Measurement of the tt¯ production cross section in the τ + jets final state in pp collisions at s√=8 TeV using the ATLAS detector

A measurement of the inclusive pp → t ¯ t þ X production cross section in the τ þ jets final state using only the hadronic decays of the τ lepton is presented. The measurement is performed using 20 . 2 fb − 1 of proton-proton collision data recorded at a center-of-mass energy of ﬃﬃﬃ s p ¼ 8 TeV with the ATLAS detector at the Large Hadron Collider. The cross section is measured via a counting experiment by imposing a set of selection criteria on the identification and kinematic variables of the reconstructed particles and jets, and on event kinematic variables and characteristics. The production cross section is measured to be σ t ¯ t ¼ 239 (cid:2) 29 pb, which is in agreement with the measurements in other final states and the theoretical predictions at this center-of-mass energy.

A measurement of the inclusive pp → tt þ X production cross section in the τ þ jets final state using only the hadronic decays of the τ lepton is presented. The measurement is performed using 20.2 fb −1 of proton-proton collision data recorded at a center-of-mass energy of ffiffi ffi s p ¼ 8 TeV with the ATLAS detector at the Large Hadron Collider. The cross section is measured via a counting experiment by imposing a set of selection criteria on the identification and kinematic variables of the reconstructed particles and jets, and on event kinematic variables and characteristics. The production cross section is measured to be σ tt ¼ 239 AE 29 pb, which is in agreement with the measurements in other final states and the theoretical predictions at this center-of-mass energy. DOI: 10.1103/PhysRevD.95.072003

I. INTRODUCTION
An important component of the Large Hadron Collider (LHC) [1] physics program is the measurement of the properties of the top quark, which is the most massive fundamental particle observed to date. With approximately one top-quark pair produced every second, the data sample used in this analysis is significantly larger than previously available samples, allowing for precise measurements of top-quark properties using final states that were previously limited by their statistical uncertainty. This article reports on a measurement of the tt production cross section in the τ þ jets final state, where the hadronic final states of the τ lepton (τ had ) are used exclusively. This measurement, which is of comparable precision to the μ þ jets and e þ jets cross-section measurements by the ATLAS Collaboration [2], provides a cross-check of the tt production cross-section measurements in the other final states. In addition, differences between measurements or between measurement and theory could lead to the discovery of non-Standard-Model physics or to limits on its possible extensions. Previous measurements in this final state have been performed by the D0 [3] and CDF [4] collaborations at the Tevatron operating at ffiffi ffi s p ¼ 1.96 TeV and by the ATLAS [5] and CMS [6] collaborations at the LHC operating at ffiffi ffi s p ¼ 7 TeV. Besides the measurement in the l þ jets (l ¼ e, μ, τ) final state at ffiffi ffi s p ¼ 8 TeV, the tt production cross section has also been measured in the dilepton (e þ e − , μ þ μ − , and e AE μ ∓ ) final state by the ATLAS and CMS collaborations [7,8]. Since the different channels in which this measurement has been performed have different backgrounds and systematic uncertainties, each measurement serves as a cross-check of the others. The final state of the process used in this measurement, tt → τ þ jets, includes one top quark decaying as t → Wb → τν τ b while the other decays as t → Wb → qq 0 b, leading to the final-state topology of one τ lepton, an imbalance of momentum in the plane transverse to the beam axis (E miss T ), and four quark jets with two of these being b-quark jets.
The decay t → τν τ b provides a unique system in which to investigate the couplings of the third-generation fermions-the top and bottom quarks, the τ lepton, and the τ neutrino ν τ -in a single process. In the framework of the Standard Model (SM), the branching ratio (BR) of the top quark decaying to a W boson and a b quark is approximately 100%. Hence, the final state is determined by the SM BRs of the W boson, which are well measured [9]. In the SM, electroweak symmetry-breaking introduces mass-and flavor-dependent couplings. Since the top quark is the most massive quark and the τ lepton the most massive lepton, these fermions along with the b quark have the largest Yukawa couplings to the Higgs boson and, hence, could lead to non-SM mass-or flavor-dependent couplings that can change the top-quark decay rate into final states with τ leptons. Therefore, any observed deviation in the BR of t → τν τ b from that predicted by the SM would be an indication of non-SM physics. For example, in type-2 two-Higgs-doublet models (2HDM) [10], such as required by the minimal supersymmetric Standard Model [11], the top quark can have a significant BR to a charged Higgs boson (H AE ) and a b quark if m H AE < m top − m b . For large values of tan β, the ratio of the vacuum expectation values of the two Higgs doublets, the charged Higgs boson preferentially decays to τν τ . This thereby increases the BR of t → τν τ b relative to the SM prediction and leads to a larger measured value of σ tt × BRðtt → τ þ jetsÞ [12][13][14]. Small values of tan β, however, would decrease the number of tt → τ þ jets events relative to the SM prediction.
