A search for high-mass resonances decaying to τ + τ − in pp collisions at √ s = 8 TeV with the ATLAS detector

A search for high-mass resonances decaying into τ + τ − ﬁnal states using proton–proton collisions at √ s = 8 TeV produced by the Large Hadron Collider is presented. The data were recorded with the ATLAS detector and correspond to an integrated luminosity of 19.5–20.3 fb − 1 . No statistically signiﬁcant excess above the Standard Model expectation is observed; 95% credibility upper limits are set on the cross section times branching fraction of Z (cid:48) resonances decaying into τ + τ − pairs as a function of the resonance mass. As a result, Z (cid:48) bosons of the Sequential Standard Model with masses less than 2.02 TeV are excluded at 95% credibility. The impact of the fermionic couplings on the Z (cid:48) acceptance is investigated and limits are also placed on a Z (cid:48) model that exhibits enhanced couplings to third-generation fermions.


Introduction
Searches for new heavy resonances decaying to tau lepton pairs are both theoretically and experimentally well motivated [1][2][3][4][5][6].Heavy Z bosons often arise in grand unified theories and while they are typically considered to obey lepton universality, this is not necessarily a requirement.In particular, some models offering an explanation for the high mass of the top quark predict that such bosons preferentially couple to third-generation fermions [7,8].Models containing non-universal Z bosons can explain the anomalous dimuon production observed at the D0 experiment [9,10] and the excess in semileptonic B-meson decays into tau leptons observed at the Belle and BaBar experiments [11][12][13].Searches in the ditau channel are also sensitive to sgoldstino-like scalars in supersymmetric models [14,15], hidden sector Z models [16] and to the anomalous tau lepton dipole moments and higherorder tau-gluon couplings [17].
In this article, a search for high-mass resonances decaying into τ + τ − final states using proton-proton (pp) collisions at a center-of-mass energy of √ s = 8 TeV produced by the Large Hadron Collider (LHC) [18] is presented.The data were recorded with the ATLAS detector [19] and correspond to an integrated luminosity of 19.5-20.3fb −1 .Tau leptons can decay into a charged lepton and two neutrinos (τ lep = τ e or τ µ ), or hadronically (τ had ), predominantly into one or three charged pions, a neutrino and often additional neutral pions.The τ had τ had , τ µ τ had and τ e τ had channels are analysed, accounting for 42%, 23% and 23% of the total τ + τ − branching fraction, respectively.A counting experiment is performed in each channel from events that pass a high-transverse-mass requirement.Due to the different dominant background contributions and signal sensitivities, each channel is analysed separately and a statistical combination is used to maximise the sensitivity.
The Sequential Standard Model (SSM), which contains a Z SSM boson with couplings identical to the Standard Model Z boson, is chosen as the benchmark model to optimise the analysis and to quantify the experimental sensitivity.Limits on the Z SSM cross section times the branching fraction in tau pairs, σ(pp → Z SSM + X) • B(Z SSM → τ + τ − ) ≡ σB SSM , are provided as a function of the resonance mass, m Z .The impact on the signal acceptance times efficiency from changing the Z SSM couplings is assessed, which allows the limits on Z SSM to be reinterpreted for a broad range of models.Limits are also placed on the nonuniversal G(221) model [8,20,21], which contains a Z NU boson that can exhibit enhanced couplings to tau leptons.
Direct searches for high-mass ditau resonances have been performed by the ATLAS and CMS collaborations using 5 fb −1 of integrated luminosity at √ s = 7 TeV [22,23].The searches exclude Z SSM with masses below 1. 4 TeV at 95% CL. 1 For comparison, the most stringent limits on Z SSM in the dielectron and dimuon decay channels combined are 2.90 TeV at 95% CL from both ATLAS [24] and CMS [25].While the limits on σ(pp → Z SSM + X) • B(Z → e + e − /µ + µ − ) are in general stronger than those on σB SSM , they may be evaded by models with weak couplings to electrons and muons.Indirect limits on Z bosons with non-universal flavour couplings have been set using measurements from LEP and LEP II [26] and translate to a lower bound on the Z mass of 1.09 TeV at 95% CL.Indirect limits have also been placed on the non-universal G(221) model [8,[27][28][29].The strongest exclude Z NU with a mass lower than 1.8 TeV at 95% CL.This article is structured as follows.Section 2 provides an overview of the ATLAS detector.The event samples used in the analysis, recorded by the ATLAS detector or simulated using the ATLAS simulation framework, are described in section 3. The reconstruction of physics objects within the event samples is described in section 4. A description of the selection criteria used to define Z signal regions is given in section 5. Section 6 describes the estimation of background contributions, followed by a description of systematic uncertainties in section 7.In section 8, the impact of altering the Z couplings on the signal acceptance is described and the non-universal G(221) model is introduced.A presentation of the results is given in section 9, followed by concluding remarks in section 10.

