Search for charged Higgs bosons decaying via $H^{\pm} \to \tau^{\pm}\nu_{\tau}$ in the $\tau$+jets and $\tau$+lepton final states with 36 fb$^{-1}$ of $pp$ collision data recorded at $\sqrt{s} = 13$ TeV with the ATLAS experiment

Charged Higgs bosons produced either in top-quark decays or in association with a top-quark, subsequently decaying via $H^{\pm} \to \tau^{\pm}\nu_{\tau}$, are searched for in 36.1 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV recorded with the ATLAS detector. Depending on whether the top-quark produced together with $H^{\pm}$ decays hadronically or leptonically, the search targets $\tau$+jets and $\tau$+lepton final states, in both cases with a hadronically decaying $\tau$-lepton. No evidence of a charged Higgs boson is found. For the mass range of $m_{H^{\pm}}$ = 90-2000 GeV, upper limits at the 95% confidence level are set on the production cross-section of the charged Higgs boson times the branching fraction $\mathrm{B}(H^{\pm} \to \tau^{\pm}\nu_{\tau})$ in the range 4.2-0.0025 pb. In the mass range 90-160 GeV, assuming the Standard Model cross-section for $t\overline{t}$ production, this corresponds to upper limits between 0.25% and 0.031% for the branching fraction $\mathrm{B}(t\to bH^{\pm}) \times \mathrm{B}(H^{\pm} \to \tau^{\pm}\nu_{\tau})$.


Introduction
The discovery of a new particle at the Large Hadron Collider (LHC) [1] in 2012 [2,3], with a measured mass close to 125 GeV [4], opens the question of whether this is the Higgs boson of the Standard Model (SM), or part of an extended scalar sector.Charged Higgs bosons1 are predicted in several extensions of the SM that add a second doublet [5,6] or triplets [7][8][9][10] to its scalar sector.In CP-conserving Two-Higgs-Doublet Models (2HDMs), the properties of the charged Higgs boson depend on its mass, the mixing angle α of the neutral CP-even Higgs bosons and the ratio of the vacuum expectation values of the two Higgs doublets (tan β).Although the search for charged Higgs bosons presented in this paper is performed in a model-independent manner, results are interpreted in the framework of the hMSSM benchmark scenario [11,12], which is a type-II 2HDM, where down-type quarks and charged leptons couple to one Higgs doublet, while up-type quarks couple to the other.For H + masses below the top-quark mass (m H + < m top ), the main production mechanism is through the decay of a top-quark, t → bH + , in a double-resonant top-quark production.In this mass range, the decay H + → τν usually dominates in a type-II 2HDM, although H + → cs and cb may also become sizeable at low tan β.For H + masses above the top-quark mass (m H + > m top ), the leading production mode is gg → tbH + (single-resonant top-quark production).Close to the alignment limit, i.e. at cos(β − α) 0, the dominant decay is H + → tb; however the branching fraction of H + → τν can reach 10-15% at large values of tan β in a type-II 2HDM.In the intermediate-mass region (m H + m top ), accurate theoretical predictions recently became available for the non-resonant top-quark production [13], which now allows a dedicated comparison of the H + models with data near the top-quark mass.Figure 1 illustrates the main production modes for charged Higgs bosons in proton-proton (pp) collisions.
The ATLAS and CMS Collaborations searched for charged Higgs bosons in pp collisions at √ s = 7-8 TeV, probing the mass range below the top-quark mass with the τν [14][15][16][17][18] and cs [19,20] decay modes, as well as the mass range above the top-quark mass with the τν and tb decay modes [16,18,21].More recently, using 3.2 fb −1 of data collected at m top were performed by ATLAS in the τν decay mode [22].In addition, H + → W Z was searched for in the vector-boson-fusion production mode at 8 TeV by the ATLAS Collaboration [23] and at 13 TeV by the CMS Collaboration [24].No evidence of charged Higgs bosons was found in any of these searches.The ATLAS and CMS Collaborations also searched for neutral scalar resonances decaying to a ττ pair [25,26], to which the hMSSM is also sensitive in some regions of its parameter space.
This paper describes a search for charged Higgs bosons using the H + → τν decay, with a subsequent hadronic decay of the τ-lepton (referred to as τ had ), in the mass range  GeV, including the intermediate-mass region.Depending on the assumption made for the decay mode of the W boson originating from the top-quark produced together with H + , two channels are targeted: τ had +jets if the W boson decays into a q q pair, or τ had +lepton if the W boson decays into an electron or muon and at least one neutrino (directly or via a leptonically decaying τ-lepton).The data used for this analysis are from pp collisions at √ s = 13 TeV, collected with the ATLAS experiment at the LHC in 2015 and 2016, corresponding to integrated luminosities of 3.2 fb −1 and 32.9 fb −1 , respectively.In Section 2, the data and simulated samples are summarised.In Section 3, the reconstruction of physics objects is described.The analysis strategy and event selection are discussed in Section 4. Section 5 describes the data-driven estimation of backgrounds with misidentified τ objects.A discussion of the systematic uncertainties and a description of the statistical analysis used to derive exclusion limits on the production of a charged Higgs boson decaying via H + → τν are presented in Sections 6 and 7, respectively.Finally, a summary is given in Section 8.

