Measurement of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar{t}$\end{document} production cross section in the tau + jets channel using the ATLAS detector

Abstract

A measurement of the top quark pair production cross section in the final state with a hadronically decaying tau lepton and jets is presented. The analysis is based on proton–proton collision data recorded by the ATLAS experiment at the LHC, with a centre-of-mass energy of 7 TeV. The data sample corresponds to an integrated luminosity of 1.67 fb⁻¹. The cross section is measured to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma_{t\bar{t}} = 194 \pm18\ (\mbox{stat}.) \pm46\ (\mbox{syst}.)~\mbox{pb}$\end{document} and is in agreement with other measurements and with the Standard Model prediction.

Introduction

Top quark pairs (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document}) are produced in abundance at the Large Hadron Collider (LHC) due to the high centre-of-mass energy of 7 TeV. The large sample of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events collected with the ATLAS detector makes it possible to study experimentally challenging decay channels and topologies. This letter describes a measurement of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} production cross section. The final state studied here consists of a hadronically decaying tau lepton (τ _had) and jets, corresponding to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar{t} \rightarrow [b \tau_{\mathrm{had}} \nu_{\tau}][bqq]$\end{document} decay, where b and q are used to denote b-quarks and lighter quarks, respectively. Such an event topology with a hadronically decaying tau lepton corresponds to approximately 10 % of all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} decays [1].

A \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} cross-section measurement in the final state with tau leptons makes it possible to probe flavour-dependent effects in top quark decays. It is also relevant to searches for processes beyond the Standard Model, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events with tau leptons in the final state are a dominant background. This measurement is particularly important for hypothetical charged Higgs boson production [2–5] in top quark decays, where the existence of a charged Higgs boson would lead to an enhancement in the cross section for the considered \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} final state. The measurement presented here is complementary to the previously published tau + lepton (electron or muon) channel measurement [6]. The most recent cross-section measurements of the tau + jets decay channel have been performed by the CDF and D0 collaborations in proton–antiproton collisions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt{s} = 1.96~\mbox{TeV}$\end{document} [7, 8]. This is the first measurement reported in this specific channel at the LHC.

In this analysis, events with at least five jets are selected, where two of the jets are identified as having originated from b-quarks. After identifying the two jets likely to come from the hadronic decay of one of the top quarks, one of the remaining jets is selected as the τ _had candidate from the other top quark. The τ _had contribution is separated from quark- or gluon-initiated jets with a one-dimensional fit to the distribution of the number of tracks associated with the τ _had candidate. Since the τ _had decays preferentially to one or three charged particles (and other neutral decay products), this variable provides good separation between hadronically decaying tau leptons and jets, as the latter typically produce a large number of charged particles. The main backgrounds to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} signal are multijet events, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events with a different final state or signal events where the wrong jet is chosen as the τ _had candidate. A small contribution from single-top and W+jets events is also present. The distributions for the backgrounds used in the fit are obtained with data-driven methods.

The ATLAS detector

The ATLAS detector [9] is a multipurpose particle physics detector with a forward-backward symmetric cylindrical geometry and a near-4π coverage in solid angle.1 The inner tracking system covers the pseudorapidity range |η|<2.5, and consists of a silicon pixel detector, a silicon microstrip detector (SCT), and, for |η|<2.0, a transition radiation tracker. The inner detector is surrounded by a thin superconducting solenoid providing a 2 T magnetic field along the beam direction. A high-granularity liquid-argon sampling electromagnetic calorimeter covers the region |η|<3.2. An iron/scintillator tile hadronic calorimeter provides coverage in the range |η|<1.7. The end-cap and forward regions, spanning 1.5<|η|<4.9, are instrumented with liquid-argon calorimeters for both electromagnetic and hadronic measurements. The muon spectrometer surrounds the calorimeters. It consists of three large air-core superconducting toroid systems and separate trigger and high-precision tracking chambers providing accurate muon tracking for |η|<2.7.