ATLAS detector
The ATLAS detector 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 (EM) and hadronic calorimeters, and a muon spectrometer incorporating large superconducting toroid magnets.
The inner-detector system is immersed in a 2 T axial magnetic field and provides charged-particle tracking in the range |η| < 2.5.2A high-granularity silicon pixel detector covers the vertex region and typically provides three measurements per track.It is followed by a silicon microstrip tracker, which usually provides four pairs of measurements per track.These silicon detectors are complemented by a transition radiation tracker (TRT), which enables radially extended track reconstruction up to |η| = 2.0.The TRT also provides electron/pion discrimination based on the fraction of hits (typically 30 in total) above a higher energy-deposit threshold corresponding to transition radiation.
The calorimeter system covers the pseudorapidity range |η| < 4.9.Within the region |η| < 3.2, EM calorimetry is provided by high-granularity barrel and endcap liquid-argon (LAr) EM calorimeters with lead absorbers, with an additional thin LAr presampler covering |η| < 1.8 to correct for upstream energy loss.Hadronic calorimetry is provided by a steel/scintillator-tile calorimeter, segmented into three barrel structures within |η| < 1.7, and two copper/LAr hadronic endcap calorimeters.Coverage in the forward region is achieved by copper/LAr and tungsten/LAr calorimeter modules optimised for EM 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 |η| < 2.7 with three layers of monitored drift tubes, complemented by cathode strip chambers in the forward region, where the background is highest.The muon trigger system covers the range |η| < 2.4 with resistive plate chambers in the barrel, and thin gap chambers in the endcap regions.
A three-level trigger system is used to select interesting events [30].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 which together reduce the event rate to a maximum of 1 kHz.

Event samples
The data used in this search were recorded with the ATLAS detector in pp collisions at a centre-of-mass energy of √ s = 8 TeV during the 2012 run of the LHC.Only data taken with pp collisions in stable beam conditions and with all ATLAS subsystems operational are used, resulting in an integrated luminosity of 20.3 fb −1 .For the analysis of the τ had τ had channel, a small fraction of data from the initial running period are discarded as the trigger conditions are not accounted for by the simulation, resulting in an integrated luminosity of 19.5 fb −1 .The τ had τ had channel uses events passing a single-tau trigger with a transverse momentum (p T ) threshold of 125 GeV, designed to select hadronic tau decays.The τ µ τ had channel uses events passing a single-muon trigger, either with a p T threshold of 24 GeV including an isolation requirement or with a threshold of 36 GeV without an isolation requirement.The τ e τ had channel uses events passing a single-electron trigger, either with a p T threshold of 24 GeV including an isolation requirement, or with a threshold of 60 GeV without an isolation requirement.Events that pass the trigger are selected if they contain a vertex with at least four associated tracks, each with p T > 0.5 GeV.Events may have several vertices satisfying this requirement due to multiple pp interactions occurring in the same or neighbouring bunch crossings, referred to as pile-up.The event vertex is chosen as the one with the largest sum of the squared track transverse momenta.
Monte Carlo (MC) simulation is used to estimate signal efficiencies and some background contributions.Simulated samples of events from the following background processes are used: Z/γ * → τ τ and Z/γ * (→ )+jets ( = e, µ) enriched in high-mass events, and W +jets, t t, single-top-quark (W t, s-channel and t-channel) and diboson (W W , W Z, and ZZ) production.Each sample is produced with one of the following event generators: Pythia 8.165 [31], Sherpa 1.4.1 [32], MC@NLO 4.01 [33][34][35], AcerMC 3.8 [36], Herwig 6.520 [37] or PowHeg-Box 1.0 [38][39][40][41].The most consistent set of available samples was chosen.The Z/γ * → τ τ process is generated at leading order so that the sample can also be reweighted to describe the Z signal.The combination of t t and single-top-quark production are referred to as top.In some cases the generators are interfaced to the following external software for parton showering, hadronisation and multiple parton interactions: Pythia 8, Pythia 6.421 [42] or Herwig (which is itself interfaced to Jimmy 4.31 [43] for multiple parton interactions).The tau lepton decay is performed by either Pythia 8, Sherpa or Tauola [44].For Pythia 8, the sophisticated tau decay option is used, which provides fully modelled hadronic currents with spin correlations for tau-lepton decays [45].In all samples other than those generated with Sherpa, final-state photon radiation is performed by Photos [46].The CTEQ6L1 [47] and CT10 [48] parton distribution functions (PDFs) and the AU2, AUET2, AUET2B [49] and CT10 [32] MC tunes are used.A summary is given in table 1.
The contributions from simulated processes are normalised using theoretical cross sections.The Z/γ * cross section is calculated up to next-to-next-to-leading order (NNLO) in QCD including next-to-leading order (NLO) electroweak corrections using FEWZ 3.1 [50] configured with the MSTW2008NNLO PDF set [51].This cross section is used to derive mass-dependent K-factors that are used to weight the simulated Z/γ * samples.Cross sections for the other background processes are calculated without the use of differential K-factors to at least NLO in QCD, as specified in table 1.
The contributions of the various Z signal models are estimated by reweighting the Z/γ * → τ τ sample using TauSpinner [60][61][62], which correctly accounts for spin effects in the tau decays.The impact of interference between Z and Z/γ * is typically small (as discussed in section 8.1), so it is not included.For each signal model, several mass Table 1.Details regarding the MC simulated samples.The following information is provided for each sample: the generator of the hard interaction, the parton shower and hadronisation (PS), multiple parton interactions (MPI) and the tau decay; the PDF set; the MC tune and the order in QCD of the cross section calculation.All cross sections are calculated at either NLO, NNLO, approximate NNLO (∼NNLO) or next-to-next-to-leading logarithm (NNLL).
hypotheses are considered, ranging from 500 to 2500 GeV in steps of 125 GeV.All generated events are propagated through a detailed Geant4 simulation [63] of the ATLAS detector and subdetector-specific digitisation algorithms [64] and are reconstructed with the same algorithms as the data.Pile-up is simulated by overlaying minimum-bias interactions generated with Pythia 8 (with an MC tune specific to the LHC [65]) on the generated signal and background events.The resulting events are reweighted so that the distribution of the number of minimum-bias interactions per bunch crossing agrees with data.Due to the high momenta of the tau decay products, however, pile-up has little impact on the analysis.The effective luminosity of most simulated samples is at least as large as the integrated luminosity of the data; the statistical uncertainty from the limited sample size is accounted for in the statistical analysis.