Data and samples of simulated events
The ATLAS experiment [27] is a multipurpose detector with a forward-backward symmetric cylindrical geometry with respect to the LHC beam-axis.2 The innermost layers of ATLAS consist of tracking detectors in the pseudorapidity range |η| < 2.5, including the insertable B-layer [28,29] installed for Run-2.This inner detector is surrounded by a thin superconducting solenoid that provides a 2 T axial magnetic field.It is enclosed by the electromagnetic and hadronic calorimeters which cover |η| < 4.9.The outermost layers consist of an external muon spectrometer within |η| < 2.7, incorporating three large toroidal magnet assemblies.A two-level trigger [30,31] reduces the event rate to a maximum of 1 kHz for offline data storage.
The dataset used in this analysis, collected during stable beam conditions and with all ATLAS subsystems fully operational, corresponds to an integrated luminosity of 36.1 ± 0.8 fb −1 , derived following a methodology similar to that detailed in Ref. [32].Data-quality criteria are applied in order to remove events where reconstructed jets are consistent with noise in the calorimeter or non-collision backgrounds [33].
Signal events with H + → τν were generated with M G 5_ MC@NLO [34] in three distinct mass regions: • In the mass range below the top-quark mass (90-150 GeV), tt events with one top-quark decaying into a charged Higgs boson and a b-quark were generated at leading order (LO).Contributions from events in which both top-quarks decay via t → bH + and from single-top-quark events with a subsequent decay t → bH + are negligible, hence not simulated.
• In the intermediate-mass region (160-180 GeV), the full process pp → H + W bb was generated at LO.
• In the mass range above the top-quark mass (200-2000 GeV), H + production in association with a top-quark was simulated at next-to-leading order (NLO).
The interference between the Feynman diagrams of Figure 1 is taken into account in the intermediate-mass region, where it is most relevant.In all cases, the matrix-element generator was interfaced to P 8.186 [35] for the simulation of the parton shower and the underlying event, with the A14 [36] set of tuned parameters (tune).The NNPDF2.3 [37] parton distribution function (PDF) sets were used for the matrix-element generation and the parton shower.
The SM background processes include the production of tt pairs, single top-quarks, W+jets, Z/γ * +jets and electroweak gauge-boson pairs (WW/W Z/Z Z), as well as multi-jet events.The tt events constitute the main background in the low-and intermediate-mass H + searches, while multi-jet events dominate for large charged Higgs boson masses.All backgrounds arising from a quark-or gluon-initiated jet misidentified as a hadronically decaying τ-lepton are estimated with a data-driven method, described in Section 5.
The generation of tt events used the P -B 2 [38][39][40] generator, with the CT10 [41] PDF set in the matrix-element calculations.Single-top-quark events were generated in the Wt-, tand s-channels using the P -B 1 generator, with the CT10 PDF set in the Wtand s-channels or the fixed 4-flavour CT10f4 [42] PDF set in the t-channel.For all processes above, top-quark spin correlations are preserved (M S [43] was used for top-quark decays in the t-channel).The parton shower and the underlying event were simulated using P 6.428 [44] with the CTEQ6L1 [45] PDF set and the corresponding Perugia 2012 [46] tune.The top-quark mass was set to 172.5 GeV.The sample of tt events is normalised to the next-to-next-to-leading-order (NNLO) cross-section, including soft-gluon resummation to next-to-next-to-leading-logarithm (NNLL) order [47].The normalisation of the sample of single-top-quark events uses an approximate calculation at NLO in QCD for the sand t-channels [48,49] and an NLO+NNLL calculation for the Wt-channel [50,51].
Events containing a W or Z boson with associated jets were simulated using S 2.2.1 [52] together with the NNPDF3.0NNLO[53] PDF set.Matrix elements were calculated for up to two partons at NLO and four partons at LO using C [54] and O L [55], and they were merged with the S parton shower [56] according to the ME+PS@NLO prescription [57].The W/Z+jets events are normalised to the NNLO cross-sections calculated using FEWZ [58][59][60].Diboson processes (WW, W Z and Z Z) were simulated at NLO using the P -B 2 generator, interfaced to the P 8.186 parton shower model.The CT10nlo PDF set was used for the hard-scatter process, while the CTEQL1 PDF set was used for the parton shower.The non-perturbative effects were modelled using the AZNLO [61] tune.E G 1.2.0 [62] was used for the properties of bottom-and charm-hadron decays, except in samples generated with S .All simulated events were overlaid with additional minimum-bias events generated with P 8.186 using the A2 [63] tune and the MSTW2008LO [64] PDF set to simulate the effect of multiple pp collisions per bunch crossing (pile-up).Simulated events were then weighted to have the same distribution of the number of collisions per bunch crossing as the data.All signal and background events were processed through a simulation [65] of the detector geometry and response based on G 4 [66] and they are reconstructed using the same algorithms as the data.