Data and simulation samples

The data used in this analysis were collected during the first half of the 2011 data-taking period and correspond to a total integrated luminosity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{L} = 1.67~\mbox{\mbox {fb$^{-1}$}}$\end{document}. The data sample was selected with a b-jet trigger that required at least four jets identified with |η|<3.2 and a transverse energy (E _T) above 10 GeV. Two of these jets were required to be identified as b-jets using a dedicated high-level-trigger b-tagging algorithm [10]. This trigger was enabled for only part of the 2011 data-taking period and is therefore the limiting factor in determining the integrated luminosity of the dataset used.

The selection efficiency for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t} \to \tau_{\mathrm{had}} + \mbox{jets}$\end{document} signal is derived from Monte Carlo (MC) simulations. The MC@NLO v4.01 [11] generator, with the parton distribution function (PDF) set CT10 [12], is used for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} signal. The theoretical prediction of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} cross section for proton–proton collisions at a centre-of-mass energy of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt{s} = 7~\mbox{TeV}$\end{document} is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma_{ t\bar {t} } = 167^{+17}_{-18}~\mbox{pb}$\end{document} for a top quark mass of 172.5 GeV. It has been calculated at approximate next-to-next-to-leading order (NNLO) in QCD with Hathor 1.2 [13] using the MSTW2008 90 % confidence level NNLO PDF sets [14], incorporating PDF and α _S uncertainties according to the MSTW prescription [15], and cross-checked with the next-to-leading-order + next-to-next-to-leading-log calculation of Cacciari et al. [16] as implemented in Top++ 1.0 [17]. Tau lepton decays are modelled with Tauola [18]. Samples of simulated events are also used to estimate the small contributions from W+jets, Z+jets, single-top-quark and diboson events, as described in Ref. [19]. The generated events were processed through the full ATLAS detector simulation using Geant4 [20, 21], followed by the trigger and offline reconstruction. The distribution of the number of pile-up events (i.e. collisions in the same, or nearby, bunch crossing as the hard-scattering event) is adjusted to match the scattering multiplicity measured in the data.

Event selection

Jets are reconstructed from clusters of calorimeter cells [22] using the anti-k _t algorithm [23, 24] with a radius parameter R=0.4. The jets are calibrated using transverse momentum- and η-dependent corrections obtained from simulation and validated with collision data [25]. Candidate events are required to contain at least five jets with a transverse momentum (p _T) larger than 20 GeV and |η|<2.5.

The identification of jets originating from b-quarks is performed using algorithms that combine secondary vertex properties and track impact parameters [26]. The algorithm identifies b-jets with an average efficiency of 60 % and provides a light-quark jet rejection factor of about 340 in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} topologies. The likelihood of misidentifying a τ _had as a b-jet in a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} event is approximately 5 %. The two jets with the highest b-tag probability are chosen as the event b-candidates; events with fewer than two b-jets are rejected.

The magnitude of the missing transverse energy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm {T}}^{\mathrm {miss}}$\end{document}) is reconstructed from energy clusters in the calorimeters. The calibration of each cluster depends on the type of physical object associated with the cluster. The transverse momentum of muons in the event is also taken into account. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm {T}}^{\mathrm {miss}}$\end{document} significance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{E_{\mathrm{T}}^{\mathrm{miss}}}$\end{document}) is defined as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm {T}}^{\mathrm {miss}} / (0.5~[\sqrt{\mathrm{GeV}}] \cdot\sqrt{ \sum E_{\mathrm{T}} })$\end{document}, where ∑E _T is the scalar sum of the transverse momentum of all objects. Using a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{E_{\mathrm{T}}^{\mathrm{miss}}}$\end{document} requirement instead of a direct \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm {T}}^{\mathrm {miss}}$\end{document} requirement allows the rejection of multijet events where the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm {T}}^{\mathrm {miss}}$\end{document} arises from energy resolution effects, while still retaining high efficiency for signal events with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm {T}}^{\mathrm {miss}}$\end{document} coming from particles which do not interact with the detector [27]. Candidate events are required to have \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{E_{\mathrm{T}}^{\mathrm{miss}}} > 8$\end{document}.

Events containing a reconstructed electron or muon [28, 29] with p _T>15 GeV and |η|<2.5 are vetoed to reduce the background due to events containing W bosons that decay to electrons or muons and to avoid overlap with other \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} cross-section measurements.