The 2HDM can also produce an excess of t → τ þ X decays if flavor-changing neutral couplings are allowed as in type-3 models [15,16]. For example, this allows t → cH and if the Higgs boson decays as H → τ þ τ − , an excess of events with t → τ þ X decays would be observed relative to the SM. The SM predicts BRðt → cHÞ ≈ 10 −15 [17], whereas type-3 models predict BRðt → cHÞ to be as large as 10 −3 [17][18][19].
This article presents an analysis using the τ had þ jets final state to measure the tt production cross section in ffiffi ffi s p ¼ 8 TeV proton-proton (pp) collisions. The data sample for this measurement was recorded using the ATLAS detector and corresponds to an integrated luminosity of 20.2 fb −1 . The ATLAS detector is briefly described in Sec. II. Section III presents the data and simulated event samples used in this measurement. The reconstruction of jets, τ leptons, and missing transverse momentum is discussed in Sec. IV. The event selection is described in Sec. V and the methods used to estimate the backgrounds are discussed in Sec. VI. The calculation of the production cross section is given in Sec. VII and the estimation of the various systematic uncertainties is presented in Sec. VIII. The results of the analysis and the interpretations are discussed in Sec. IX. Finally, the analysis is summarized in Sec. X.

II. ATLAS DETECTOR
The ATLAS detector [20] at the LHC covers nearly the entire solid angle around the collision point. It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer incorporating three large superconducting toroid magnets. The inner detector (ID) is immersed in a 2 T axial magnetic field and provides charged-particle tracking in the range jηj < 2.5, where η is the pseudorapidity of the particle. 1 The high-granularity silicon pixel detector covers the interaction region and typically provides three position measurements per track. It is followed by the silicon microstrip tracker, which usually provides four twodimensional measurement points per track. These silicon detectors are complemented by the transition radiation tracker, which enables radially extended track reconstruction up to jηj ¼ 2.0. The transition radiation tracker also provides electron identification information based on the fraction of hits above a higher energy-deposition threshold corresponding to transition radiation.
The calorimeter system covers the pseudorapidity range jηj < 4.9. Within the region jηj < 3.2, electromagnetic calorimetry is provided by barrel and endcap highgranularity lead/liquid-argon (LAr) electromagnetic calorimeters, with an additional thin LAr presampler covering jηj < 1.8 to correct for energy loss in material upstream of the calorimeters. Hadronic calorimetry is provided by the steel/scintillator-tile calorimeter, segmented into three barrel structures within jηj < 1.7, and two copper/LAr hadronic endcap calorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules optimized for electromagnetic and hadronic measurements, respectively.
The muon spectrometer comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by superconducting air-core toroids. The precision chamber system covers the region jηj < 2.7 with three layers of monitored drift tubes, complemented by cathode strip chambers in the innermost layer of the forward region, where the background is highest. The muon trigger system covers the range jηj < 2.4 with resistive plate chambers in the barrel, and thin gap chambers in the end-cap regions.
A three-level trigger system is used to select interesting events [21]. The Level-1 trigger is implemented in hardware and uses a subset of detector information to reduce the event rate to a design value of at most 75 kHz. This is followed by two software-based trigger levels that together reduce the event rate to about 400 Hz.

III. DATA AND SIMULATION SAMPLES
The pp collision data sample used in this measurement was collected with the ATLAS detector at the LHC and corresponds to the full 20.2 fb −1 of integrated luminosity collected at this energy with the requirement of stable beam conditions and an operational detector.
In order to estimate the effects of detector resolution and acceptance on signal and background, and to estimate the backgrounds, a full GEANT4-based detector simulation is utilized [22,23]. In addition, to estimate the modeling uncertainties of the various physics processes in an efficient manner, a detector simulation using parameterized calorimeter showers is also used [24]. To account for an average of 20.7 interactions per bunch crossing, pp interactions are generated using PYTHIA v8.165 [25,26] and overlaid on the signal and background Monte Carlo (MC) simulation samples in accordance with the average observed number of interactions per bunch crossing. All simulated samples are reconstructed and analyzed with the same algorithms 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the z axis along the beam pipe. The x axis points from the IP to the center of the LHC ring, and the y axis points upwards. Cylindrical coordinates ðr; ϕÞ are used in the transverse plane, ϕ being the azimuthal angle around the z axis. The pseudorapidity is defined in terms of the polar angle θ as η ¼ − ln tanðθ=2Þ. Angular distance is measured in units of ΔR ≡ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðΔηÞ 2 þ ðΔϕÞ 2 p . and techniques as for the recorded pp collision data. Only events with at least one charged lepton (e, μ, τ) in the final state are generated.
