Search for additional heavy neutral Higgs and gauge bosons in the ditau final state produced in 36 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A search for heavy neutral Higgs bosons and $Z^{\prime}$ bosons is performed using a data sample corresponding to an integrated luminosity of 36.1 fb$^{-1}$ from proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded by the ATLAS detector at the LHC during 2015 and 2016. The heavy resonance is assumed to decay to $\tau^+\tau^-$ with at least one tau lepton decaying to final states with hadrons and a neutrino. The search is performed in the mass range of 0.2-2.25 TeV for Higgs bosons and 0.2-4.0 TeV for $Z^{\prime}$ bosons. The data are in good agreement with the background predicted by the Standard Model. The results are interpreted in benchmark scenarios. In the context of the hMSSM scenario, the data exclude $\tan\beta>1.0$ for $m_A$ = 0.25 TeV and $\tan\beta>42$ for $m_A$ = 1.5 TeV at the 95% confidence level. For the Sequential Standard Model, $Z^{\prime}_\mathrm{SSM}$ with $m_{Z^{\prime}}<2.42$ TeV is excluded at 95% confidence level, while $Z^{\prime}_\mathrm{NU}$ with $m_{Z^{\prime}}<2.25$ TeV is excluded for the non-universal $G(221)$ model that exhibits enhanced couplings to third-generation fermions.


Introduction
The discovery of a scalar particle [1, 2] at the Large Hadron Collider (LHC) [3] has provided important insight into the mechanism of electroweak symmetry breaking. Experimental studies of the new particle [4-8] demonstrate consistency with the Standard Model (SM) Higgs boson [9-14]. However, it remains possible that the discovered particle is part of an extended scalar sector, a scenario that is predicted by a number of theoretical arguments [15,16]. ( Figure 1(d)), there is little gain in splitting the data into b-tag and b-veto categories. Hence, the Z analysis uses an inclusive selection instead.
The paper 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 reported in Section 3. The event reconstruction is presented in Section 4. A description of the event selection criteria is given in Section 5. Section 6 explains the estimation of background contributions, followed by a description of systematic uncertainties in Section 7. Results are presented in Section 8, followed by concluding remarks in Section 9.

ATLAS detector
The ATLAS detector [43] at the LHC covers nearly the entire solid angle around the collision point. 3 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 system is immersed in a 2 T axial magnetic field and provides chargedparticle tracking in the range |η| < 2.5.
The high-granularity silicon pixel detector covers the vertex region and typically provides four measurements per track. The innermost layer, known as the insertable B-Layer [44], was added in 2014 and provides high-resolution hits at small radius to improve the tracking performance. The pixel detector is surrounded by the silicon microstrip tracker, which usually provides four two-dimensional measurement 3 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the interaction point to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, φ) 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 = − ln tan(θ/2). Angular distance is measured in units of ∆R ≡ (∆η) 2 + (∆φ) 2 . points per track. These silicon detectors are complemented by the transition radiation tracker, which enables radially extended track reconstruction up to |η| = 2.0. The transition radiation tracker also provides electron identification information 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, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) electromagnetic calorimeters, with an additional thin LAr presampler covering |η| < 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 |η| < 1.7, and two copper/LAr hadronic endcap calorimeters that cover 1.5 < |η| < 3.2. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules, optimised for electromagnetic and hadronic measurements respectively, in the region 3.1 < |η| < 4.9.
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 two-level trigger system is used to select interesting events [45,46]. The level-one trigger is implemented in hardware and uses a subset of detector information to reduce the event rate to a design value of at most 100 kHz. This is followed by the software-based high-level trigger, which reduces the event rate to 1 kHz.

