$ being the most sensitive bin, as shown in Figure 4 (right).

3 CONCLUSIONS

Measurements of $m_{t}^{pole}$ using alternative methods have been performed by both the ATLAS and CMS experiments using data collected at $\sqrt{s}=$ 7 and 8 TeV at LHC. The latest CMS [22] results obtained using di-lepton $t\overline{t}$ events at 7 and the 8 TeV give a $m_{t}^{pole}=$ 173.6 $\pm^{+1.7}_{1.8}$ GeV. The normalized differential cross section for $t\overline{t}$ production in association with at least 1-jet studied by the ATLAS experiment [39] at 7 TeV give a measurement of $m_{t}^{pole}=$ 173.7 $\pm 1.5_{stat}\pm 1.4_{syst}$ GeV. All the extracted values of $m_{t}^{pole}$ are consistent with $m_{t}$ measurements obtained using standard kinematic reconstruction of $t\overline{t}$ events.

4 ACKNOWLEDGMENTS

I would like to thank the ATLAS and CMS Collaborations for giving me the opportunity to give this talk at this conference and the top-quark groups conveners of both experiments for providing me the material presented here.