To estimate the acceptance of the event selection for tt events, several MC samples are generated with the topquark mass set to m top ¼ 172.5 GeV. The nominal sample is generated using the next-to-leading-order (NLO) matrix element (ME) event generator POWHEG-BOX [27][28][29][30] with the CT10 [31] NLO parton distribution functions (PDF). The output of POWHEG-BOX is then processed by PYTHIA v6.426 [25] to perform the parton showering (PS), hadronization, and generation of the underlying event (UE). For the UE generation to agree with data, PYTHIA v6.426 uses the leading-order (LO) CTEQ6L1 PDF set [32] and a set of tuned parameters referred to as the Perugia 2011C tune [33]. To regulate high-p T radiation in POWHEG-BOX and provide ME/PS matching, the resummation damping factor h damp is set to m top [34]. The tt sample is normalized using the theoretical production cross section, which for pp collisions at ffiffi ffi s p ¼ 8 TeV is σ tt ¼ 253 þ13 −15 pb assuming a top-quark mass of 172.5 GeV. It has been calculated at next-to-next-to-leading order (NNLO) in α S including resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms with top++2.0 [35][36][37][38][39][40][41]. The systematic uncertainty in the cross section due to the uncertainties in the PDF and α S is calculated using the PDF4LHC prescription [42] with the MSTW2008 68% CL NNLO [43,44], CT10 NNLO [31,45], and NNPDF2.3 five flavor number [46] PDF sets and added in quadrature to the uncertainties due to the renormalization and factorization scales.
Systematic uncertainties associated with the tt modeling are evaluated using alternative sets of simulated events that are compared to the nominal sample, with the nominal and alternative sets processed using the parameterized detector simulation [24]. Since the choice of the ME event generator can affect the estimate of the acceptance, the ME event generator MC@NLO v4.01 [47] and the PS/UE simulator HERWIG v6.520 [48], with JIMMY v4.31 [49] is compared to the POWHEG-BOX [29] event generator where the PS is simulated by HERWIG+JIMMY. The effect of the PS and hadronization models on the acceptance is investigated by comparing the POWHEG+PYTHIA event generator with h damp ¼ ∞ to the POWHEG+HERWIG event generator. Finally, the effect of initial-and final-state radiation (ISR and FSR) is estimated using two tt samples generated in the same manner as the nominal sample, but with the renormalization and factorization scales multiplied by 2.0 (0.5), the regularization parameter h damp set to m top (2m top ), and using the Perugia 2012 radLo (radHi) UE tune, giving less (more) radiation. Table I summarizes the samples used to calculate the systematic uncertainties for the tt process.
A variety of MC event generators are used to simulate the backgrounds containing charged leptons in the final state, which are summarized in Table II. Vector-boson production with additional jets (pp → V þ jets, with V ¼ W, Z and two to seven jets) is simulated using the LO parton-level ME event generator ALPGEN [50] with the PS/UE generated by PYTHIA v6.426, as for the nominal tt samples. In order to avoid double counting, final states generated by the LO parton-level event generator ALPGEN and the parton-level shower evolution of PYTHIA, the MLM matching algorithm is used [51]. The matching algorithm is applied inclusively to the V þ 5 light-parton events and exclusively to the other events. Associated production of vector bosons with heavyflavor partons (V þ c þ jets, V þ cc þ jets, V þ bb þ jets) is simulated separately. Inclusive V þ jets samples are formed by combining the light-and heavy-quark samples according to their respective cross section. An overlap removal scheme is used to avoid double counting the contribution of additional heavy flavor partons. The cross sections used to normalize the samples are calculated at NNLO [52,53].
Electroweak production of the top quark (single-top) is simulated using POWHEG-BOX [54] and PYTHIA v6.426 with the CT10 PDF set. The MC sample for the t-channel process is normalized using the NNLO calculation in Ref. [55] while the s-channel sample is normalized with the NNLO þ NNLL cross section in Ref. [56] and the Wt channel is normalized with the NNLO þ NNLL calculation in Ref. [57]. In order to remove the overlap with tt production, the Wt sample is produced using the "diagram removal" generation scheme [58]. In addition, diboson (WW, WZ) production samples are generated using HERWIG with the CTEQ6L1 PDF set. These samples are normalized using the NLO calculation in Ref. [59].