Data and simulated event samples
The results in this paper use proton-proton collision data at a centre-of-mass energy of √ s = 13 TeV collected by the ATLAS detector at the LHC during 2015 and 2016. The data correspond to a total integrated luminosity of 36.1 fb −1 after requiring that all relevant components of the ATLAS detector are in good working condition. Selected events must satisfy criteria designed to reduce backgrounds from cosmic rays, beam-induced events and calorimeter noise [47]. They must also contain at least one primary vertex with at least two associated tracks. The primary vertex is chosen as the proton-proton vertex candidate with the highest sum of the squared transverse momenta of the associated tracks.
Simulated events are used to estimate the signal efficiencies and some of the background contributions. The simulated event samples are normalised using their theoretical cross sections and the integrated luminosity. Simulated events with a heavy neutral MSSM Higgs boson produced via gluon-gluon fusion and in association with b-quarks were generated at next-to-leading order (NLO) with Powheg-Box v2 [48-50] and MG5_aMC@NLO 2.1.2 [51, 52] (using the four-flavour scheme), respectively. The CT10 [53] set of parton distribution functions (PDFs) was used in the generation of gluon-gluon fusion events while CT10nlo_nf4 [54] was used to produce the b-associated signal samples. Pythia 8.210 [55] with the AZNLO [56] (A14 [57]) set of tuned parameters (tune) was used together with the CTEQ6L1 [58] (NNPDF2.3LO [59]) PDF set for the parton shower calculation at leading order (LO), underlying event and hadronisation in the gluon-gluon fusion (b-associated) production. The gluon-gluon fusion sample was generated assuming SM couplings and underestimates the loop contribution from b-quarks at high tan β, which can impact the Higgs boson p T spectrum. Generator-level studies indicate this has a negligible impact on the final mass distribution and only a few percent impact on the signal acceptance, except for mass hypotheses below 400 GeV where the impact can be up to 10%, so the effect is neglected.
using the ME+PS@NLO prescription [103]. The CT10nlo PDF set was used in conjunction with dedicated parton shower tuning developed by the Sherpa authors. The W+ jets production is normalised to the NNLO cross sections with FEWZ [94,104,105].
For the generation of tt or a single top quark in the Wt-channel and s-channel, the Powheg-Box v2 event generator was used with the CT10 PDF set in the matrix element calculation. Electroweak t-channel single-top-quark events were generated with the Powheg-Box v1 event generator. This event generator uses the four-flavour scheme for the NLO matrix elements calculations together with the fixed fourflavour PDF set CT10f4. For all top processes, top-quark spin correlations were preserved (for t-channel, top quarks were decayed with MadSpin [106]). The parton shower, hadronisation, and the underlying event were simulated using Pythia 6.428 with the CTEQ6L1 PDF sets and the corresponding Perugia 2012 tune [107]. The top mass was set to 172.5 GeV. The tt production sample is normalised to the predicted production cross section as calculated with the Top++2.0 program to NNLO in perturbative QCD, including soft-gluon resummation to next-to-next-to-leading-log (NNLL) order (Ref. [108] and references therein). For the single-top-quark event samples, an approximate calculation at NLO in QCD for the s-channel and t-channel [109,110] and an NLO+NNLL calculation for the Wt-channel [111] are used for the normalisation.
Diboson processes were modelled using the Sherpa 2.1.1 event generator and they were calculated for up to one (ZZ) or no (WW, WZ) additional partons at NLO and up to three additional partons at LO using Comix and OpenLoops merged with the Sherpa parton shower using the ME+PS@NLO prescription. The CT10 PDF set was used in conjunction with dedicated parton shower tuning developed by the Sherpa authors. The event generator cross sections are used in this case (already at NLO). In addition, the Sherpa diboson sample cross section was scaled down to account for its use of α QED = 1/129 rather than 1/132 corresponding to the use of current PDG parameters as input to the G µ scheme.
Properties of the bottom and charm hadron decays were set with the EvtGen v1.2.0 program [112] in samples that were not produced with Sherpa. Simulated minimum-bias events were overlaid on all simulated samples to include the effect of multiple proton-proton interactions in the same and neighbouring bunch crossings ("pile-up"). These minimum-bias events were generated with Pythia 8.186, using the A2 tune [113] and the MSTW2008LO PDF [114]. Each sample was simulated using the full Geant 4 [115,116] simulation of the ATLAS detector, with the exception of the b-associated MSSM Higgs boson signal, for which the AtlfastII [117] fast simulation framework was used. Finally, the simulated events are processed through the same reconstruction software as the data.

Event reconstruction
Electron candidates are reconstructed from energy deposits in the electromagnetic calorimeter associated with a charged-particle track measured in the inner detector [118][119][120]. The electron candidates are required to pass a "loose" likelihood-based identification selection, to have a transverse momentum p T > 15 GeV and to be in the fiducial volume of the inner detector, |η| < 2.47. The transition region between the barrel and endcap calorimeters (1.37 < |η| < 1.52) is excluded.
Muon candidates are reconstructed in the range |η| < 2.5 by matching tracks found in the muon spectrometer to tracks found in the inner detector [121]. The tracks of the muon candidates are re-fitted using the complete track information from both detector systems. They are required to have a transverse momentum p T > 7 GeV and to pass a "loose" muon identification requirement.
The selected lepton (electron or muon) in the τ lep τ had channel must then have p T > 30 GeV and pass a "medium" identification requirement. This lepton is considered isolated if it meets p T -and η-dependent isolation criteria utilising calorimetric and tracking information. The criteria correspond to an efficiency of 90% (99%) for a transverse momentum of p T = 25 (60) GeV. The efficiency increases with lepton p T as the requirements are relaxed to account for the decreased background from misidentified jets.
Jets are reconstructed from topological clusters of energy depositions [122] in the calorimeter using the anti-k t algorithm [123,124], with a radius parameter value R = 0.4. The average energy contribution from pile-up is subtracted according to the jet area and the jets are calibrated as described in Ref [125]. They are required to have p T > 20 GeV and |η| < 2.5. To reduce the effect of pile-up, a jet vertex tagger algorithm is used for jets with p T < 60 GeV and |η| < 2.4. It employs a multivariate technique based on jet energy, vertexing and tracking variables to determine the likelihood that the jet originates from or is heavily contaminated by pile-up [126]. In order to identify jets containing b-hadrons (b-jets), a multivariate algorithm is used, which is based on the presence of tracks with a large impact parameter with respect to the primary vertex, the presence of displaced secondary vertices and the reconstructed flight paths of b-and c-hadrons associated with the jet [127,128]. The algorithm has an average efficiency of 70% for b-jets and rejections of approximately 13, 56 and 380 for c-jets, hadronic tau decays and jets initiated by light quarks or gluons, respectively, as determined in simulated tt events.
Hadronic tau decays are composed of a neutrino and a set of visible decay products (τ had-vis ), typically one or three charged pions and up to two neutral pions. The reconstruction of the visible decay products is seeded by jets [129]. The τ had-vis candidates must have p T > 25 (45) GeV in the τ lep τ had (τ had τ had ) channel, |η| < 2.5 excluding 1.37 < |η| < 1.52, one or three associated tracks and an electric charge of ±1. The leading-p T τ had-vis candidate in the τ lep τ had channel and the two leading-p T τ had-vis candidates in the τ had τ had channel are then selected and all remaining candidates are considered as jets. A Boosted Decision Tree (BDT) identification procedure, based on calorimetric shower shapes and tracking information is used to reject backgrounds from jets [130,131]. Two τ had-vis identification criteria are used: "loose" and "medium", specified in Section 5. The criteria correspond to efficiencies of about 60% (50%) and 55% (40%) in Z/γ * → ττ events and rejections of about 30 (30) and 50 (100) in multijet events, for one-track (three-track) τ had-vis candidates, respectively. An additional dedicated likelihood-based veto is used to reduce the number of electrons misidentified as τ had-vis in the τ lep τ had channel, providing 95% efficiency and a background rejection between 20 and 200, depending on the pseudorapidity of the τ had-vis candidate.
Geometrically overlapping objects are removed in the following order: (a) jets within ∆R = 0.2 of selected τ had-vis candidates are excluded, (b) jets within ∆R = 0.4 of an electron or muon are excluded, (c) any τ had-vis candidate within ∆R = 0.2 of an electron or muon is excluded, (d) electrons within ∆R = 0.2 of a muon are excluded.
The missing transverse momentum, E miss T , is calculated as the negative vectorial sum of the p T of all fully reconstructed and calibrated physics objects [132,133]. This procedure includes a "soft term", which is calculated using the inner-detector tracks that originate from the hard-scattering vertex but are not associated with reconstructed objects. 5 Event selection 5.1 τ had τ had channel Events in the τ had τ had channel are recorded using single-tau triggers with p T thresholds of 80, 125 or 160 GeV, depending on the data-taking period. Events must contain at least two τ had-vis candidates with p T > 65 GeV and no electrons or muons. The leading-p T τ had-vis candidate must be geometrically matched to the trigger signature and must exceed the trigger p T threshold by 5 GeV. The leading and sub-leading τ had-vis candidates must satisfy the "medium" and "loose" identification criteria, respectively. They must also have opposite electric charge and be back to back in the transverse plane: |∆φ(p τ 1 T , p τ 2 T )| > 2.7 rad, as tau leptons from the decay of heavy neutral resonances are typically produced back to back in the transverse plane. The signal acceptance times efficiency for this selection (calculated with respect to all possible ditau final states) varies between 1% and 7% for signals with masses of 0.35 TeV or higher. The maximum occurs for signals with masses of around 0.9 TeV, degradations occur at lower masses due to the τ had-vis p T thresholds and at higher masses due to the τ had-vis reconstruction and identification efficiencies. A summary of the selection is given in Table 1 of Section 6.