In each event, a single τ _had candidate is selected from the reconstructed jets using the following procedure. First, the reconstruction of the hadronically decaying top quark is attempted by selecting the three jets (including exactly one of the two b-candidates) which, when their four-momenta are added vectorially, give the highest p _T sum. The remaining jet with the highest p _T, excluding the remaining b-candidate, is selected as the τ _had candidate. Events where the τ _had candidate p _T is below 40 GeV are rejected.

The main contributions to the selected τ _had candidates in the signal region come from the signal (τ _had from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events), electrons from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events and misidentified jets from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document}, single-top-quark production, W+jets and multijet events. The contributions from Z/γ ^⋆+jets and diboson processes are negligible.

Data analysis

The majority of τ _had decays are characterised by the presence of one or three charged hadrons in the final state, which can be reconstructed as charged particle tracks in the inner detector. The number of tracks (n _track) originating from the interaction point associated with a τ _had candidate is used to separate the τ _had contribution from the misidentified jet background.

All selected tracks with p _T>1 GeV located in a core region spanning ΔR<0.2 around the jet axis are counted. To increase the discriminating power, tracks in the outer cone 0.2<ΔR<0.6 are also counted, using a variable p _T requirement that is dependent on both the ΔR of the outer track and the p _T of the core tracks. This variable p _T requirement is designed to reduce the contribution from pile-up and underlying event tracks, and is explained in Ref. [30]. The separation power of the n _track variable is illustrated in Fig. 1 where a comparison of the n _track distribution is shown for τ _had, electrons and misidentified jets from multijet events.

Fig. 1.

Distribution of n _track for τ _had from MC \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events (solid black line), electrons from MC \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events (dashed red line), and for jets from multijet events from data (blue triangles). The multijet event selection uses a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{E_{\mathrm{T}}^{\mathrm{miss}}}$\end{document} sideband region as described in Sect. 5. All distributions are normalised to unity (Color figure online)

To extract the signal from the n _track distribution, the data sample is fitted with three probability density functions (templates): a tau/electron template, a gluon-jet template and a quark-jet template. The τ _had component from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events constitutes the signal in the event sample. Real electrons from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events (either prompt or from leptonic tau decays) which failed to be rejected by the electron veto also contribute significantly to the event sample. The electron and τ _had templates are combined into a single tau/electron template to ensure a stable fit, using MC predictions to determine their relative contributions. The tau/electron template is obtained from simulated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events. The small expected contributions to the real tau/electron component of the fit from single-top-quark and W+jets events do not change the shape of the template.

The remaining significant contributions come from misidentified jets, and are separated into two templates. The gluon-jet template describes the QCD multijet processes which are dominated by gluon-initiated jets, and the quark-jet template describes the remaining processes (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document}, single-top quark and W+jets) that are enriched in quark-initiated jets.

The gluon-jet template is determined using a sideband region where the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{E_{\mathrm{T}}^{\mathrm{miss}}}$\end{document} requirement is changed to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$3 < S_{E_{\mathrm{T}}^{\mathrm{miss}}} < 4$\end{document}. This selection greatly enhances the contribution from multijet events, reducing other contributions (e.g. from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events) to less than 1 %. The regions defined by the selection \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2 < S_{E_{\mathrm{T}}^{\mathrm{miss}}} < 3$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$4 < S_{E_{\mathrm{T}}^{\mathrm{miss}}} < 5$\end{document} are also used to study any correlations between the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{E_{\mathrm{T}}^{\mathrm{miss}}}$\end{document} criteria and the n _track distribution.

The quark-jet template is obtained from a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} control sample where the τ _had candidate is replaced by a muon candidate. The reconstructed muon [29] is required to have p _T>20 GeV, |η|<2.5 and no jet within a distance ΔR=0.4. The requirement on the number of non-b-tagged jets is changed from three to two as the jet corresponding to the τ _had is now replaced by a muon. The other selection requirements are the same as for the signal region. This isolates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events with very high purity; the contribution from backgrounds is estimated from MC predictions to be at the 5 % level, and consists mainly of single-top-quark and W+jets events. The two highest-p _T jets that are not identified as b-jet candidates are selected as τ _had candidates. The template is corrected using MC simulations for differences in the transverse momentum distribution between the signal region and the control sample, and for the expected contribution to the control sample from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} dilepton events (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t} \rightarrow \mu + \tau_{\mathrm{had}} + X$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t} \rightarrow \mu + e + X$\end{document}).