IV. OBJECT RECONSTRUCTION
The final state in this measurement contains four quark jets of which two are b-quark jets, a W boson decaying to a neutrino and a τ lepton that decays to hadrons (τ had ) and a neutrino. Jets are reconstructed using the anti-k t algorithm [60,61] with the radius parameter set to R ¼ 0.4. To account for inhomogeneities and the noncompensating response of the calorimeter, the reconstructed jet energies are corrected through p T -and η-dependent factors that are derived in MC simulation and validated in data. Any remaining discrepancies in the jet energy scale are calibrated using an in situ technique where a well-defined reference object is momentum-balanced with a jet [62]. To ensure that jets originate from the vertex that produced the event, the fraction of the scalar p T sum of all tracks matched to the jet and originating at this vertex (jet vertex fraction) to the scalar p T sum of all tracks associated with this jet but originating from any vertex must be > 0.5 for jets with E T < 50 GeV and jηj < 2.4.
To identify jets initiated by b quarks (b-tagging), a multivariate algorithm is employed [63]. This algorithm uses the impact parameter and reconstructed secondary vertex information of the tracks contained in the jet as input for a neural network. Jets initiated by b quarks are selected by setting the algorithm output threshold such that a 70% selection efficiency is achieved in simulated tt events with a 1% misidentification rate for light-flavor jets. Since the b-quark selection efficiency differs between data and MC simulation, p T dependent correction factors are derived to correct for this difference [63]. These correction factors differ from unity by less than 3% over the entire p T range.
Decays of the τ lepton into hadrons and a neutrino are classified as either single prong (τ 1-prong ), where the τ lepton decays to a single charged particle, or three prong (τ 3-prong ), where the decay products are three charged particles with a net unit charge, and for each classification zero or more π 0 mesons can be present. Identification of a τ had begins with a reconstructed jet, as described above, having p T > 10 GeV and jηj < 2.5. The τ had classification is achieved by counting the number of tracks with p T > 1 GeV in a cone of size ΔR ¼ 0.2 around the jet axis. To discriminate against quark-or gluon-initiated jets, a set of discriminating variables is used to train a multivariate boosted decision tree (BDT) separately for single-prong and three-prong τ decays using τ had from simulated samples of vector-bosons decaying into τ leptons that cover the kinematic range expected in data and a background sample enriched in dijet events from data [64]. Three categories of discriminating variables are used. The first category comprises those variables that apply to all candidates. These are associated with the jet shape in both the tracking system and calorimeter. The second category are those variables that apply only to the single-prong τ lepton decays. These include the impact parameter significance and the number of tracks in an isolation region (0.2 < ΔR < 0.4) around the jet axis. The third and final category are those that apply to the three-prong τ lepton decays. These variables include the decay length significance in the transverse plane, the invariant mass of the reconstructed tracks, and the maximum track separation (ΔR) from the jet axis. An additional set of variables is used for those τ had containing π 0 mesons. These include the number of π 0 mesons, the invariant mass of the tracks plus π 0 mesons, and the ratio of track plus π 0 p T to the calorimeter energy only measurement. Furthermore, any jet that satisfies ΔR < 0.2 of a τ had is removed. In addition, a BDT that includes discriminating variables against electrons is trained to reduce the electron contamination for the τ 1-prong candidates. Low p T muons that stop in the calorimeter and overlap with energy deposits from other sources can mimic a τ had . These are characterized by a large fraction of energy deposited in the electromagntic calorimeter and a small ratio of track-p T to calorimeter-E T . Muons that produce large energy deposits in the calorimeter can also be misidentified as a τ had . These are characterized by a small fraction of energy in the electromagnetic calorimeter and a large track-p T to calorimeter-E T ratio. Strict selection requirements based on the two variables described are applied to avoid muons being misidentified as τ had . In addition, the reconstructed four-vector of the τ had candidate is not corrected for the unobserved neutrino kinematics.
Since undetected neutrinos occur in the final state, a momentum imbalance in the transverse plane is expected. The missing transverse momentum (E miss T ) is calculated as the negative of the vector sum of the transverse momentum of all reconstructed objects and of the calorimeter energy deposits not associated to any reconstructed object after the appropriate energy corrections have been applied [65].