Physics object reconstruction
The search reported in this paper makes use of most of the physics objects reconstructed in ATLAS: charged leptons (electrons and muons), jets (including those compatible with the hadronisation of bquarks or hadronic decays of τ-leptons) and missing transverse momentum.These physics objects are detailed below.
Electrons are reconstructed by matching clustered energy deposits in the electromagnetic calorimeter to a track reconstructed in the inner detector [67].They are required to have p T > 20 GeV and |η| < 2.47 (the transition region between the barrel and end-cap calorimeters, 1.37 < |η| < 1.52, is excluded).In the τ had +jets (τ had +lepton) channel, electrons must satisfy a loose (tight) identification criterion based on a likelihood discriminant.
Muon candidates are required to contain matching inner-detector and muon-spectrometer tracks [68], as well as to have p T > 20 GeV and |η| < 2.5.The final muon tracks are re-fitted using the complete track information from both detector systems.In the τ had +jets (τ had +lepton) channel, muons must satisfy a loose (tight) identification criterion.
In order to ensure that electrons (muons) originate from the primary vertex, defined as the vertex with the highest sum of the p 2 T of its associated tracks, the track associated with the lepton is required to have a longitudinal impact parameter and a transverse impact parameter significance that fulfil, respectively, |z 0 sin θ| < 0.5 mm and |d 0 /σ(d 0 )| < 5 (3).In order to reduce contamination by leptons from hadron decays or photon conversion, isolation requirements are applied.The calorimeter-based isolation relies on energy deposits within a cone of size ∆R = 0.2 around the electron or muon, while the track-based isolation uses a variable cone size starting at ∆R = 0.2 for electrons or ∆R = 0.3 for muons, and then decreasing as p T increases.The efficiency of the calorimeter-and track-based isolation requirements are, respectively, 96% and 99% in the τ had +lepton channel (looser isolation requirements are applied in the τ had +jets channel, with efficiencies of 99%).
Jets are reconstructed from energy deposits in the calorimeters using the anti-k t algorithm [69] implemented in the F J package [70] with a radius parameter value of R = 0.4.Jets are corrected for pile-up energy and calibrated using energy-and η-dependent corrections [33].Only jets with a transverse momentum p T > 25 GeV and within |η| < 2.5 are considered in the following.A multivariate technique (jet vertex tagger) that allows identification and selection of jets originating from the hard-scatter interaction through the use of tracking and vertexing information is applied to jets with p T < 60 GeV and |η| < 2.4 [71].In order to identify jets containing b-hadrons (referred to as b-jets in the following), an algorithm is used, which combines impact parameter information with the explicit identification of secondary and tertiary vertices within the jet into a multivariate discriminant [72,73].Operating points are defined by a single threshold in the range of discriminant output values and are chosen to provide a specific b-jet efficiency in simulated tt events.The 70% working point is used in this analysis.It has rejection factors of 13, 56 and 380 against c-jets, hadronic τ decays and jets from light quarks or gluons, respectively.
The detection and reconstruction of hadronically decaying τ-leptons is seeded by anti-k t jets depositing a transverse energy E T > 10 GeV in the calorimeter [74] and with one or three associated tracks reconstructed in the inner detector within a cone of ∆R = 0.2 around the axis of the object associated with the visible decay products of the hadronically decaying τ-leptons.Referred to as τ had-vis in the following, these objects are required to have a visible transverse momentum (p τ T ) of at least 30 GeV and to be within |η| < 2.3 (the transition region between the barrel and end-cap calorimeters, 1.37 < |η| < 1.52, is excluded).In order to distinguish τ had-vis candidates from quark-or gluon-initiated jets, a boosted decision tree (BDT) is used, separately for candidates with one and three charged-particle tracks [75,76].For the nominal definition of τ had-vis candidates, a working point with an identification efficiency of 75% (60%) for 1-prong (3-prong) hadronic τ decays in Z → ττ events is chosen, corresponding to rejection factors of 30-80 (200-1000) against quark-and gluon-initiated jets in multi-jet events.An additional likelihood-based veto is used to reduce the number of electrons misidentified as τ had-vis candidates, providing a constant 95% efficiency as a function of τ had-vis p T and η, as well as a background rejection of 20-200, depending on η.
When several objects overlap geometrically, the following procedure is applied.First, any τ had-vis object is removed if found within ∆R = 0.2 of either an electron or a muon with loose identification criteria and with a transverse momentum above 20 GeV or 7 GeV, respectively.Then, any electron sharing an inner-detector track with a muon is discarded.Next, jets within ∆R = 0.2 of an electron or muon are removed, unless they are b-tagged, have a large p T relative to that of the lepton and, in the case of an overlap with a muon, a high track multiplicity.Then, electrons and muons are removed if found within ∆R = 0.4 of a remaining jet.Finally, jets are discarded if they are within ∆R = 0.2 of the highest-p T τ had-vis candidate.
The magnitude of the missing transverse momentum, E miss T [77], is reconstructed from the negative vector sum of transverse momenta of reconstructed and fully calibrated objects, with an additional term that is calculated from inner-detector tracks that are matched to the primary vertex and not associated with any of the selected objects.

Analysis strategy
This paper describes a search for a charged Higgs boson decaying via H + → τν in topologies where it is produced either in top-quark decays or in association with a top-quark.Depending on whether the top-quark produced with the H + decays hadronically or semileptonically, two channels are targeted: τ had-vis +jets or τ had-vis +lepton, respectively.The corresponding signal regions are described below.

Event selection in the τ had-vis +jets channel
The analysis of the τ had-vis +jets channel is based on events accepted by an E miss T trigger with a threshold at 70, 90 or 110 GeV, depending on the data-taking period and thereby accounting for different pile-up conditions.The efficiency of these triggers is measured in data and used to reweight the simulated events, with the same method as in Ref. [22].At least one vertex with two or more associated tracks with p T > 400 MeV is required, and the following event selection criteria are applied: • at least one τ had-vis candidate with p τ T > 40 GeV; • no loose leptons (electron or muon) with p T > 20 GeV; • at least three jets with p T > 25 GeV, of which at least one is b-tagged; Here, the transverse mass m T of the highest-p T τ had-vis candidate and E miss T is defined as, where ∆φ τ,miss is the azimuthal angle between the τ had-vis candidate and the direction of the missing transverse momentum.