Physics objects
In this section the reconstruction of electrons, muons, hadronic tau decays and the missing transverse momentum is described.Preliminary selections are applied to all electrons, muons and tau candidates.Further selection is applied to some of the objects as part of the event selection described in section 5.
The reconstruction of hadronic tau decays in ATLAS is described in detail in ref. [66].Candidates for hadronic tau decays are built from jets reconstructed using the anti-k t algorithm [67,68] with a radius parameter value of 0.4.The jets are calibrated to the hadronic energy scale with correction factors based on simulation and validated using testbeam and collision data [69].Only the visible tau-decay products (all products excluding neutrinos), τ had-vis , are considered when calculating kinematic properties.The calculation of the four-momentum uses clusters with ∆R < 0.2 from the initial jet-axis and includes a final tau-specific calibration derived from simulated samples, which accounts for out-ofcone energy, energy lost in dead material, underlying-event and pile-up contributions and the typical composition of hadrons in hadronic tau decays.Candidates are required to have either one or three associated tracks (prongs) reconstructed in the inner detector.The tau charge is reconstructed from the sum of the charges of the associated tracks and is required to be ±1.The charge misidentification probability is found to be negligible.Hadronic tau decays are identified with a multivariate algorithm that employs boosted decision trees (BDTs) to discriminate against quark-and gluon-initiated jets using shower shape and tracking information.Working points with a tau identification (ID) efficiency for 1-prong/3-prong candidates of about 55%/40% (medium) for the τ µ τ had and τ e τ had channels and 65%/45% (loose) for the τ had τ had channel are chosen, leading to rates of false identification for quark-and gluon-initiated jets of below a percent.The tau ID efficiency is independent of p T and pile-up.Candidates arising from the misidentification of electrons are rejected using a separate BDT.In the τ µ τ had channel, a dedicated selection is applied to suppress candidates arising from the misidentification of muons.Tau candidates are required to have p T > 30 GeV and to be in the fiducial volume of the inner detector, |η| < 2.47.The transition region between the barrel and endcap EM calorimeters, with 1.37 < |η| < 1.52, is excluded.In the τ lep τ had channels, candidates that have the highestp T track in the range |η| < 0.05 are rejected.This region corresponds to a gap in the TRT, which reduces the power of electron/pion discrimination.
Muon candidates are reconstructed by combining an inner-detector track with a track from the muon spectrometer.The candidates are required to have p T > 10 GeV and |η| < 2.5.Muon quality criteria are applied to achieve a precise measurement of the muon momentum and reduce the misidentification rate [70].These quality requirements correspond to a muon reconstruction and identification efficiency greater than 95%.
Electrons are reconstructed by matching clustered energy deposits in the EM calorimeter to tracks reconstructed in the inner detector [71].The tracks are then refitted using the Gaussian Sum Filter algorithm [72], which accounts for energy loss through bremsstrahlung.The electron candidates are required to have p T > 15 GeV and to be within the fiducial volume of the inner detector, |η| < 2.47 (the EM calorimeter transition region is excluded).The candidates are required to satisfy quality criteria based on the expected calorimeter shower shape and amount of radiation in the TRT.These quality requirements correspond to an electron identification efficiency of approximately 95% [73].
Electrons and muons are considered isolated if they are away from large deposits of energy in the calorimeter and tracks with large p T consistent with originating from the same vertex.Lepton isolation is defined using the sum of the transverse energy, E T , deposited in calorimeter cells with ∆R < 0.2 from the lepton, E 0.2 T , and the scalar sum of the p T of tracks with p T > 0.5 GeV consistent with the same vertex as the lepton and with ∆R < 0.3, p 0.3 T .Muons are considered isolated if they have p 0.3 T /p T < 5%.Isolated electrons must have p 0.3 T /p T < 5% and E 0.2 T < 5 GeV + 0.7% × p T and must pass a tighter identification requirement corresponding to an efficiency of approximately 70%.
Geometric overlap of objects with ∆R < 0.2 is resolved by selecting only one of the overlapping objects in the following order of priority: muons, electrons, tau candidates.The missing transverse momentum, with magnitude E miss T , is calculated from the vector sum of the transverse momenta of all high-p T objects reconstructed in the event, as well as a term for the remaining activity in the calorimeter [74].Clusters associated with electrons, hadronic tau decays and jets are calibrated separately.The remaining clusters are weighted using tracking information to reduce the effect of pile-up on the E miss T resolution.A single weight is calculated for each event using all tracks that are not matched to high-p T objects.The tracks are categorised based on whether or not they are matched to the primary vertex.The weight is then defined as the ratio of the sum of the p T of tracks originating from the primary vertex to the sum of the p T of all tracks.