τ lep τ had channel
Events in the τ lep τ had channel are recorded using single-electron and single-muon triggers with p T thresholds ranging from 20 to 140 GeV and various isolation criteria. The events must contain at least one τ had-vis candidate passing the medium identification, exactly one isolated lepton (from here on referred to as ) that is geometrically matched to the trigger signature (implying |η| < 2.4 in the τ µ τ had channel), and no additional reconstructed leptons. The identified τ had-vis candidate must have |η| < 2.3 to reduce background from misidentified electrons. The isolated lepton and identified τ had-vis candidate must have opposite electric charge and be back to back in the transverse plane: |∆φ(p T , p τ had-vis T )| > 2.4 rad. To reduce background from W+ jets production, the transverse mass of the isolated lepton and the missing transverse momentum, must be less than 40 GeV. To reduce background from Z → ee production in the τ e τ had channel, events where the isolated lepton and identified τ had-vis candidate have an invariant mass between 80 and 110 GeV are rejected. The signal acceptance times efficiency for this selection also varies between 1% and 7%, but the maximum occurs at lower masses due to the lower p T thresholds on the tau decay products. A summary of the selection is given in Table 2 of Section 6.

Event categories
Events satisfying the selection criteria in the τ lep τ had and τ had τ had channels are categorised to exploit the different production modes in the MSSM. Events containing at least one b-tagged jet enter the b-tag category, while events containing no b-tagged jets enter the b-veto category. The categorisation is not used for the Z search.

Ditau mass reconstruction
The ditau mass reconstruction is important for achieving good separation between signal and background. However, ditau mass reconstruction is challenging due to the presence of neutrinos from the τ-lepton decays. Therefore, the mass reconstruction used for both the τ had τ had and τ lep τ had channels is the total transverse mass, defined as: where p τ 1 T and p τ 2 T are the momenta of the visible tau decay products (including τ had and τ lep ) projected into the transverse plane. More complex mass reconstruction techniques were investigated, but they did not improve the expected sensitivity.

Background estimation
The dominant background contribution in the τ had τ had channel is from multijet production, which is estimated using a data-driven technique, described in Section 6.1. Other important background contributions come from Z/γ * → ττ production at high m tot T in the b-veto category, tt production in the b-tag category, and to a lesser extent W(→ ν)+jets, single top-quark, diboson and Z/γ * (→ )+jets production. These contributions are estimated using simulation. Corrections are applied to the simulation to account for mismodelling of the trigger, reconstruction, identification and isolation efficiencies, the electron to τ had-vis misidentification rate and the momentum scales and resolutions. To further improve the modelling in the τ had τ had channel, events in the simulation that contain quark-or gluon-initiated jets (henceforth called jets) that are misidentified as τ had-vis candidates are weighted by fake-rates measured in W+ jets and tt control regions in data.
The dominant background contribution in the τ lep τ had channel arises from processes where the τ had-vis candidate originates from a jet. This contribution is estimated using a data-driven technique similar to the τ had τ had channel, described in Section 6.2. The events are divided into those where the selected lepton is correctly identified, predominantly from W+ jets (tt) production in the b-veto (b-tag) channel, and those where the selected lepton arises from a jet, predominantly from multijet production. Backgrounds where both the τ had-vis and lepton candidates originate from electrons, muons or taus (real-lepton) arise from Z/γ * → ττ production in the b-veto category and tt production in the b-tag category, with minor contributions from Z/γ * → , diboson and single top-quark production. These contributions are estimated using simulation. To help constrain the normalisation of the tt contribution, a control region rich in tt events (CR-T) is defined and included in the statistical fitting procedure. The other major background contributions can be adequately constrained in the signal regions. Events in this control region must pass the signal selection for the b-tag category, but the m T (p T , E miss T ) selection is replaced by m T (p T , E miss T ) > 110 (100) GeV in the τ e τ had (τ µ τ had ) channel. The tighter selection in the τ e τ had channel is used to help suppress the larger multijet contamination. The region has ∼90% tt purity.