V. EVENT SELECTION
Events are selected that satisfy the E miss T > 80 GeV trigger with an offline reconstruction requirement of E miss T > 150 GeV. This is the point at which the trigger has almost reached full efficiency. Furthermore, events are required to contain a hard collision primary vertex with at least four associated charged particle tracks of p T > 0.4 GeV. If there are multiple primary vertices in an event, the one with the largest sum of track p 2 T is selected. To reduce contamination from events with tt → eðμÞ þ jets, an event is rejected if it contains an electron (p e T > 25 GeV) [66] or a muon (p μ T > 20 GeV) candidate [67], each with jηj < 2.5 that satisfy the corresponding selection in the ATLAS tt → eðμÞ þ jets crosssection measurement [2]. The event must also contain at least two jets with E T > 25 GeV and jηj < 2.5. In addition, at least two of the jets in the event must be identified as b-quark jets using a b-tagging requirement with 70% efficiency. Each event is also required to contain at least one τ had that decays to either one or three charged particles with E T > 20 GeV and jηj < 2.5 and a τ lepton identification requirement that discriminates against quark and gluon initiated jets such that the efficiency is 40% for single-prong and 35% for three-prong τ had with a rejection factor between 100 and 1000 depending on the p T and η for each. This identification requirement defines the standard τ had selection. Since the background for τ 1-prong and τ 3-prong identification is different, the two samples are analyzed separately with the τ 1-prong (τ 3-prong ) analysis requiring one or more τ 1-prong (τ 3-prong ) only. In each case, the highest-p T τ had is used with less than 1% of events containing more than a single τ had . The combined result is produced by requiring an event to contain either one or more τ 1-prong or τ 3-prong and selecting the highest-p T τ had in the event. In order to preferentially select events where the τ had and E miss T originate from W-boson decays, the transverse mass is required to satisfy m T < 90 GeV, where m T comprises the τ had with the largest p T and the value of the E miss T of the event. The square of the transverse mass is defined as m 2 T ¼ p τ had T E miss T ½1 − cos Δϕðτ had ; E miss T Þ and Δϕðτ had ; E miss T Þ is the azimuthal angle between the direction of the τ had and the E miss T of the event.

VI. BACKGROUND ESTIMATION
To determine the number of pp → tt þ X → τ had þ jets events in the data sample, estimates of the various backgrounds are subtracted. These originate from two sources: the backgrounds with real τ had and those with misidentified τ had in the final state. The backgrounds containing real τ had in the final state include single-top-quark events, V þ jets events, and diboson events. These backgrounds are estimated in simulation and normalized using their theoretical cross sections as discussed in Sec. III. The misidentified (fake) τ had background consists of events from processes where a charged lepton (e AE and μ AE ) is misidentified as a τ had and multijet events that have a mismeasured E miss T and a quark-or gluon-initiated jet that is misidentified as a τ had .
Misidentification of electrons and muons as τ had is significantly reduced by applying the selection criteria discussed in Sec. IV. The tt background where an electron or a muon is misidentified as a τ had is simulated in POWHEG+PYTHIA and normalized using the theoretical tt production cross section. The contribution from other processes where an electron or a muon is misidentified as a τ had is found to be negligible.
To estimate the fraction of events in which a jet is misidentified as a τ had , a data-based method is used where this fraction is evaluated in a control sample that is divided into two components: one with the standard τ had selection and the other with an inverted τ had selection. The transfer factor is the ratio of the number of events with misidentified τ had in the nominal sample to that in the inverted sample. This transfer factor, which is referred as the fake-factor FF, is then applied to the signal sample with the inverted τ had selection, which yields the fraction of misidentified τ had in the signal sample with the nominal τ had selection. The inverted τ had selection is determined such that the fraction of quark-and gluon-jets that can be misidentified as a τ had is similar to the fractions when the standard τ had selection is applied, as derived from MC simulation. All other requirements are the same as for the signal sample. This technique, known as the fake-factor method, has been used in previous ATLAS measurements [68].
To ensure a large fraction of events with jets misidentified as τ had , the control sample is required to satisfy a muon trigger with only a single reconstructed muon satisfying the requirement p T > 25 GeV and jηj < 2.5. In addition, each event is also required to satisfy the following criteria: (1) contain a primary vertex with at least four associated tracks, (2) contain at least two jets and no jet in the event satisfying the b-jet criteria, and (3) contain a single τ had satisfying selection criteria that are less restrictive than the nominal. The control sample is then separated into a component satisfying the standard τ had identification and a second component that satisfies the inverted identification criteria. This set of selections ensures that the control sample is enriched with misidentified τ had for both the standard and the inverted τ had identification criteria. The number of data events selected with the standard τ had identification is 28 397, where the contribution from real τ had is 38% as estimated from simulation. For the inverted τ had identification, the number of data events is 84 975 with a contribution of 9% from real τ had . The transfer factor is calculated in bins of p T and η after the real τ had contributions are subtracted. The FF averaged over the full kinematic range of this measurement has a value of 0.23 AE 0.01ðstatÞ.