Event selection
Selected events in the τ had τ had channel must contain no electrons with p T > 15 GeV or muons with p T > 10 GeV and at least two tau candidates: one with p T > 150 GeV that is matched to the object that passed the trigger and the other with p T > 50 GeV.This constitutes the preselection.If multiple tau candidates are selected, the two highest-p T candidates are chosen.This decision is made before applying the BDT tau ID, to avoid kinematic biases in control regions defined by reversing the ID requirement.The tau candidates are then required to have charges of opposite sign (OS).Finally, the angle between the tau candidates in the transverse plane, ∆φ(τ 1 , τ 2 ), must be greater than 2.7 radians, as tau leptons from the decay of heavy neutral resonances are typically produced back-to-back in the transverse plane.
Selected events in the τ lep τ had channels must contain exactly one isolated muon with p T > 30 GeV or one isolated electron with p T > 30 GeV; no additional electrons with p T > 15 GeV or muons with p T > 10 GeV; and at least one tau candidate with p T > 30 GeV.This constitutes the preselection.If multiple tau candidates are selected, the highest-p T candidate is chosen.As in the τ had τ had channel, this choice is made before applying the BDT tau ID.The angle between the lepton and tau candidate in the transverse plane, ∆φ( , τ ), must be greater than 2.7 radians, and they must have opposite charge.The transverse mass is defined as: where p A and p B are two reconstructed physics objects with transverse momenta p A T and p B T , respectively, which subtend an angle of ∆φ(p A , p B ) in the transverse plane.The W +jets background is suppressed by requiring the transverse mass of the lepton-E miss T system, m T ( , E miss T ), to be less than 50 GeV.The search in all channels is performed by counting events in signal regions with total transverse mass above thresholds optimised separately for each signal mass hypothesis in each channel to give the best expected exclusion limits.The same thresholds are found to be optimal for all channels.The total transverse mass, m tot T , is defined as where τ 1 and τ 2 denote the reconstructed visible decay products of the two tau leptons (e, µ or τ had-vis ).

Background estimation
The dominant background process in the τ had τ had channel at high mass is Z/γ * → τ τ , which is estimated using simulation.The modelling of the pp → Z/γ * process has been shown to be very reliable by using decays to electrons and muons [24,75].Additional uncertainties related to the modelling of high-p T tau decays are also considered, as described in section 7.
Multijet production makes a large contribution at low mass in the τ had τ had channel and is estimated by weighting events in data where the subleading tau candidate fails tau ID, with fake-factors that parameterise the rate for jets to pass tau ID (section 6.1).Due to the relatively large size of the sample that fails tau ID, this procedure provides high statistical precision, which is particularly crucial in the high-mass tail.The fake-factors are measured from data in a separate control region.Diboson, W +jets, t t, Z/γ * (→ )+jets, and singletop-quark production make minor contributions and are estimated using simulation.To improve the modelling of these background processes, events in the simulation that contain jets misidentified as hadronic tau decays are weighted by fake-rates measured in a W +jets control region in data (section 6.3).
The dominant background contributions in the τ lep τ had channels come from Z/γ * → τ τ , which is estimated using simulation, and from processes in which a jet is misidentified as a hadronic tau decay.The latter is mainly composed of W +jets events and is estimated using fake-factors to weight events in data where the tau candidate fails ID, similarly to the procedure in the τ had τ had channel (section 6.2).Diboson, t t, Z/γ * (→ )+jets and single-top-quark production in which the tau candidate does not originate from a jet make minor contributions and are estimated using simulation.In the following subsections, the data-driven background estimates are described in more detail.

Multijet background in the τ had τ had channel
To estimate the multijet background in the τ had τ had channel, two control regions are used.Events in the first control region are required to pass the same selection as in the analysis, except for the subleading tau candidate, which is required to fail the BDT tau ID.The multijet contribution in the signal region is estimated by weighting these events with a tau ID fake-factor.The fake-factor, f tau−ID , is defined as the ratio of the number of tau candidates that pass the BDT tau ID, N pass tau−ID , to the number that fail, N fail tau−ID .The fake-factors are calculated from a second control region that is highly pure in multijet events, the multijet control region (described below), and they depend on the p T and track multiplicity, N track , of the subleading tau candidate: The fake-factors have no significant dependence on η.The number of multijet events in a bin of p T , N track and any additional variable that is uncorrelated to the BDT tau ID, x, is given by: The multijet control region is designed to be as similar to the signal region as possible, while avoiding contamination from hadronic tau decays.This is achieved by loosening the tau ID requirements.Specifically, the selection for this control region is the same as for the signal region except with the following alterations.The BDT tau ID is not applied to either tau candidate.Instead of using the single-tau trigger, events are selected using single-jet triggers with thresholds ranging from 45 to 360 GeV, with all but the highest threshold trigger being prescaled.The p T of the subleading tau candidate must be at least 40% of the p T of the leading tau candidate to avoid bias at low p T due to the disproportionate fraction of events coming from the unprescaled 360 GeV jet trigger.The opposite-sign requirement on the charges of the two tau candidates is removed to increase the sample size.
Figures 1(left) and 1(right) show the fake-factors for 1-prong and 3-prong candidates, respectively.Use of these fake-factors relies on the assumption that they are insensitive to the alteration of the selection between the signal region and multijet control region.Systematic uncertainties on the fake-factors are derived by altering the selection on the p T -balance, the charge product, and the identification of the leading-p T tau candidate.These variations make a significant contribution to the uncertainty on the fake-factors at low p T , while at high p T the statistical uncertainty dominates.