Event selection in the τ had-vis +lepton channel
The τ had-vis +electron and τ had-vis +muon sub-channels are based on events accepted by single-lepton triggers.Triggers for electrons or muons with low E T or p T thresholds respectively (24-26 GeV depending on the data-taking period, for both the electrons and muons) and isolation requirements are combined in a logical OR with triggers having higher (E T , p T ) thresholds (60-140 GeV for electrons, 50 GeV for muons) and looser isolation or identification requirements in order to maximise the efficiency.Following the same vertex requirement as in the τ had-vis +jets channel, events are selected as follows: • exactly one lepton matched to the single-lepton trigger object, with p T > 30 GeV.Depending on whether the lepton is an electron or a muon, two sub-channels, τ had-vis +electron and τ had-vis +muon, are considered; • exactly one τ had-vis candidate with p τ T > 30 GeV and an electric charge opposite to that of the lepton; • at least one b-tagged jet with p T > 25 GeV;

Multivariate discriminant
Following the event selections above, kinematic variables that differentiate between the signal and backgrounds are identified and combined into a multivariate discriminant.The output score of BDTs is then used in order to separate the H + signal from the SM background processes.The training of the BDTs is performed using the FastBDT [78] library via the TMVA toolkit [79].
The simulated signal samples are divided into five H + mass bins chosen to ensure that within each bin both the kinematic distributions of the input variables and the event topology are similar.The mass bins used in both channels are 90-120 GeV, 130-160 GeV (in that case, an additional signal sample with a 160 GeV H + arising solely from top-quark decays is used), 160-180 GeV, 200-400 GeV and 500-2000 GeV.All available H + signal samples corresponding to a given mass bin are normalised to the same event yield and combined into one inclusive signal sample.The BDTs are trained separately for τ had-vis +jets and τ had-vis +lepton events, and depending on whether the leading τ had-vis candidate has one or three associated tracks.The variables entering the BDT training differ for the two types of final states considered in this search, and they are summarised in Table 1.If there is more than one τ had-vis candidate or more than one b-tagged jet, the object that has the largest p T is considered in the BDT input variables.
At low H + masses, the kinematics of the t → bH + and t → bW decay products are similar.In that case, the polarisation of the τ-lepton is employed as a discriminating variable: in the main SM background processes, the τ had-vis object originates from a vector-boson decay, whereas it is generated in the decay of a scalar particle in the case of H + signal [80].The polarisation of the τ had-vis candidates can be measured by the asymmetry of energies carried by the charged and neutral pions from the 1-prong τ-lepton decay, measured in the laboratory frame.For this purpose, the variable Υ is introduced [81]: It is defined for all τ had-vis candidates with only one associated track, and p τ-track T is the transverse momentum of that track.For H + masses in the range 90-400 GeV, the BDT training is performed separately for events with a selected 1-or 3-prong τ had-vis object, and Υ is included in the BDT discriminant for events where τ had-vis has only one associated track.While Υ is one of the most discriminating input variables of the BDT at low H + masses, the importance of other kinematic variables in the BDT training becomes much greater at large H + masses, in particular the three variables entering the computation of the tranvserse mass, i.e.E miss T , p τ T and ∆φ τ,miss .Hence, for the mass range 500-2000 GeV, the BDT discriminant does not contain the variable Υ and is thus inclusive in the number of tracks associated with the τ had-vis candidate.

Background modelling
The dominant background processes are categorised according to the object that gives rise to the identified τ had-vis candidate.Simulation is used to estimate backgrounds in which τ had-vis arises from a hadronically decaying τ-lepton, electron or muon at the event-generator level; however, in the case of tt events, the normalisation is obtained from a fit to the data.If τ had-vis arises from a quark-or gluon-initiated jet, a data-driven method is employed to estimate the corresponding background.
Table 1: List of kinematic variables used as input to the BDT in the τ had-vis +jets and τ had-vis +lepton channels.Here, refers to the selected lepton (electron or muon).∆φ X, miss denotes the difference in azimuthal angle between a reconstructed object X (X = τ had-vis , b-jet, ) and the direction of the missing transverse momentum.The variable Υ is related to the polarisation of the τ-lepton and is only defined for 1-prong τ had-vis candidates.Hence, for H + masses in the range 90-400 GeV, where the variable Υ is used, the BDT training is performed separately for events with a selected 1-or 3-prong τ had-vis candidate.In the mass range 500-2000 GeV, Υ is not used, hence the BDT training is inclusive in number of tracks associated with τ had-vis candidates.