To extract the number of misidentified τ had in the signal sample, the nominal selection with the inverted τ had identification is applied to data. To correct for real τ had in this sample, an estimate of the number of real τ had is derived from simulation and subtracted from this sample. Next, the derived FF is applied to the resulting data sample according to the p T and η of the selected τ had taking into account the number of τ had in the event. This yields the number of misidentified τ had in the signal sample.
In order to validate this procedure, the derived FF is applied to a data set that does not overlap with the nominal analysis sample. Each event in the sample is required to satisfy a single-muon trigger and contain only one reconstructed muon of p T > 25 GeV. In addition, a single τ had satisfying the same criteria as the signal sample is required. The validation is performed for different jet multiplicities and numbers of b-quark jets by dividing the sample into the following six categories: (1) two inclusive jets; (2) three inclusive jets; (3) four inclusive jets; with each listed jet multiplicity containing either zero b-quark jets or at least one b-quark jet. Good agreement between the data and the background estimate is seen in all categories. An additional validation sample that is dominated by real τ had is formed by selecting Z → τ þ τ − events, where one τ lepton decays to a final state containing a μ and the other containing hadrons. This sample is selected by requiring: (1) cos Δϕðμ; E miss T Þ þ cos Δϕðτ had ; E miss T Þ > −0.15; (2) Δϕðμ; τ had Þ > 2.4; (3) m μ T < 50 GeV, where m μ T is the transverse mass of the μ and the E miss T of the event; (4) ð42 < mðμ; τ had Þ < 82Þ GeV, the invariant mass of the μ-τ had system; (5) ð25 < p μ T < 40Þ GeV. Figure 1 shows an example of a comparison between the data and the prediction for regions dominated by misidentified and real τ had .

VII. EXTRACTION OF THE tt PRODUCTION CROSS SECTION
In order to determine the tt cross section, the estimated background, given in Table III, is subtracted from the number of recorded events after the event selection is applied, then normalized to the integrated luminosity R LðtÞdt and corrected by the efficiency ϵ tt ¼ 5 × 10 −4 , which is calculated from the fraction of events satisfying the geometric, kinematic, trigger, and object identification selection, and the effects of the detector reconstruction. Therefore, the cross section is given as Furthermore, since the calculated efficiency corresponds to all tt final states containing leptons only, the BRðtt → l þ XÞ ¼ 0.54 is used. The number of background events (N bkg ) comprises backgrounds with real τ had that are estimated from the simulated samples and events containing a misidentified τ had that is estimated using the fakefactor method discussed in Sec. VI. As also discussed in Sec. VI, to estimate the number of misidentified τ had , the real τ had contribution must be subtracted including those from tt events. Since this would require the use of the tt cross section, which is the quantity being measured, Eq. (1) is reformulated as where N bkg-nontt represents the backgrounds estimated from the simulated samples and the misidentified τ had component estimated using the fake-factor method but excludes the subtraction of the tt component. The efficiency ϵ FF-tt ¼ 7 × 10 −5 represents tt events satisfying the inverted τ had identification.

VIII. SYSTEMATIC UNCERTAINTIES
Systematic uncertainties are grouped into those pertaining to object identification along with its energy and momentum measurement, theoretical modeling, background evaluation, and the luminosity. The systematic uncertainties are evaluated by performing a variation of each parameter related to the associated quantity and propagating the overall uncertainty to the cross section assuming that the individual uncertainties are uncorrelated. The procedures and results for the individual quantities considered are summarized below. The systematic uncertainties are calculated for the τ 1-prong , τ 3-prong , and the combined τ had analyses separately, with the resulting values given in Table IV.
The uncertainty in the cross section due to jet reconstruction is split into three components: the jet energy scale, its energy resolution, and its reconstruction efficiency. The uncertainty from the jet energy scale is calculated by varying the jet energies according to the uncertainties derived from simulation and the in situ calibration using a model containing 22 independent components [62]. The difference between the jet energy resolution in data and MC simulated events is evaluated by smearing the jet p T in the MC sample according to the measured jet resolution in bins of η and p T [69]. The uncertainty in the jet reconstruction efficiency is evaluated by randomly removing jets according to the difference in data and MC jet reconstruction efficiencies [62]. The variation in the jet energies is also propagated to the E miss T calculation. In the nominal analysis, the b-tagging efficiency in simulation is corrected to agree with data by using p Tand η-dependent correction factors. The uncertainty in the correction factors is obtained independently for b-jets, c-jets, and light-flavor jets assuming that they are uncorrelated. The uncertainties of the inefficiency correction factors that are applied when a jet is not tagged are treated as fully anticorrelated with the corresponding efficiency correction factor [63]. This uncertainty is propagated to the cross section by varying the correction factors by one standard deviation with respect to the central value.