Results

An extended binned-likelihood fit is used to extract the different contributions from the n _track distribution. To improve the fit stability, a soft constraint is applied to the ratio of quark-jet events to tau/electron events, which are dominated by the same process (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events). The constraint, based on MC predictions, is a Gaussian with a width of 19 % of its central value. This width was estimated based on studies of the associated systematic uncertainties using the same methodology as described in Sect. 7. The statistical uncertainties on the fit parameters are calculated using the shape of the fit likelihood. The systematic uncertainties on the shapes of the templates are propagated using a pseudo-experiment approach, taking into account the bin-by-bin correlations. This yields a final number of tau/electron events of 270 ± 24 (stat.) ± 11 (syst.).

The fit results are shown in Fig. 2. A comparison between the fit results, and the expected event yields from the MC predictions is presented in Table 1. The numbers are in good agreement.

Fig. 2.

The n _track distribution for τ _had candidates after all selection cuts. The black points correspond to data, while the solid black line is the result of the fit. The red (dashed), blue (dotted) and magenta (dash-dotted) histograms show the fitted contributions from the tau/electron signal, and the gluon-jet and quark-jet backgrounds, respectively (Color figure online)

Table 1.

Comparison of the numbers of events from MC expectations and from the results of the fit to the data for the three templates. The uncertainties on the MC expectations include the systematic uncertainties of the selection efficiency described in Sect. 7. No MC predictions are available for the gluon-jet contribution

Source	Number of events
tau/electron
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} (τ had)	170 ± 40
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} (electrons)	47 ± 11
Single top	12 ± 2
W+jets	9 ± 5
Total expected	240 ± 50
Fit result	270 ± 24 (stat.) ± 11 (syst.)
quark-jet
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} (jets)	540 ± 160
Single top	24 ± 4
W+jets	21 ± 12
Total expected	580 ± 160
Fit result	520 ± 97 (stat.) ± 78 (syst.)
gluon-jet
Fit result	960 ± 77 (stat.) ± 74 (syst.)

To extract the number of signal events, predictions from simulation are used to subtract the backgrounds from W+jets and single-top events (9 ± 5 and 12 ± 2, respectively) from the fitted number of tau/electron events. The number is then scaled by the expected ratio, N _τ/(N _τ+N _e), of τ _had and electrons passing the selection in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} sample. This ratio is estimated from MC simulation to be 0.78 ± 0.03 (stat.) ± 0.03 (syst.). This yields a final number of observed signal events of N _τ = 194 ± 18 (stat.) ± 11 (syst.).

The cross section is obtained using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma_{t\bar{t}} = {N_{\tau}}/({\mathcal{L} \cdot \varepsilon})$\end{document}. The efficiency (ε) is estimated from MC simulation to be (6.0 ± 1.4) ×10⁻⁴. It includes the branching fractions for the various \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} decays and the acceptance, and assumes Br(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document}→τ _had + jets) to be 0.098 ± 0.002 [1]. The efficiency is corrected for a 13 % difference between MC simulation and data in the trigger and b-tagging efficiencies [26]. The method used for obtaining the uncertainty on the cross section is detailed in Sect. 7.

The cross section is measured to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma_{t\bar{t}}= 194 \pm 18~(\mbox{stat}.) \pm 46~(\mbox{syst}.)~\mbox{pb}$\end{document}.

Systematic uncertainties

A summary of all systematic uncertainties on the cross section is given in Table 2.

Table 2.