Jet background estimate in the τ had τ had channel
The data-driven technique used to estimate the dominant multijet background in the τ had τ had channel is described in Section 6.1.1. The method used to weight simulated events to estimate the remaining Table 1: Definition of signal, control and fakes regions used in the τ had τ had channel. The symbol τ 1 (τ 2 ) represents the leading (sub-leading) τ had-vis candidate.

Region Selection
background containing events with τ had-vis candidates that originate from jets is described in Section 6.1.2. A summary of the signal, control and fakes regions used in these methods is provided in Table 1. The associated uncertainties are discussed in Section 7.2.

Multijet events
The contribution of multijet events in the signal region (SR) of the τ had τ had channel is estimated using events in two control regions (CR-1 and DJ-FR). Events in CR-1 must pass the same selection as SR, but the sub-leading τ had-vis candidate must fail τ had-vis identification. The non-multijet contamination in this region, N CR−1 non−MJ , amounts to ∼1.6% (∼7.0%) in the b-veto (b-tag) channel, and is subtracted using simulation. Events in DJ-FR (the dijet fakes-region) are used to measure fake-factors ( f DJ ), which are defined as the ratio of the number of τ had-vis that pass to those that fail the identification. The fake-factors are used to weight the events in CR-1 to estimate the multijet contribution: The selection for the DJ-FR is designed to be as similar to the signal selection as possible, while avoiding contamination from τ had-vis . Events are selected by single-jet triggers with p T thresholds ranging from 60 to 380 GeV, with all but the highest-threshold trigger being prescaled. They must contain at least two τ had-vis candidates, where the leading candidate has p T > 85 GeV and also exceeds the trigger threshold by 10%, and the sub-leading candidate has p T > 65 GeV. The τ had-vis candidates must have opposite charge sign, be back to back in the transverse plane, |∆φ(p τ 1 T , p τ 2 T )| > 2.7 rad and the p T of the sub-leading τ had-vis must be at least 30% of the leading τ had-vis p T . The fake-factors are measured using the subleading τ had-vis candidate to avoid trigger bias and to be consistent with their application in CR-1. They are parameterised as functions of the sub-leading τ had-vis p T and the sub-leading τ had-vis track multiplicity. The purity of multijet events that pass the τ had-vis identification is 98-99% (93-98%) for the b-veto (b-tag) categories. The non-multijet contamination is subtracted using simulation. The fake-factors are shown in Figure 2.

Non-multijet events
In the τ had τ had channel, backgrounds originating from jets that are misidentified as τ had-vis in processes other than multijet production (predominantly W+ jets in the b-veto and tt in the b-tag categories) are estimated using simulation. Rather than applying the τ had-vis identification to the simulated jets, they are weighted by fake-rates as in Ref.
[41]. This not only ensures the correct fake-rate, but also enhances the statistical precision of the estimate, as events failing the τ had-vis identification are not discarded. The fakerate for the sub-leading τ had-vis candidate is defined as the ratio of the number of candidates that pass the identification to the total number of candidates. The fake-rate for the leading τ had-vis candidate is defined as the ratio of the number of candidates that pass the identification and the single-tau trigger requirement to the total number of candidates.
The fake-rates applied to tt and single-top-quark events are calculated from a fakes region enriched in tt events (T-FR), while the fake-rates for all other processes are calculated in a fakes region enriched in W+ jets events (W-FR). Both T-FR and W-FR use events selected by a single-muon trigger with a p T threshold of 50 GeV. They must contain exactly one isolated muon with p T > 55 GeV that fired the trigger, no electrons and at least one τ had-vis candidate with p T > 50 GeV. The events must also satisfy |∆φ(p µ T , p τ had-vis T )| > 2.4 rad and m T (p µ T , E miss T ) > 40 GeV. The events are then categorised into b-tag and b-veto categories, defining T-FR and W-FR, respectively. Backgrounds from non-tt (non-W+ jets) processes are subtracted from T-FR (W-FR) using simulation. The fake-rates are measured using the leading-p T τ had-vis candidate and are parameterised as functions of the τ had-vis p T and track multiplicity.