As in b-tagging, correction factors are used to correct for the difference in the τ had -tagging efficiency and the τ had electron veto efficiency between data and simulation. The uncertainties in the correction factors depend on p T , η, and the τ had identification criteria. In addition, the τ had energy scale can affect the final result due to the τ had p T requirement. The energy of the τ had is calculated using MC simulation to correct the observed energy to the true energy scale [64]. Additional small data-based corrections are then applied. The uncertainties due to each of these effects are propagated to the cross section by varying the correction factors by one standard deviation.
The systematic uncertainty of E miss T is evaluated along with the systematic uncertainty of the associated energy and momentum of the reconstructed objects as discussed above. Not included in that calculation are the contributions from low-p T jets and energy deposits in the calorimeter cells not associated with a reconstructed object. This source of uncertainty is evaluated using the difference between TABLE III. The number of events observed in data and obtained from simulation along with the associated statistical uncertainty for background and expected signal processes for the different τ had types and the combined sample. The τ 1-prong (τ 3-prong ) samples require all τ had in an event to be of that type, while the combined sample can have either τ had type.  IV. Relative percent uncertainties in the measured cross section in the τ 1-prong , τ 3-prong and combined τ 1-prong and τ 3-prong (τ had ) final states. In the τ 1-prong (τ 3-prong ) analysis, all τ had in the event are required to be τ 1-prong (τ 3-prong ). For the combined analysis, the τ had in an event could be of either type. Uncertainty data and simulated Z → μ þ μ − events containing no jets, which is similar to the procedure used in Ref.
[65]. The systematic uncertainty due to tt modeling is split into two components. The first is that associated with the choice of ME event generator and PS/UE event simulation. The uncertainty associated with the choice of ME event generator is estimated by comparing the acceptance from the MC@NLO event generator with that from the POWHEG-BOX event generator. Events from both event generators are processed through the PS/UE simulator HERWIG+JIMMY. The uncertainty due to the PS on the acceptance is estimated by comparing the POWHEG+PYTHIA event generator to the POWHEG+HERWIG event generator. The second component of the modeling uncertainty corresponds to the effect of ISR and FSR on the event selection due to possible extra jets and changes in the kinematics of the final-state particles and jets. The nominal tt sample is compared to samples with variations of the renormalization and factorization scales and the regularization parameter as described in Sec. III.
The systematic uncertainties due to the various backgrounds that contain real τ had , are derived using the MC samples described in Sec. III and the uncertainties of the theoretical cross sections. The two largest sources of real τ had backgrounds are single-top and W þ jets events. All other background contributions to the systematic uncertainty are negligible. For single-top, the uncertainty in the cross section of the MC sample is varied by one standard deviation and propagated to the cross section. For the W þ jets background, the same procedure is followed but is validated using a method based on the W-boson charge asymmetry in data as described in Refs. [70][71][72], which gives agreement with the estimation based on the theoretical uncertainty.
To estimate the systematic uncertainty in the number of misidentified τ had , the effect of variations of the main components of this analysis are examined. The main components are: (1) the MC-based background subtraction of the real τ had , (2) uncertainty in the flavor dependence of the FF, (3) uncertainty associated with the η-p T binning of the FF. In calculating the FF, the largest contribution from real τ had is from Z þ jets events, as the final state Z → τ þ τ − → τ had μ þ X satisfies the selection. To estimate this component of the uncertainty, the Z þ jets cross section is varied by AE1 standard deviation. This variation leads to an average uncertainty of 5% over the p T -η range for this component of the FF. The FF is calculated in a sample dominated by light-flavor jets. To estimate the systematic uncertainty of the flavor composition, the FF is also derived in a gluon-jet-dominated sample with four jets and low E miss T . Using this sample the FF is calculated and applied to the signal sample, resulting in an uncertainty of 20% in the number of misidentified τ had events. Since the FF is calculated in p T -η bins, the bin size is also varied to estimate the uncertainty in the final result. The uncertainty in the final result is found to be approximately 5% of the calculated number of misidentified τ had events.
The absolute luminosity scale is derived from beamseparation scans performed in November 2012. From the calibration of the absolute luminosity scale, the uncertainty in the total integrated luminosity is evaluated following the procedure described in Ref. [73] and is found to be 1.9%.  This uncertainty is then propagated to the cross-section measurements yielding a 2.3% uncertainty, which is reported independent of the other systematic uncertainties.

IX. RESULTS AND INTERPRETATION
The number of events observed for each τ had type and for the combined analysis are reported in Table III along with the predicted number of background events. The uncertainties associated with the cross-section measurement from each of the different sources are reported in Table IV. Figure 2 shows the kinematic distributions of the predicted background and signal processes with the observed data superimposed, where the signal-tobackground ratio is approximately 4∶1.