Data-driven fake-factor method
Background processes where a quark-or gluon-initiated jet is reconstructed and selected as a τ had-vis candidate are estimated from data.For this purpose, an anti-τ had-vis selection is defined by requiring that the τ had-vis candidate does not satisfy the BDT-based identification criteria of the nominal selection.Meanwhile, a loose requirement on the τ had-vis BDT output score is maintained in order to ensure that the relative fractions of gluon-and quark-initiated jets mimicking τ had-vis candidates are similar in the signal region and the corresponding anti-τ had-vis region.Then, a fake factor (FF) is defined as the ratio of the number of jets reconstructed as τ had-vis candidates that pass the nominal τ had-vis selection to the number that pass the anti-τ had-vis selection in a given control region (CR): The actual computation of FFs is described later in the text.Events are selected with the nominal criteria described in Section 4, except that an inverted identification criterion for the τ had-vis candidate is required.In this sample, the τ had contribution is subtracted using simulated events in which a τ had at generator level fulfils the anti-τ had-vis criterion.The resulting number of events is N anti-τ had-vis .Then, the number of events with a misidentified τ had-vis candidate (N τ had-vis fakes ) is derived from the subset of anti-τ had-vis candidates as follows: where the index i refers to each bin in the parameterisation of the FF, in terms of p τ T and number of associated tracks.
In order to account for different sources of misidentified τ had-vis candidates in the signal region and the corresponding anti-τ had-vis region, FFs are measured in two control regions of the data with different fractions of quark-and gluon-initiated jets, and then combined.A first control region with a significant fraction of gluon-initiated jets (referred to as the multi-jet CR) is defined by applying the same event selection as for the τ had-vis +jets channel, but with a b-jet veto and E miss T < 80 GeV.Such events are collected using a combination of multi-jet triggers instead of the E miss T trigger.A second control region enriched in quark-initiated jets (referred to as the W+jets CR) is defined by applying the same event selection as for the combined τ had-vis +lepton channel, but with a b-jet veto, no requirement on E miss T and the requirement 60 GeV < m T ( , E miss T ) < 160 GeV, where the transverse mass of the lepton and the missing transverse momentum is computed by replacing the τ had-vis candidate by a lepton in Eq. ( 1).The FFs measured in these two control regions are shown in Figure 2(a).
In the anti-τ had-vis regions corresponding to the nominal event selections of Section 4, the fractions of τ had-vis candidates arising from quark-and gluon-initiated jets are then measured using a template-fit approach, based on variables that are sensitive to the differences in quark-and gluon-fractions between these two types of jets.For 3-prong τ had-vis candidates, the τ had-vis BDT output score is used as a template.For 1-prong τ had-vis candidates, the so-called τ had-vis width is used, defined as: for tracks satisfying ∆R (τ had-vis , track) < 0.4.Two binned templates, denoted f multi-jet and f W +jets , are obtained in the multi-jet and W+jets control regions defined above, respectively.Each corresponds to a linear combination of templates of gluon-and quark-initiated jets, where the fraction of gluon-initiated jets is by construction larger in the multi-jet control region.Then, a linear combination of the two templates is defined as with a free parameter α MJ (here, f (x) is the τ had-vis width or BDT score).This linear combination is fitted to the normalised distribution of the τ had-vis width or BDT score measured in the anti-τ had-vis regions corresponding to the nominal event selections, by varying α MJ and separately minimising a χ 2 -function in every bin of the fake factors, separately in the τ had-vis +jets and τ had-vis +lepton channels.From the best-fit values of α MJ , combined fake factors are then given by: FF where the index i refers to each bin in the parameterisation of the FF, and where FF multi-jet and FF W +jets indicate the FF calculated in the two respective control regions.The combined FFs, used in the τ had-vis +jets and τ had-vis +lepton channels, are shown in Figure 2(b).
The data-driven method as described does not correctly predict the shape of Υ measured in the signal region.Indeed, the distribution of Υ is found to be different for τ had-vis and anti-τ had-vis candidates, because this variable is strongly correlated with the leading-track momentum fraction, which is one of the input variables used for the identification of τ had-vis candidates.On the other hand, Υ shows no correlation with any of the other variables used as input to the final BDT discriminant.Hence, an inverse transform sampling method [82] can be employed in order to model the shape of Υ for misidentified τ had-vis candidates in the signal regions.In the control regions where FFs are measured, cumulative distribution functions F(Υ) are calculated from the shapes of Υ, obtained separately for τ had-vis and anti-τ had-vis candidates.Then, in the signal regions, the shape of Υ predicted for τ had-vis candidates is derived from that measured for anti-τ had-vis candidates, as follows: where F −1 stands for the inverse of the cumulative distribution function.This procedure is only applied to 1-prong objects, since Υ is not used in the training of the final BDT discriminant for 3-prong τ had-vis candidates.

Validation of the background modelling
The modelling of the backgrounds, especially tt and events with a misidentified τ had-vis candidate, is validated in signal-depleted regions.A region enriched in tt events is defined with the same event selection as the τ had-vis +lepton channel, but with the requirement of having an eµ pair (with p T above 30 GeV for both the electron and muon) instead of the e/µ + τ had-vis pair.This control region is included as a single-bin distribution in the statistical analysis described in Section 7. The modelling of the background with misidentified τ had-vis objects is validated in a region that is defined with the same selection criteria as the τ had-vis +lepton channel, but with a veto on b-tagged jets.Predicted and measured BDT score distributions are compared in the two regions discussed above, and they are found to be in good agreement prior to any fit to the data, as shown in Figures 3 and 4.This procedure validates the modelling of the two main SM background processes.Figure 4: BDT score distribution for the predicted backgrounds and data in a region with the same event selection as for the τ had-vis +lepton channel, except that it has exactly zero b-tagged jet (as described in the text).The five H + mass range trainings are shown.The lower panel of each plot shows the ratio of data to the SM background prediction.The uncertainty bands include all statistical and systematic uncertainties.