Jet background estimate in the τ lep τ had channel
The background contribution from events where the τ had-vis candidate originates from a jet in the τ lep τ had channel is estimated using a data-driven method, which is similar to the one used to estimate the multijet contribution in the τ had τ had channel. Events in the control region CR-1 must pass the same selection as the τ lep τ had SR, but the τ had-vis candidate must fail τ had-vis identification. These events are weighted to estimate the jet background in SR, but the weighting method must be extended to account for the fact that

CR-1
Fail lepton isolation Fail tau ID High transverse mass

CR-2
No loose tau

Low transverse mass Pass lepton isolation
Low transverse mass Pass lepton isolation Figure 3: Schematic of the fake-factor background estimation in the τ lep τ had channel. The fake-factors, f X (X = MJ, W, L), are defined as the ratio of events in data that pass/fail the specified selection requirements, measured in the fakes-regions: MJ-FR, W-FR and L-FR, respectively. The multijet contribution is estimated by weighting events in CR-2 by the product of f L and f MJ . The contribution from W+ jets and tt events where the τ had-vis candidate originates from a jet is estimated by subtracting the multijet contribution from CR-1 and then weighting by f W .
There is a small overlap of events between L-FR and the CR-1 and CR-2 regions. The contribution where both the selected τ had-vis and lepton originate from leptons is estimated using simulation (not shown here).
CR-1 contains both multijet and W+ jets (or tt) events, which have significantly different fake-factors. This is mainly due to a different fraction of quark-initiated jets, which are typically more narrow and produce fewer hadrons than gluon-initiated jets, and are thus more likely to pass the τ had-vis identification. The procedure, depicted in Figure 3, is described in the following. A summary of the corresponding signal, control and fakes regions is provided in Table 2. The associated uncertainties are discussed in Section 7.2.

Multijet events
The multijet contributions in both CR-1 (N CR−1 multijet ) and SR (N SR multijet ) are estimated from events where the τ had-vis fails identification and the selected lepton fails isolation (CR-2). The non-multijet background is subtracted using simulation and the events are weighted first by the lepton-isolation fake-factor ( f L ), Table 2: Definition of signal, control and fakes regions used in the τ lep τ had channel. The symbol represents the selected electron or muon candidate and τ 1 represents the leading τ had-vis candidate.

Region Selection
Pass SR except: τ 1 (very-loose, fail medium) CR-2 Pass SR except: τ 1 (very-loose, fail medium), (fail isolation) MJ-FR Pass SR except: τ 1 (very-loose), (fail isolation) W-FR Pass SR except: yielding N CR−1 multijet , and then by the multijet tau fake-factor ( f MJ ): The fake-factor f MJ is measured in the multijet fakes-region (MJ-FR) defined in Section 6.2.3 and the fake-factor f L is measured in the lepton fakes-region (L-FR) defined in Section 6.2.4.

Non-multijet events
The contribution from W+ jets (and tt) events where the τ had-vis candidate originates from a jet is estimated from events in CR-1 that remain after subtracting the multijet contribution and the real-lepton contribution (estimated using simulation). The events are weighted by the W+ jets tau fake-factor ( f W ): The fake-factor f W is measured in the W+ jets fakes-region (W-FR) defined in Section 6.2.3.

Tau identification fake-factors
Both f W and f MJ are parameterised as functions of τ had-vis p T , τ had-vis track multiplicity and |∆φ(p τ had-vis T , E miss T )|. The |∆φ(p τ had-vis T , E miss T )| dependence is included to encapsulate correlations between the τ had-vis identification and energy response, which impact the E miss T calculation. Due to the limited size of the control regions, the |∆φ(p τ had-vis T , E miss T )| dependence is extracted as a sequential correction and is only applied in the b-veto channel. The selection for W-FR and MJ-FR are the same as for SR with modifications described in the following. The medium τ had-vis identification criterion is replaced by a very loose criterion with an efficiency of about 99% for τ had-vis and a rejection of about 2 (3) for one-track (three-track) jets. Events passing the medium identification criterion enter the fake-factor numerators, while those failing enter the denominators. The very loose identification reduces differences between f W and f MJ , as it tends to reject gluon-initiated jets, enhancing the fraction of quark-initiated jets in W-FR and MJ-FR. This selection is also applied consistently to CR-1. In MJ-FR, the selected lepton must fail isolation. The multijet purity for events that pass the τ had-vis identification in this region is ∼88% for the b-veto category and ∼93% for the b-tag category. All nonmultijet contamination is subtracted from MJ-FR using simulation. The fake-factor f MJ is further split by category (b-veto, b-tag) and by data-taking period (2015, 2016) to account for changing isolation criteria in the trigger that affect MJ-FR differently to SR.
In the W-FR, the m T (p T , E miss T ) criterion is replaced by 70(60) < m T (p T , E miss T ) < 150 GeV in the τ e τ had (τ µ τ had ) channel. The purity of W+ jets events that pass the τ had-vis identification is ∼85% in the bveto category. The b-tag category is dominated by tt events, but the purity of events where the τ had-vis candidate originates from a jet is only ∼40% due to the significant fraction of τ had-vis from W boson decays. The multijet and real-lepton backgrounds are subtracted from W-FR analogously to CR-1 in the W+ jets estimate. Due to the large τ had-vis contamination in the b-tag region, f W is not split by category, but the b-veto parameterisation is used in the b-tag region, with a p T -independent correction factor of 0.8 (0.66) for one-track (three-track) τ had-vis . The correction factor is obtained from a direct measurement of the fake-factors in b-tag events.

Lepton isolation fake-factor
The fake-factor f L is measured in L-FR, which must have exactly one selected lepton, m T (p T , E miss T ) < 30 GeV and no τ had-vis candidates passing the loose identification but rather at least one selected jet (not counting the b-tagged jet in the b-tag region). The selection is designed to purify multijet events while suppressing W+ jets and tt events. Events where the selected lepton passes (fails) isolation enter the f L numerator (denominator). All non-multijet contributions are subtracted using simulation. The fake-factors are parameterised as a function of lepton |η|, and are further split by lepton type (elec-tron, muon), category (b-veto, b-tag) and into two regions of muon p T , due to differences in the isolation criteria of the low-and high-p T triggers in the τ µ τ had channel.