The cross sections for each τ had type measured separately are σ tt ðτ 1-prong þ jetsÞ ¼ 237 AE 5ðstatÞ AE26ðsystÞ AE5ðlumiÞ pb; σ tt ðτ 3-prong þ jetsÞ ¼ 243 AE 14ðstatÞ þ34 −38 ðsystÞ AE6ðlumiÞ pb; and the cross section for the combined analysis is σ tt ¼ 239 AE 4ðstatÞ AE 28ðsystÞ AE 5ðlumiÞ pb: The combined cross section has an uncertainty of 12% and is in agreement with the previous measurements of the ATLAS Collaboration for the e þ jets and μ þ jets final states [2]. Since the analysis is performed at a fixed top-quark mass, samples are generated at various masses to study the dependence of the measured cross section on m top . The variation is found to be ðΔσ=σÞ=Δm top ¼ −2.6% GeV −1 . In order to quantify the compatibility of this result with the SM and explore the allowed range for non-SM processes, a frequentist significance test using a background-only hypothesis is used to compare the observed number of events with the SM prediction. In this procedure, the tt → τ þ X process is considered a background and estimated according to the SM prediction taking into account the corresponding uncertainty. This statistical analysis is also used to derive a limit in a model-independent manner on possible beyond-the-SM (BSM) physics. A confidence level for the background-only hypothesis (CL b ) of 0.48 corresponding to a p-value of 0.52 is observed, which indicates good agreement between the observed data and the SM processes. An upper limit at 95% confidence level (CL) on the number of BSM events is derived using the CL s likelihood ratio method described in Ref. [74]. The upper limit is calculated with the observed number of events, the expected background, and the background uncertainty. Dividing the upper limits on the number of BSM events by the integrated luminosity of the data sample, the resulting value can be interpreted as the upper limit on the visible BSM cross section, σ vis ¼ σ × ϵ, where σ (ϵ) is the production cross section (efficiency) for the BSM process. Table V summarizes the observed number of events, the estimated SM background yield, and the expected and observed upper limits on the event yields and on the σ vis from any BSM process. The efficiency for each SM process used to calculate this limit is reported in Table VI. Using the same data sample as the cross-section measurement, an upper limit on the flavor changing process t → qH → qτ þ τ − is set by performing a modified analysis and then calculating a limit in a manner that is similar to that of the model-independent limit. In the modified analysis, exactly one identified b-jet and two τ had are required. Performing the same statistical analysis as for the cross-section measurement, a 95% CL observed (expected) upper limit of 0.6% (0.9%) is set on the BRðt → qHÞ × BRðH → ττÞ. At present, this is the only analysis that can explore the channel t → qH → qττ and, hence, is the first search using the H → ττ final state. Assuming the SM BRðH → ττÞ ¼ 6%, the 95% CL observed (expected) upper limit set on the BRðt → qHÞ is 10% (15%). A dedicated ATLAS measurement achieves a 95% CL upper limit of 0.45% on the BRðt → qHÞ in the combination of Higgs boson final states H → bb, H → γγ and H → multileptonðe; μÞ [75].

X. SUMMARY
A measurement of the pp → tt þ X cross section at ffiffi ffi s p ¼ 8 TeV using 20.2 fb −1 of integrated luminosity collected with the ATLAS detector has been performed in the tt → τν τ qq 0 bb final state using hadronic decays of the τ lepton. The cross section is measured separately for hadronic decays of the τ lepton into one or three charged particles. A single analysis using a combination of both decay modes is also performed. The cross section measured in the single analysis is σ tt ¼ 239 AE 4ðstatÞ AE 28ðsystÞ AE 5ðlumiÞ pb, assuming a top-quark mass of m top ¼ 172.5 GeV. The measured cross section is in agreement with the SM prediction of 253 þ13 −15 pb. A statistical analysis is performed to check the consistency of the observed number of events in data with the predicted number of events from various SM processes. Following a frequentist approach, the confidence level observed with the SM-only hypothesis is 0.48 and the calculated p-value is 0.52, which indicates good agreement of the SM prediction with the observed data. A model-independent upper limit on the visible cross section for any non-SM process is also calculated. The observed (expected) upper limit at 95% confidence level on the visible cross section of any non-SM processes is 22ð22 þ2 −1 Þ fb.

ACKNOWLEDGMENTS
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT  [5] ATLAS Collaboration, Measurement of the tt production cross section in the τ þ jets channel using the ATLAS detector, Eur. Phys. J. C 73, 2328 (2013).
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