Systematic uncertainties on the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} cross section

Source of uncertainty	Relative uncertainty
ISR/FSR	15 %
Event generator	11 %
Hadronisation model	6 %
PDFs	2 %
Pile-up	1 %
b-jet tagging efficiency	9 %
Jet energy scale	5 %
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm {T}}^{\mathrm {miss}}$\end{document} significance mismodelling	5 %
b-jet trigger efficiency	3 %
Jet energy resolution	2 %
Fit systematic uncertainties	4 %
Luminosity	4 %
Total uncertainty	24 %

The uncertainty on the selection efficiency due to the choice of the configuration for the MC simulation is estimated by using alternative MC samples and reweighting procedures. The difference in the efficiency obtained from various configurations is taken as the uncertainty. The uncertainty on the modelling of the ISR/FSR is taken into account by using AcerMC [31] samples with specific tunes aimed at conservatively varying the amount of parton showering [32]. The uncertainty due to the choice of the matrix element event generator is estimated by comparing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} samples generated using MC@NLO, Powheg [33–35], and Alpgen [36]. To study the impact of different hadronization models, events generated using Powheg are processed with two different hadronization programs: Herwig and Pythia. The uncertainty of the choice of PDFs is estimated using a number of current PDF sets [37].

Uncertainties on the simulation of the detector response are taken into account using dedicated studies of the reconstructed physics objects (electrons, muons, jets, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm {T}}^{\mathrm {miss}}$\end{document}). The uncertainties considered are associated with the jet energy scale, jet energy resolution, b-tagging efficiency, trigger efficiency and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm {T}}^{\mathrm {miss}}$\end{document} calculation [25, 26]. The uncertainty due to mismodelling of the lepton veto is estimated using the uncertainties on the muon and electron reconstruction efficiencies determined from independent data samples, and is found to be negligible.

To obtain the uncertainty on the fit results, variations are applied to the templates to describe various systematic effects. As the tau/electron template is taken directly from MC-simulated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events, the systematic uncertainties on this template are taken from estimates of the mismodelling of the simulation. The dominant contributions come from variations in the amount of ISR/FSR in the simulation (1 %), the modelling of the pile-up (1 %), and the statistical uncertainties (1 %). Uncertainties on the track reconstruction efficiency, jet energy scale, and the ratio of τ _had to electrons are found to be negligible. The quark-jet template is obtained from a μ+jets control sample of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} events in data. The dominant contributions to the uncertainty come from the statistical uncertainties (4 %), the difference in shape between the μ+jets template and the expected quark-jet distribution, estimated from MC samples (2 %), and the MC-based subtraction of the dilepton contribution (1 %). The uncertainty on the MC-based kinematic correction is found to be negligible. The gluon-jet template is derived from a background-dominated sideband region with small values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{E_{\mathrm{T}}^{\mathrm{miss}}}$\end{document}. The two sources of uncertainties are the dependence of the template on the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{E_{\mathrm{T}}^{\mathrm{miss}}}$\end{document} criterion of the control region, obtained by varying the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{E_{\mathrm{T}}^{\mathrm{miss}}}$\end{document} requirement (1 %), and the statistical uncertainty of the control region (1 %). The total systematic uncertainty on the fit is found to be 4 %.

The uncertainty on the luminosity is calculated to be 3.7 % as described in Ref. [38]. The total systematic uncertainty on the cross section is 24 %.

Conclusions

This letter presents a measurement of the top quark pair production cross section in the final state corresponding to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar{t} \rightarrow [b \tau_{\mathrm{had}} \nu_{\tau}][bqq]$\end{document} decay. The measurement uses a dataset corresponding to an integrated luminosity of 1.67 fb⁻¹ of proton–proton collision data at a centre-of-mass energy of 7 TeV recorded by the ATLAS experiment at the LHC. The signal has been extracted by fitting the number of tracks associated with tau lepton candidates using templates derived from simulation for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar{t}$\end{document} signal and from the data for the backgrounds.

The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t\bar {t}$\end{document} production cross section is measured to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma_{t\bar{t}}= 194 \pm 18\ (\mbox{stat}.) \pm 46\ (\mbox{syst}.)~\mbox{pb}$\end{document}. This result is compatible with the highest precision ATLAS measurements [39, 40], and with the result of 186 ± 13 (stat.) ± 20 (syst.) ± 7 (lum.) pb obtained in the complementary tau + lepton (electron or muon) channel [6]. It is also in good agreement with the theoretical prediction of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$167_{-18}^{+17}~\mbox{pb}$\end{document}.