Systematic uncertainties
Several sources of systematic uncertainty affect the normalisation of the signal and background processes, as well as the shape of the BDT score distribution used as the final discriminant.Individual sources of systematic uncertainty are assumed to be uncorrelated.However, when the systematic variations are applied to different samples of simulated events, correlations of a given systematic uncertainty are taken into account across processes.
All instrumental sources of systematic uncertainty, i.e. the reconstruction and identification efficiencies, as well as the energy scales and resolutions of electrons, muons, (b-tagged) jets and τ had-vis candidates, are considered, including their impact on the reconstructed E miss T .In both the τ had-vis +jets and τ had-vis +lepton channels, the dominant systematic uncertainties come from the jet energy scale [33] (between 1% and 4.5% depending on the jet p T ), the b-tagging efficiency [83] (ranging from 2% to 10% depending on the jet p T ), the reconstruction and identification efficiencies of τ had-vis candidates (3% and 6%, respectively), and their energy scale (2-3%) [76].Additional uncertainties based on multi-jet data and single-particle response are added for the identification efficiency and the energy scale of τ had-vis objects at high p T , respectively.The probability for electrons to be misidentified as τ had-vis is measured with a precision of 3-14%.The uncertainty of 2.1% in the integrated luminosity is applied directly to the event yields of all simulated events.In the τ had-vis +lepton channel, the impact of the systematic uncertainty in the single-lepton trigger efficiency is at most 1%.In the τ had-vis +jets channel, the efficiency of the E miss T trigger is measured in a control region of the data, as described in Ref. [22].The associated systematic uncertainty in the event yield of the signal region is 1.4%.
In the estimation of backgrounds with jets misidentified as τ had-vis candidates, the sources of systematic uncertainty are: • the loose requirement on the τ had-vis BDT output score used in the definition of the anti-τ had-vis sample, which modifies the corresponding fractions of quark-and gluon-initiated jets, as well as the event topology (assessed by considering the shape of the final discriminant obtained for two alternative thresholds for the BDT output score that are symmetric around the nominal threshold); • the level of contamination of true τ had-vis candidates fulfilling the anti-τ had-vis selection (varied by 50%); • the statistical uncertainties in the event yields entering the computation of FFs, in each bin of their parameterisation and for each control region; • the statistical uncertainty of the best-fit value of α MJ ; • the modelling of heavy-flavour jets mimicking τ had-vis candidates, obtained by computing the fake factors separately for light-and heavy-quark-initiated jets, as in Ref.
[22], and comparing those with the nominal predictions, then using the difference as a systematic uncertainty; • for the Υ distribution only, the uncertainty in the inverse transform sampling method, taken as the difference between the computations obtained in the two control regions where the FFs are measured.
The dominant background with a true τ had-vis candidate is from tt pairs and single-top-quark events.A normalisation factor is computed for this background by including the control region of the τ had-vis +lepton channel with an eµ pair and at least one b-jet as a single-bin distribution in the statistical analysis.Systematic uncertainties in the modelling of the tt background are included.Those due to the choice of parton shower and hadronisation models are derived by comparing tt events generated with P -B 2 interfaced to either P 6 or Herwig++ [84].The systematic uncertainties arising from additional radiation, which modify the jet production rate, are computed with the same packages as for the baseline tt event generation, by varying the shower radiation, the factorisation and renormalisation scales, as well as the NLO radiation.The uncertainty due to the choice of matrix-element generator is evaluated by comparing tt samples generated with M G 5_ MC@NLO or P -B , both using the CT10 PDF set and interfaced to Herwig++.The impacts of the three systematic uncertainties listed above on the event yield of the tt background are, respectively, 14%, 4%, 13% in the τ had-vis +jets channel and 13%, 8%, 9% in the τ had-vis +lepton channel.For the W+jets and Z+jets backgrounds, uncertainties of 35% and 40% based on variations of the scales in S are considered, respectively.An additional uncertainty in the heavy-flavour jet modelling is derived by comparing the predictions of S and M G 5_ MC@NLO interfaced to P 6: it is about 6% in the τ had-vis +jets channel and 14% in the τ had-vis +lepton channel.For the small diboson backgrounds, an uncertainty of 50%, arising from the inclusive cross-section and additional jet production, is used [85].
Systematic uncertainties in the H + signal generation are estimated as follows.The uncertainty arising from the missing higher-order corrections is assessed by varying the factorisation and renormalisation scales up and down by a factor of two.The largest variation of the signal acceptance is then symmetrised and taken as the scale uncertainty, 4-8% depending on the H + mass hypothesis.The signal acceptances are computed with various PDF sets, following the PDF4LHC prescriptions [86], and their envelope is taken as a systematic uncertainty.The impact of A14 tune variations on the signal acceptance is estimated by adding in quadrature the excursions from a subset of tune variations that cover underlying-event and jet-structure effects, as well as different aspects of extra jet production.This uncertainty amounts to 8-10%.
In the low-and intermediate-mass H + search, the main systematic uncertainties arise from the estimation of the background with misidentified τ had-vis candidates, as well as the reconstruction and identification of τ had-vis candidates.For large H + masses, systematic uncertainties from the signal modelling and the estimation of the background with misidentified τ had-vis candidates dominate, but the search is also limited by the number of selected events.The impact of the systematic uncertainties on the sensitivity of the analysis is discussed in Section 7.