Jet background in the τ lep τ had channel
The background contributions originating from quark-and gluon-initiated jets that are misidentified as hadronic tau decays in the τ lep τ had channels are modelled using a fakefactor method, similar to that used in the τ had τ had channel.In contrast to the τ had τ had channel, the background is dominated by W +jets production, with a minor contribution from multijet production.To reduce the sensitivity to the differing fake-factors in W +jets and multijet events (due to a different quark/gluon fraction), events failing a very loose level of BDT tau identification (corresponding to efficiencies of 98% and 90% for 1-prong and 3-prong hadronic tau decays, respectively) are rejected.This significantly suppresses the gluon contribution, which typically consists of wider jets with higher hadron multiplicity which are more readily rejected by the tau ID.In the τ lep τ had channels, there is also a nonnegligible contribution to the first control region (fail-ID control region) from background processes containing hadronic tau decays, which is subtracted using simulation.The fakefactors are measured in a high-purity W +jets control region and they depend on p T , η and N track of the tau candidate.The W +jets control region uses the same selection as the signal region but with the medium BDT tau ID replaced by very loose BDT tau ID and the m T requirement replaced by 70 GeV ≤ m T ≤ 200 GeV.A second control region high in multijet purity is used to motivate a systematic uncertainty on the fake-factors.This control region uses the same selection as the W +jets control region but the lepton is required to fail isolation, the m T requirement is replaced by m T < 30 GeV and E miss T < 30 GeV is required.A 30% systematic uncertainty on the fake-factors is derived by comparing the fake-factors in the two regions.Figures 2(left) and 2(right) show the fake-factors measured in each of the two control regions in the τ µ τ had channel, integrated across all |η| regions, for 1-prong and 3-prong candidates, respectively.The fake-factors in the τ e τ had channel are similar.
Finally, in the τ lep τ had channel, two additional steps are taken to ensure E miss T is modelled well by the fake-factor estimate.Firstly, the standard E miss T reconstruction treats the selected tau candidate in the fail-ID control region as a jet rather than a hadronic tau decay.Therefore, the E miss T is recalculated in the fail-ID control region using the tau hypothesis for the selected tau candidate.Following this, a slight bias in the shape of the E miss T distribution is corrected for by reweighting in bins of the E miss T projected along the direction of the tau candidate.To cover the effects of this reweighting, an additional 20% uncertainty is applied.

Jet background other than multijet in the τ had τ had channel
In the τ had τ had channel, backgrounds originating from quark-and gluon-initiated jets that are misidentified as hadronic tau decays in processes other than multijet production are estimated using simulation (predominantly W +jets). Rather than applying the tau ID to the simulated jets, they are weighted by fake-rates measured in a W +jets control region.This not only ensures the correct fake-rate, but enhances the statistical precision of the estimate, as events failing the tau ID are not discarded.Events in the W +jets control region are selected by a single-muon trigger with a p T threshold of 36 GeV.The events are required to contain one isolated muon that: has p T > 40 GeV, has E 0.2 T /p T < 6% and is matched to the object that passed the trigger.There must be no additional muons or electrons and at least one tau candidate with opposite charge to the muon.The remaining contamination from multijet events is suppressed by requiring cos ∆φ(µ, E miss T ) + cos ∆φ(τ had-vis , E miss T ) < −0.15, which disfavours back-to-back topologies where the E miss T vector points either in the direction of the muon or the tau candidate.The leading-p T tau candidate is used to measure the fake-rate, which is defined as the ratio of the number of tau candidates that pass tau ID to the total number of tau candidates.The fake-rates depend on p T and N track of the tau candidate, and whether the tau candidate was required to pass the single-tau trigger.Figures 3(left) and 3(right) show the fake-rate for 1-prong and 3-prong tau candidates that are not required to pass the trigger, respectively.The fake-rates including the trigger requirement in the numerator have a similar behaviour but are a factor of two to four lower.For comparison, the fake-rates are also calculated for events where the tau candidate has the same charge sign as the muon.The higher fake-rate in events with oppositely charged tau candidates is partly due to an enhanced quark fraction coming from the leading-order qg → W q process where the quark and W boson are oppositely charged.Two uncertainties are considered when applying the fake-rates to simulated jets: the statistical uncertainty from the limited size of the W +jets control region and a systematic uncertainty to account for differences in the jet composition in different background processes.A 60% uncertainty is assumed for the composition uncertainty, which covers the range of the measured fake-rates for events with opposite-or same-sign tau candidates.The uncertainty is omitted for W +jets events as they are expected to have the same jet composition as events in the control region.