Systematic uncertainties
Uncertainties affecting the simulated signal and background contributions are discussed in Section 7.1. These include uncertainties associated with the determination of the integrated luminosity, the detector simulation, the theoretical cross sections and the modelling from the event generators. Uncertainties associated with the data-driven background estimates are discussed in Section 7.2.

Uncertainties in simulation estimates
The uncertainty in the combined 2015+2016 integrated luminosity is 3.2%, which affects all simulated samples. It is derived, following a methodology similar to that detailed in Ref.
[134], from a preliminary calibration of the luminosity scale using x-y beam-separation scans performed in August 2015 and May 2016. The uncertainty related to the overlay of pile-up events is estimated by varying the average number of interactions per bunch crossing by 9%. The uncertainties related to the detector simulation manifest themselves through the efficiency of the reconstruction, identification and triggering algorithms, and the energy scale and resolution for electrons, muons, τ had-vis , (b-)jets and the E miss T soft term. These uncertainties are considered for all simulated samples; their impact is taken into account when estimating signal and background contributions and when subtracting contamination from regions in the data-driven estimates. The effects of the particle energy-scale uncertainties are propagated to E miss T . The uncertainty in the τ had-vis identification efficiency as determined from measurements of Z → ττ events is 5-6%. 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 20%/TeV (25%/TeV) for one-track (three-track) τ had-vis candidates with p T > 150 GeV is assigned. The τ had-vis trigger efficiency uncertainty is 3-14%. The uncertainty in the τ had-vis energy scale is 2-3%. The probability for electrons to be misidentified as τ had-vis is measured with a precision of 3-14% [131]. The electron, muon, jet and E miss T systematic uncertainties described above are found to have a very small impact.
Theoretical cross-section uncertainties are taken into account for all backgrounds estimated using simulation. For Z/γ * +jets production, uncertainties are taken from Ref.
[135] and include variations of the PDF sets, scale, α S , beam energy, electroweak corrections and photon-induced corrections. A single 90% CL eigenvector variation uncertainty is used, based on the CT14nnlo PDF set. The variations amount to a ∼5% uncertainty in the total number of Z/γ * +jets events within the acceptance. For diboson production, an uncertainty of 10% is used [99,136]. For tt [108] and single top-quark [109,110] production, the assigned 6% uncertainty is based on PDF, scale and top-quark mass variations. Additional uncertainties related to initial-and final-state radiation modelling, tune and (for tt only) the choice of hdamp parameter value in Powheg-Box v2, which controls the amount of radiation produced by the parton shower, are also taken into account [137]. The uncertainty due to the hadronisation model is evaluated by comparing tt events generated with Powheg-Box v2 interfaced to either Herwig++ [138] or Pythia 6. To estimate the uncertainty in generating the hard scatter, the Powheg and MG5_aMC@NLO event generators are compared, both interfaced to the Herwig++ parton shower model. The uncertainties in the W+ jets cross section have a negligible impact in the τ had τ had channel and the W+ jets simulation is not used in the τ lep τ had channel.
For MSSM Higgs boson samples, various sources of uncertainty which impact the signal acceptance are considered. The impact from varying the factorisation and renormalisation scales up and down by a factor of two, either coherently or oppositely, is taken into account. Uncertainties due to the modelling of initialand final-state radiation, as well as multiple parton interaction are also taken into account. These uncertainties are estimated from variations of the Pythia 8 A14 tune [57] for the b-associated production and the AZNLO Pythia 8 tune [56] for the gluon-gluon fusion production. The envelope of the variations resulting from the use of the alternative PDFs in the PDF4LHC15_nlo_nf4_30 (PDF4LHC15_nlo_100) [139] set is used to estimate the PDF uncertainty for the b-associated (gluon-gluon fusion) production. The total uncertainty for the MSSM Higgs boson samples is typically 1-4%, which is dominated by variations of the radiation and multiple parton interactions, with minor impact from scale variations. The Z signal acceptance uncertainties are expected to be negligible.
For both the MSSM Higgs boson and Z samples, uncertainties in the integrated cross section are not included in the fitting procedure used to extract experimental cross-section limits. The uncertainty for Z is included when overlaying model cross sections, in which case it is calculated using the same procedure as for the Z/γ * +jets background.