Results
The statistical interpretation is based on a simultaneous fit of the parameter of interest, e.g.µ ≡ σ(pp → tbH + ) × B(H + → τν), and the nuisance parameters θ that encode statistical and systematic uncertainties, by means of a negative log-likelihood minimisation.The test statistic qµ [87] used to test the compatibility of the data with the background-only and signal+background hypotheses is computed from the profile likelihood ratio, and the asymptotic approximation is used throughout the statistical analysis.Three signal regions and one control region enriched in tt events are considered in the simultaneous fit: • Binned likelihood functions are used for the BDT score distributions in the three signal regions (τ had-vis +jets, τ had-vis +electron and τ had-vis +muon).The binning of the discriminating variable is optimised to maximise the sensitivity of the analysis prior to looking at the data in the signal regions.
• A single-bin likelihood is used in the control region enriched in tt events, defined with the same event selection as the τ had-vis +lepton channel, but with the requirement of an eµ pair instead of the e/µ + τ had-vis pair.
The expected number of events for all SM processes and the measured event yields in the signal regions are shown in Tables 2 and 3, prior to using the multivariate discriminant and applying the statistical fitting procedure.The contributions from hypothetical charged Higgs bosons are also shown, assuming a mass of 170 GeV or 1000 GeV, and with σ(pp → tbH + ) × B(H + → τν) set to the prediction from the hMSSM scenario for tan β = 40, as computed using Refs.[13] and [88][89][90][91][92] for the production cross-section and HDECAY [93] for the branching fraction.The signal acceptances for a charged Higgs boson mass hypothesis of 170 GeV, as evaluated in a sample of simulated events where both the τ-lepton and the topquark decay inclusively, are 0.9%, 0.6% and 0.5% in the τ had-vis +jets, τ had-vis +electron and τ had-vis +muon signal regions, respectively.They become 11.6%, 0.9% and 1.2% for a charged Higgs boson mass of 1 TeV.The event yields observed in 36.1 fb −1 of data collected at 13 TeV are consistent with the expected SM backgrounds, but very little sensitivity to H + signals can be obtained from the comparison of event yields only.
The BDT score distributions in the five charged Higgs boson mass ranges considered in the analysis are shown in Figure 5 for the signal region of the τ had-vis +jets channel, as well as in Figures 6 and 7 for the τ had-vis +electron and τ had-vis +muon sub-channels, respectively.All plots are obtained after the statistical fitting procedure with the background-only hypothesis.The binning shown in the figures is also used in the statistical analysis.
The data are found to be consistent with the background-only hypothesis (the smallest p 0 -value is 0.3 around 350 GeV).Exclusion limits are set at the 95% confidence level (CL), by using the CL s procedure [94], on σ(pp → tbH + ) × B(H + → τν) for the full mass range investigated, as well as on B(t → bH + ) × B(H + → τν) in the low H + mass range.Figure 8 shows the expected and observed exclusion limits as a function of the H + mass hypothesis.The observed limits range from 4.2 pb to 2.5 fb over the mass range considered in this search.The limits are interpolated between the H + mass regions which are tested explicitly.The bias in the expected limits from this interpolation is found to be smaller than the statistical uncertainty.
For the mass range between 90 and 160 GeV, the limits on σ(pp → tbH + ) × B(H + → τν) translate into observed limits between 0.25% and 0.031% for the branching fraction B(t → bH + ) × B(H + → τν) if one assumes that the production cross-section is equal to that of tt pairs.
The impact from the various sources of systematic uncertainty is estimated by comparing the expected 95% CL limits on σ(pp → tbH + ) × B(H + → τν) when taking only statistical uncertainties into account and those obtained when a certain set of systematic uncertainties is added in the limit-setting procedure, as summarised in Table 4 for H + masses of 170 GeV and 1000 GeV.Table 4: Impact of systematic uncertainties on the expected 95% CL limit on σ(pp → tbH + )×B(H + → τν), for two H + mass hypotheses: 170 GeV and 1000 GeV.The impact is obtained by comparing the expected limit considering only statistical uncertainties (stat.only) with the expected limit when a certain set of systematic uncertainties is added in the limit-setting procedure.In the absence of correlations and assuming Gaussian uncertainties, the row "All" would be obtained by summing in quadrature (linearly) the individual contributions of the systematic uncertainties if these were much larger (smaller) than the statistical uncertainties.

Conclusion
A search for charged Higgs bosons produced either in top-quark decays or in association with a top-quark, and subsequently decaying via H + → τν, is performed in the τ+jets and τ+lepton channels, according to the hadronic or semileptonic decay of the top quark produced together with H + .The dataset contains 36.1 fb −1 of pp collisions at √ s = 13 TeV, recorded with the ATLAS detector at the LHC.The data are found to be in agreement with the background-only hypothesis.Upper limits at the 95% confidence level are set on the H + production cross-section times the branching fraction B(H + → τν) between 4.2 pb and 2.5 fb for a charged Higgs boson mass range of 90-2000 GeV, corresponding to upper limits between 0.25% and 0.031% for the branching fraction B(t → bH + ) × B(H + → τν) in the mass range 90-160 GeV.These exclusion limits are about 5-7 times more stringent than those obtained by ATLAS with 3.2 fb −1 of 13 TeV data for H + masses above 200 GeV [22] and with Run-1 data in the H + mass range 90-160 GeV [16]

√ s = 13 Figure 1 :
Figure 1: Examples of leading-order Feynman diagrams contributing to the production of charged Higgs bosons in pp collisions: (a) non-resonant top-quark production, (b) single-resonant top-quark production that dominates at large H + masses, (c) double-resonant top-quark production that dominates at low H + masses.The interference between these three main diagrams becomes most relevant in the intermediate-mass region.