Systematic uncertainties
Systematic effects on the contributions of signal and background processes estimated from simulation are discussed in this section.These include theoretical uncertainties on the cross sections of simulated processes and experimental uncertainties on the trigger, reconstruction and identification efficiencies; on the energy and momentum scales and resolutions; Same-sign events Figure 3. Tau identification fake-rate measured in W (→ µν)+jets data events for the BDT loose identification working point for (left) 1-prong and (right) 3-prong tau candidates.The fake-rate is parameterised in the charge product of the muon and fake tau candidate.Opposite-sign events are depicted by black circles and same-sign events by blue stars.The systematic uncertainty covers differences due to jet composition and is added to the statistical uncertainty in quadrature.and on the measurement of the integrated luminosity.Uncertainties on the background contributions estimated from data are discussed in their respective sections.
The overall uncertainty on the Z signal and the Z/γ * → ee/µµ/τ τ background due to choice of the PDFs, α S , and the renormalisation and factorisation scales is estimated to be 14% for a ditau mass of 1750 GeV, dominated by the PDF uncertainty [24].The uncertainty is evaluated using 90% CL MSTW2008NNLO PDF error sets and also takes into account potential differences between the following PDFs at the same α S : MSTW2008NNLO, CT10NNLO, NNPDF2.3 [76], ABM11 [77] and HERAPDF1.5 [78].Additionally, for Z/γ * → τ τ , a mass-dependent systematic uncertainty of up to 4% is attributed to electroweak corrections [24].This uncertainty is not considered for the signal as it is strongly model dependent.An uncertainty of 5% is estimated for diboson production, derived from scale, PDF and α S variations.A 6% uncertainty on the W +jets normalisation is derived from comparisons to data in the W +jets control region used to measure jet-to-tau fake-rates in the τ had τ had channel.For t t and single-top-quark production, the uncertainties from variations in the renormalisation and factorisation scales are in the range of 3-6% [57,79,80], while those related to the proton PDFs amount to 8% [48,51,[81][82][83].
The uncertainty on the integrated luminosity is 2.8%.It is derived from a preliminary calibration of the luminosity scale derived from beam-separation scans performed in November 2012, following the same methodology as that detailed in ref. [84].Comparisons of the efficiency of the hadronic tau trigger measured in data and in simulation are used to derive an uncertainty of 10% on the trigger efficiency.Differences between data and simulation in the reconstruction and identification efficiency and the energy scale of hadronic tau decays are taken into account.The associated uncertainties for muons and electrons are negligible for this analysis.
The systematic uncertainty on the identification efficiency of hadronic tau decays is estimated at low p T from data samples enriched in Z → τ τ events, yielding an uncertainty of 2-7% depending on the number of tracks and |η| of the tau candidate.At high p T , there are no abundant sources of real hadronic tau decays from which an efficiency measurement could be made.Rather, the tau identification is studied in high-p T dijet events as a function of the jet p T , which indicates that there is no degradation in the modelling of the detector response as a function of the p T of tau candidates.Based on the limited precision of these studies, an additional uncertainty of 14% • p T /TeV for 1-prong tau candidates and 8% • p T /TeV for 3-prong tau candidates is added in quadrature to the low-p T uncertainty for candidates with p T > 100 GeV.The reconstruction efficiency for 3-prong tau candidates decreases at high p T due to track merging.An uncertainty of 50% • p T /TeV above p T = 150 GeV is assigned for 3-prong candidates, derived from data/MC comparisons of tracking performance within jets.The energy scale uncertainty for hadronic tau decays and jets is evaluated based on the single-hadron response in the calorimeters [66,69].In addition, the tau energy scale is validated in data samples enriched in Z → τ τ events.The systematic uncertainty related to the tau energy scale is a function of η, p T and the number of prongs, and is generally near 3%.Energy scale and resolution uncertainties for all objects are propagated to the E miss T calculation.The uncertainty on the E miss T due to clusters that do not belong to any reconstructed object has a minor effect.
Table 2 summarises the systematic uncertainties across all channels for the 1750 GeV Z SSM mass point.In the τ had τ had channel the dominant uncertainties on both the signal and background come from the tau efficiency and energy scale, while in the τ lep τ had channels the statistical uncertainty on the background coming from the fake-factor estimate also makes a major contribution.The uncertainties are the same for background and similar for the signal for all higher signal mass points, since the same m tot T thresholds are used.The uncertainties for the lower mass points are typically very similar, except for the tau ID efficiency, the 3-prong tau reconstruction efficiency, the Z/γ * cross section and the statistical uncertainties, which are all a few percent lower, and the uncertainty on the tau energy scale for the signal, which can be up to 11% at low mass since the m tot T requirement is much tighter relative to the Z mass.The small data-driven uncertainty contribution to the signal in the τ had τ had channel comes from jets that are misidentified as hadronic tau decays.

Z signal models
In this section, the impact on the signal acceptance times efficiency from altering the Z couplings and from including interference between Z and Z/γ * is discussed.The acceptance times efficiency for a given Z model is defined as: Table 2. Uncertainties on the estimated Z SSM contribution (m Z SSM = 1750 GeV) and the corresponding total background contribution in percent for each channel.A dash denotes that the uncertainty is not applicable.The statistical uncertainty corresponds to the uncertainty due to the limited size of the samples produced via simulation or selected in control regions.The total consists of all uncertainties added in quadrature.
where N S is the expected number of Z events passing the full analysis selection, σB is the Z production cross section times τ + τ − branching fraction and L int is the integrated luminosity.The impact on Aε is presented as a fraction of the SSM value, Aε SSM .The corresponding impact on the acceptance alone, A, is also evaluated by replacing N S with the expected number of Z events after applying the kinematic selection directly to the generated particles before simulation.A Z model that couples preferentially to thirdgeneration fermions is also discussed.

Z signal acceptance
Changing the fermionic couplings of the Z from their SSM values can alter the signal acceptance of the analysis.Such changes are primarily due to alterations in either the tau polarisation or the total Z decay width.Alteration of the tau polarisation changes the tau decay kinematics.Most importantly it affects the visible momentum fraction, which enters the analysis through the p T thresholds of the reconstructed visible tau decay products and via the threshold on m tot T .The most extreme impact on the acceptance is seen for models that couple only to left-handed or right-handed tau leptons: Z L and Z R , respectively.Alteration of the quark couplings can impact the acceptance if it alters the tau polarisation.However, the maximum impact is much smaller than when altering the couplings to tau leptons.As the kinematic limit (due to the collision energy) for highmass Z production is approached, the signal exhibits an increased fraction of low-mass off-shell production.The fraction of off-shell events increases rapidly as a function of the decay width.Figure 4 shows Aε for the Z L and Z R models, and two models with artificially altered decay widths: Z narrow (Γ/m Z = 1%) and Z wide (Γ/m Z = 20%), each divided by Aε for Z SSM (Γ/m Z ≈ 3%).Interference between Z and Z/γ * is not included.The statistical uncertainty is typically below 5% but can be up to 14% at low mass.A smoothing is applied to reduce fluctuations.For Z L and Z R , the largest impact is observed at low mass, where the p T and m tot T thresholds are much more stringent on the signal.In this case, alteration of the tau couplings can lead to changes of up to +50% and −25%.The impact on the τ had τ had and τ lep τ had channels are different due to the different effect of polarisation on leptonic and hadronic tau decays.For Z narrow and Z wide , the impact is most prominent at high mass where changes of up to +20% and −45% are observed.At low mass, Aε only changes for widths above 10%.The impact is the same for all channels.For all Z models, the change in A is very similar to that in Aε, indicating that the efficiency is insensitive to changes in the Z couplings.The impact of interference between Z and Z/γ * is typically small.For the SSM, it leads to a reduction in the expected Z contribution of up to 10% for m Z ≤ 2 TeV, and up to 35% for the highest mass hypotheses.For Z L , Z R and Z narrow the impact is negligible.For Z wide the impact can be substantial and is highly dependent on the choice of the fermionic couplings.An exhaustive treatment is outside the scope of this article.Reinterpretations of the SSM results for models with large widths should specifically calculate the impact from interference.Signal acceptance times efficiency for Z L , Z R , Z narrow and Z wide divided by the acceptance times efficiency for Z SSM as a function of m Z , separately for the τ had τ had (solid lines with filled markers) and τ lep τ had (dashed lines with empty markers) channels.The statistical uncertainty is typically below 5% but can increase to 14% at low mass.