Uncertainties in data-driven estimates
Uncertainties in the multijet estimate for the τ had τ had channel (Section 6.1.1) arise from the fake-factors f DJ . These include a 10-50% uncertainty from the limited size of the DJ-FR and an uncertainty of up to 50% from the subtraction of the non-multijet contamination. An additional uncertainty is considered when applying the fake-factors in the b-tag category, which accounts for changes in the jet composition with respect to the inclusive selection of the DJ-FR. As the differences are extracted from comparisons in control regions, they are one-sided.
The uncertainty in the fake-rates used to weight simulated non-multijet events in the τ had τ had channel (Section 6.1.2) is dominated by the limited size of the fakes regions and can reach 40%.
Uncertainties in the multijet estimate for the τ lep τ had channel (Section 6.2.1) arise from the fake-factors f MJ and f L . The applicability of f MJ measured in MJ-FR to CR-1 is investigated by studying f MJ as a function of the lepton isolation and the observed differences are assigned as a systematic uncertainty. The statistical uncertainty from the limited size of MJ-FR is significant, particularly for the smaller 2015 dataset. The impact of a potential mismodelling in the subtraction of simulated non-multijet events containing non-isolated leptons is investigated by varying the subtraction by 50%, but is found to be small compared to the other sources of systematic uncertainty. A constant uncertainty of 20% in f MJ is used to envelop these variations. A 50% uncertainty is assigned to the sequential |∆φ(p τ had-vis T , E miss T )| correction. The applicability of f L measured in L-FR to events in MJ-FR is investigated by altering the m T (p T , E miss T ) selection and the observed differences are assigned as a systematic uncertainty. A 20% uncertainty in the background subtraction in L-FR is considered, motivated by observations of the tau identification performance in W+ jets events. The statistical uncertainty from the limited size of L-FR is also considered, but is relatively small. The total uncertainty in f L is 5-50%.
Uncertainties in the data-driven W+ jets and tt estimates for the τ lep τ had channel (Section 6.2.2) arise from the fake-factors f W and the subtraction of contributions from CR-1. The applicability of f W measured in W-FR to CR-1 is investigated by studying f W as a function of m T (p T , E miss T ) and the observed differences (up to ∼10%) are assigned as a systematic uncertainty. A 30% uncertainty is assigned to the sequential |∆φ(p τ had-vis T , E miss T )| correction, based on variations observed as a function of τ had-vis p T . Due to the large contamination for b-tag events in W-FR, a 50% uncertainty is assigned to the correction factor applied to the b-veto parameterisation. The subtraction of the simulated samples in CR-1 is affected by experimental uncertainties and uncertainties in production cross sections, which amount to 10%. The total uncertainty in the multijet estimate in CR-1 is also propagated to the subtraction.

Results
The number of observed events in the signal regions of the τ lep τ had and τ had τ had channels together with the predicted event yields from signal and background processes are shown in Table 3. In the τ lep τ had channel, all events estimated using the data-driven fake-factor technique are grouped as Jet → τ fake, while events where the τ had-vis originates from a jet are removed from the other processes. In the τ had τ had channel, the multijet process is estimated using the fake-factor technique while contributions from all other processes are estimated using simulation with data-driven corrections for the τ had-vis candidates that originate from jets. The numbers are given before (pre-fit) and after (post-fit) applying the statistical fitting procedure described in Section 8.1. The observed event yields are compatible with the expected event yields from SM processes, within uncertainties. The m tot T distributions in the signal regions are shown in Figures 5(a)-5(d) and in the CR-T in Figure 6.

Fit model
The parameter of interest is the signal strength, µ. It is defined as the ratio of the observed to the predicted value of the cross section times branching fraction, where the prediction is evaluated at a particular point in the parameter space of the theoretical model in question (MSSM or Z benchmark scenarios). Hence, the value µ = 0 corresponds to the absence of a signal, whereas the value µ = 1 indicates the presence of a signal as predicted by the model. To estimate µ, a likelihood function constructed as the product of Poisson probability terms is used. A term is included for each bin in the m tot T distributions from the τ e τ had , τ µ τ had and τ had τ had channels. When fitting MSSM models to the data, the distributions are separated into b-tag and b-veto events to enhance sensitivity to the gluon-gluon fusion and b-associated production modes, while the inclusive distributions are used for Z models. In all cases, the distributions in the CR-T regions of the τ e τ had and τ µ τ had channels are added, which help constrain uncertainties in the tt background. Signal and background predictions depend on systematic uncertainties, which are parameterised as nuisance parameters that are constrained using Gaussian probability density functions. The asymptotic approximation is used with the test statisticq µ [141] to compare the likelihoods of the null hypothesis (SM only) and the assumed signal hypothesis (SM plus signal) given the data. The bin widths are chosen to ensure a sufficient number of background events in each bin. The results from the τ e τ had , τ µ τ had and τ had τ had channels are combined to improve the sensitivity to signal. For ditau resonance masses below about 0.6 TeV, the sensitivity is dominated by the τ lep τ had channels, while the τ had τ had channel is most sensitive in the higher mass range.      of the τ had τ had channel. The label "Others" refers to contributions from diboson, Z/γ * (→ )+jets and W(→ ν)+jets production. In the τ lep τ had channel, events containing τ had-vis candidates that originate from jets are removed from all processes other than Jet → τ fake. The binning displayed is that entering into the statistical fit discussed in Section 8, with minor modifications needed to combine the τ lep τ had channels and with underflows and overflows included in the first and last bins, respectively. The predictions and uncertainties for the background processes are obtained from the fit under the hypothesis of no signal. The combined prediction for A and H bosons with masses of 300, 500 and 800 GeV and tan β = 10 in the hMSSM scenario are superimposed. The significance of the data given the fitted model and its uncertainty is computed in each bin following Ref. [140] and is shown in the lower panels. The expected significance of the hypothetical Higgs boson signals are also overlaid. Table 3: Observed number of events and predictions of signal and background contributions in the b-veto and btag categories of the τ lep τ had and τ had τ had channels. The background predictions and uncertainties (including both the statistical and systematic components) are obtained before (pre-fit) and after (post-fit) applying the statistical fitting procedure discussed in Section 8. The individual uncertainties are correlated, and do not necessarily add in quadrature to the total background uncertainty. The label "Others" refers to contributions from diboson, Z/γ * (→ )+jets and W(→ ν)+jets production. In the τ lep τ had channel, events containing a τ had-vis candidate that originate from jets are removed from all processes other than Jet → τ fake. The expected pre-fit contributions from A and H bosons with masses of 300, 500 and 800 GeV and tan β = 10 in the hMSSM scenario are also shown.