Non-universal G(221) model
The non-universal G(221) model [8,20,21] (also known by other names such as Topflavor) is an extension of the SM, containing additional heavy gauge bosons, Z NU and W ± NU , that may couple preferentially to third-generation fermions.The model is motivated by the idea that the large mass of the top-quark may suggest that the third fermion generation has a dynamical behaviour different from the first two generations.Accordingly, the SM weak SU (2) gauge group is split into two parts: one coupling to light fermions (the first two generations), SU (2) l and one coupling to heavy fermions (the third generation), SU (2) h .
The extended gauge group breaks to the SM SU (2) l+h at a high energy scale, u, and then eventually to U (1) EM at the usual electroweak scale, v = 246 GeV: The mixing between SU (2) l and SU (2) h is described by the parameter sin 2 φ.The Z NU and W ± NU bosons are degenerate in mass; the mass is defined at tree level by sin 2 φ and u.Large mixing between τ and µ leptons has been considered as an additional feature of the model, but is ignored here as it would lead to stronger limits via the dielectron and dimuon searches.The Z NU couples almost exclusively to left-handed fermions, and while the coupling strength differs for light and heavy fermions, it is largely insensitive to the electric charge or weak isospin, leading to almost universal couplings for all light and heavy fermions.
Figure 5(left) shows the Z NU cross section times τ + τ − branching fraction, σB NU , divided by σB SSM .For much of the parameter space σB NU is larger than σB SSM , peaking at moderate values of sin 2 φ.For extreme values of sin 2 φ either the cross section is suppressed by weakened couplings to light quarks (sin 2 φ ∼ 0) or the branching fraction is suppressed by weakened couplings to tau leptons (sin 2 φ ∼ 1).Figures 5(middle) and 5(right) show the Z NU acceptance times efficiency, Aε NU , divided by Aε SSM , for the τ had τ had and τ lep τ had channels, respectively.In general Aε NU is lower than Aε SSM .At low mass this is mainly due to the left-handed couplings, which result in softer visible tau decays.Near sin 2 φ ∼ 0 and sin 2 φ ∼ 1, the acceptance loss comes mainly from the significantly increased decay width, which causes a large fraction of the signal to be produced off shell.

Results and discussion
A summary of the expected number of events remaining after successively applying each selection requirement, up to the m tot T threshold, for the signal and dominant background processes is given in table 3. Figures 6(left) and 6(right) show the m tot T distribution after event selection in the τ had τ had and τ lep τ had channels, respectively.The numbers of observed and expected events (including their total uncertainties) after applying the m tot T thresholds in all channels are summarised in table 4. In all cases, the number of observed events is consistent with the expected Standard Model background.Therefore, upper limits are set on the production of a high-mass resonance decaying to τ + τ − pairs.The acceptance and acceptance times efficiency for Z SSM is shown in figure 7. The statistical combination of the channels employs a likelihood function constructed as the product of Poisson-distributed random numbers describing the total number of events observed in each channel.The probability in each channel is evaluated for the observed number of data events given the signal-plus-background expectation.Systematic uncertainties on the expected number of events are incorporated into the likelihood via nuisance parameters constrained by Gaussian distributions.Correlations between signal and background and across channels are taken into account.A signal-strength parameter multiplies the expected signal in each channel, for which a positive uniform prior probability distribution is assumed.Theoretical uncertainties on the signal cross section are not included in the calculation of the experimental limit as they are model dependent.
Bayesian 95% credibility upper limits are set on σB SSM as a function of m Z , using the Bayesian Analysis Toolkit [85].Figures 8(left) and 8(right) show the limits for the individual channels and for the combination, respectively.The resulting 95% CL lower limit on the mass of a Z SSM decaying to τ + τ − pairs is 2.02 TeV, with an expected limit of 1.95 TeV.The observed and expected limits in the individual channels are, respectively: 1.89 and 1.80 TeV (τ had τ had ); 1.59 and 1.59 TeV (τ µ τ had ); and 1.55 and 1.65 TeV (τ e τ had ).Alteration of the Z couplings can impact the signal acceptance as described in section 8.1.These changes translate linearly to the limits on σB SSM .Limits on the Z L and Z R models are shown in figure 8 (right).The impact of the choice of the prior on the signal-strength parameter is evaluated by also considering the reference prior [86].Use of the reference Figure 6.The m tot T distribution after event selection in the (left) τ had τ had and (right) τ lep τ had channels.The estimated contributions from SM processes are stacked and appear in the same order as in the legend.The expected contributions from three Z SSM signals with masses of 750, 1250 and 1750 GeV are shown, stacked on the total SM expectation.The events observed in data are overlaid.The hatched area indicates the uncertainty on the total estimated background.The bins have a constant width of (left) 0.153 and (right) 0.184 in log(m tot T ).The last bin includes overflow events.The inset shows the ratio of the observed events over the total expected SM contribution.The statistical uncertainty from the observed events and the expected SM contribution are shown on the points and by the yellow band, respectively.The red band depicts the total systematic and statistical uncertainties on the SM contribution added in quadrature.
[GeV]    ) and observed (N ) events in the τ had τ had and τ lep τ had channels.The signal mass (m Z ) and corresponding m tot T thresholds are given in units of GeV.The total uncertainty (statistical and systematic added in quadrature) in the least significant digit(s) is shown in parentheses.
prior improves the limit on σB SSM by a maximum of 10%, corresponding to an increase of 20 GeV in the observed mass limit.
Limits on the non-universal G(221) model are also calculated.The signal contributions in the τ had τ had and τ lep τ had channels are rescaled by σB NU /σB SSM •Aε NU /Aε SSM (as derived in section 8.2).In addition, the systematic uncertainties are re-evaluated for each point in parameter space.Figure 9 shows the region in the Z NU parameter space excluded at 95% credibility: Z NU bosons with masses below 1.3-2.1 TeV are excluded in the range 0.03 < sin 2 φ < 0.5 assuming no µ-τ mixing.Indirect limits are also overlaid. .Bayesian 95% credibility upper limits on the cross section times ditau branching fraction for a Z in the Sequential Standard Model.The figure shows (left) an overlay of the observed (solid lines with filled markers) and expected (dashed lines with empty markers) limits in each channel and for the combination, and (right) the combined limit with 1σ and 2σ uncertainty bands and an overlay of the impact of the Z L /Z R models.The width of the Z SSM theory band represents the theoretical uncertainty from the PDF error set, the choice of PDF as well as the strong coupling constant.221) parameter space from the combination of the τ had τ had and τ lep τ had channels (blue).Indirect limits at 95% CL from fits to electroweak precision measurements (EWPT) [27], lepton flavour violation (LFV) [28], CKM unitarity [29] and the original Z-pole data [8] are overlaid.