Cross-section limits
The data are found to be in good agreement with the predicted background yields, and the results are given in terms of exclusion limits. These are set  Events containing τ had-vis candidates that originate from jets are removed from all processes other than Jet → τ fake. The binning displayed is that entering into the statistical fit discussed in Section 8, with minor modifications needed to combine the τ lep τ had channels and with underflows and overflows included in the first and last bins, respectively. The predictions and uncertainties for the background processes are obtained from the fit under the hypothesis of no signal. The combined prediction for A and H bosons with masses of 300, 500 and 800 GeV and tan β = 10 in the hMSSM scenario are superimposed. The significance of the data given the fitted model and its uncertainty is computed in each bin following Ref. [140] and is shown in the lower panel. The expected significance of the hypothetical Higgs boson signals are also overlaid. followed by a mild excess in the range 300-400 GeV in Figure 5(c), and by a consistent deficit of events across the whole range in Figure 5(d). Modifications of the Z chiral coupling structure can result in changes of up to 40% in the Z cross-section limits. Reducing the Z width can improve the limits by up to ∼30%, while increasing the width to 36% can degrade the limits by up to ∼70%. Figures 8(a) and 8(b) show the observed and expected 95% CL upper limits on the production cross section times branching fraction for φ → ττ as a function of the fractional contribution from b-associated production (σ bb /[σ bb + σ gg ]) and the scalar boson mass.
The impact of systematic uncertainties on the φ → ττ 95% CL cross section upper limits are calculated by comparing the expected upper limit in the case of no systematic uncertainties, µ 95 stat , with a limit calculated by introducing a group of systematic uncertainties, µ 95 i . The systematic uncertainty impacts are shown in Figure 9(a) for gluon-gluon fusion production and Figure 9(b) for b-associated production as functions of the scalar boson mass. The major uncertainties are grouped according to their origin, while minor uncertainties are collected as "Others".
In the low mass range, the sensitivity is dominated by the τ lep τ had channel, and the major uncertainties arise from the estimate of the dominant W+ jets background. Due to the large contribution the fit is able to significantly constrain the uncertainties in this background. In the intermediate mass range the tau energy scale uncertainty becomes dominant. The fit is able to effectively constrain this conservative uncertainty due to the large contribution from Z/γ * → ττ and tt in each of the categories. At very high masses, the uncertainty in the identification efficiency for high-p T τ had-vis candidates becomes dominant, and due to the lack of significant Z/γ * → ττ and tt at high mass, this uncertainty remains relatively unconstrained.   The addition of the CR-T region distributions to the fit allows the uncertainties in the tt modelling to be well constrained and as such, they have little impact on the sensitivity.

MSSM interpretations
The data are interpreted in terms of the MSSM. Figure 10 shows regions in the m A -tan β plane excluded at 95% CL in the m mod+ h and hMSSM scenarios. In the MSSM m mod+ h scenario, the observed (expected) 95% CL upper limits exclude tan β > 5.1 (7.0) for m A = 0.25 TeV and tan β > 51 (57) for m A = 1.5 TeV. Constraints in the hMSSM scenario are stronger due to the presence of low-mass neutralinos in the m mod+ h scenario that reduce the H/A → ττ branching fraction and which are absent in the hMSSM scenario. In the hMSSM scenario, the most stringent observed (expected) constraints on tan β for the combined search exclude tan β > 1.0 (5.5) for m A = 0.25 TeV and tan β > 42 (48) for m A = 1.5 TeV at 95% CL. The expected exclusion limit and bands around m A = 350 GeV reflect the behaviour of the A → ττ branching fraction close to the A → tt kinematic threshold for low tan β, allowing for some exclusion in this region. However, when m A is above the A → tt production threshold, this additional decay mode reduces the sensitivity of the A → ττ search for low tan β.

Z interpretations
The data are also interpreted in terms of Z models. As shown in Figure 7(c), the observed (expected) lower limit on the mass of a Z SSM boson is 2.42 (2.47) TeV at 95% CL. Limits at 95% CL are also placed on Z NU bosons as a function of m Z and the mixing angle between the heavy and light SU(2) gauge groups, φ, as shown in Figure 11. Masses below 2.25-2.60 TeV are excluded in the range 0.03 < sin 2 φ < 0.5 assuming no µ-τ mixing.

Conclusion
A search for neutral Higgs bosons as predicted in the Minimal Supersymmetric Standard Model and Z bosons decaying to a pair of τ-leptons is performed using a data sample from proton-proton collisions at √ s = 13 TeV recorded by the ATLAS detector at the LHC, corresponding to an integrated luminosity of 36.1 fb −1 . The τ e τ had , τ µ τ had and τ had τ had channels are analysed and no indication of an excess over the expected SM background is found. Upper limits on the cross section for the production of scalar and Z bosons times the branching fraction to ditau final states are set at 95% CL, significantly increasing the sensitivity and the explored mass range compared to previous searches. They are in the range 0.78-0.0058 pb (0.70-0.0037 pb) for gluon-gluon fusion (b-associated) production of scalar bosons with masses of 0.2-2.25 TeV and 1.56-0.0072 pb for Drell-Yan production of Z bosons with masses of 0.2-4 TeV. In the context of the hMSSM scenario, the most stringent limits for the combined search exclude tan β > 1.0 for m A = 0.25 TeV and tan β > 42 for m A = 1.5 TeV at 95% CL. In the context of the Sequential Standard Model, Z SSM bosons with masses less than 2.42 TeV are excluded at 95% CL, while m Z NU < 2.25-2.60 TeV is excluded in the range 0.03 < sin 2 φ < 0.5 in the non-universal G(221) model.   [8] ATLAS and CMS Collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at √ s = 7 and 8 TeV, JHEP 08 (2016) 045, arXiv: 1606.02266 [hep-ex].