Conclusion
A search for high-mass ditau resonances was performed using 19.5-20.3fb −1 of data collected with the ATLAS detector in pp collisions at √ s = 8 TeV at the LHC.The τ had τ had , τ µ τ had and τ e τ had channels are analysed.The observed number of events in regions with high total transverse mass are consistent with the SM expectations.Limits are set on the cross section times branching fraction for such resonances.The resulting lower limit on the mass of a Z decaying to τ + τ − in the Sequential Standard Model is 2.02 TeV at 95% credibility, in agreement with the expected limit of 1.95 TeV in the absence of a signal.The impact on the Z acceptance from altering the Z couplings and the total decay width is found to be significant, and can be up to 50%.The impact from interference between Z and Z/γ * is only important when the total decay width of the Z is large.Limits on the non-universal G(221) model are also established, where Z bosons with masses below 1.3-2.1 TeV are excluded in the range 0.03 < sin 2 φ < 0.5 assuming no µ-τ mixing.

Figure 1 .
Figure 1.Tau ID fake-factors for (left) 1-prong and (right) 3-prong tau candidates, measured in the multijet control region of the τ had τ had channel.The statistical and systematic uncertainties are shown, successively added in quadrature.

Figure 2 .
Figure 2. Tau ID fake-factors for (left) 1-prong and (right) 3-prong tau candidates, measured in the W +jets control region of the τ µ τ had channel, integrated across all |η| regions.The statistical and systematic uncertainties are shown, successively added in quadrature.The fake-factors measured in the alternative multijet control region are overlaid.
Figure 4.Signal acceptance times efficiency for Z L , Z R , Z narrow and Z wide divided by the acceptance times efficiency for Z SSM as a function of m Z , separately for the τ had τ had (solid lines with filled markers) and τ lep τ had (dashed lines with empty markers) channels.The statistical uncertainty is typically below 5% but can increase to 14% at low mass.

Figure 5 .
Figure 5. Signal production cross section times τ + τ − branching fraction for Z NU , σB NU , divided by σB SSM (left) and acceptance times efficiency for Z NU , Aε NU , divided by Aε SSM for the (middle) τ had τ had and (right) τ lep τ had channels, as a function of sin 2 φ and m Z .

Figure 7 .
Figure 7. Acceptance (dashed lines with empty markers) and acceptance times efficiency (solid lines with filled markers) for Z SSM as a function of the Z SSM mass.Contributions from the individual channels and the full analysis are given.

Figure 8
Figure 8. Bayesian 95% credibility upper limits on the cross section times ditau branching fraction for a Z in the Sequential Standard Model.The figure shows (left) an overlay of the observed (solid lines with filled markers) and expected (dashed lines with empty markers) limits in each channel and for the combination, and (right) the combined limit with 1σ and 2σ uncertainty bands and an overlay of the impact of the Z L /Z R models.The width of the Z SSM theory band represents the theoretical uncertainty from the PDF error set, the choice of PDF as well as the strong coupling constant.

Table 3 .
γ * +jets Top + diboson Z SSM Number of expected signal (m Z SSM = 1750 GeV) and background events in the τ had τ had and τ lep τ had channels after successively applying each selection criterion.The statistical uncertainty in the least significant digit(s) is shown in parentheses.

Table 4 .
Number of expected Z SSM signal (N S ), background (N B