Figure 2 :
Figure 2: Fake factors parameterised as a function of p τ T and the number of charged τ decay products (two categories: 1-prong and 3-prong), as obtained (a) in the multi-jet and W+jets CRs, (b) after reweighting by α MJ in the τ had-vis +jets and τ had-vis +lepton channels.Details about the computation of fake factors in the different control regions are given in the text.The errors shown represent the statistical uncertainty in a given p τ T bin (a) and with additional systematic uncertainties obtained from the combination in a given p τ T bin (b).

Figure 3 :
Figure3: BDT score distribution for the predicted backgrounds and data in a region with the same event selection as for the τ had-vis +lepton channel, except for the requirement of an eµ pair instead of the e/µ + τ had-vis pair (as described in the text).The five H + mass range trainings are shown.The lower panel of each plot shows the ratio of data to the SM background prediction.The uncertainty bands include all statistical and systematic uncertainties.

Figure 9
Figure9shows the 95% CL exclusion limits on tan β as a function of the charged Higgs boson mass in the context of the hMSSM scenario.All tan β values are excluded for m H + 160 GeV.At tan β = 60, above which no reliable theoretical calculations exist, the charged Higgs boson mass range up to 1100 GeV is excluded, hence significantly improving on the limits based on the dataset collected in 2015, which corresponds to an integrated luminosity of 3.2 fb −1 .

Figure 5 :
Figure 5: BDT score distributions in the signal region of the τ had-vis +jets channel, in the five mass ranges used for the BDT trainings, after a fit to the data with the background-only hypothesis.The lower panel of each plot shows the ratio of data to the SM background prediction.The uncertainty bands include all statistical and systematic uncertainties.The normalisation of the signal (shown for illustration) corresponds to the integral of the background.

Figure 6 :
Figure6: BDT score distributions in the signal region of the τ had-vis +electron sub-channel, in the five mass ranges used for the BDT trainings, after a fit to the data with the background-only hypothesis.The lower panel of each plot shows the ratio of data to the SM background prediction.The uncertainty bands include all statistical and systematic uncertainties.The normalisation of the signal (shown for illustration) corresponds to the integral of the background.

Figure 7 :
Figure 7: BDT score distributions in the signal region of the τ had-vis +muon sub-channel, in the five mass ranges used for the BDT trainings, after a fit to the data with the background-only hypothesis.The lower panel of each plot shows the ratio of data to the SM background prediction.The uncertainty bands include all statistical and systematic uncertainties.The normalisation of the signal (shown for illustration) corresponds to the integral of the background.

Figure 8 :
Figure 8: Observed and expected 95% CL exclusion limits on (a) σ(pp → tbH + ) × B(H + → τν) and (b) B(t → bH + ) × B(H + → τν) as a function of the charged Higgs boson mass in 36.1 fb −1 of pp collision data at √ s = 13 TeV, after combination of the τ had-vis +jets and τ had-vis +lepton channels.In the case of the expected limits, one-and two-standard-deviation uncertainty bands are also shown.As a comparison, the observed exclusion limits on B(t → bH + )×B(H + → τν) obtained with the Run-1 data at √ s = 8 TeV [16] and on σ(pp → tbH + )×B(H + → τν) obtained with the dataset collected in 2015 at √ s = 13 TeV [22] are also shown.

Figure 9 :
Figure 9: 95% CL exclusion limits on tan β as a function of m H + , shown in the context of the hMSSM, for the regions in which theoretical predictions are available (0.5 ≤ tan β ≤ 60).In the case of the expected limits, oneand two-standard-deviation uncertainty bands are also shown.As a comparison, the red curves near the upper-left corner show the observed and expected exclusion limits based on the dataset of 3.2 fb −1 collected in 2015 at √ s = 13 TeV [22].

Table 2 :
Expected event yields for the backgrounds and a hypothetical H + signal after applying all τ had-vis +jets selection criteria, and comparison with 36.1 fb −1 of data.All yields are evaluated prior to using the multivariate discriminant and applying the statistical fitting procedure.The values shown for the signal assume a charged Higgs boson mass of 170 GeV and 1000 GeV, with a cross-section times branching fraction σ(pp → tbH + )× B(H + → τν) corresponding to tan β = 40 in the hMSSM benchmark scenario.Statistical and systematic uncertainties are quoted, respectively.

Table 3 :
Expected event yields for the backgrounds and a hypothetical H + signal after applying all τ had-vis +lepton selection criteria, and comparison with 36.1 fb −1 of data.All yields are evaluated prior to using the multivariate discriminant and applying the statistical fitting procedure.The values shown for the signal assume a charged Higgs boson mass of 170 GeV and 1000 GeV, with a cross-section times branching fraction σ(pp → tbH + )× B(H + → τν) corresponding to tan β = 40 in the hMSSM benchmark scenario.Statistical and systematic uncertainties are quoted, respectively.
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Roy, The Hadronic τ decay signature of a heavy charged Higgs boson at LHC, Phys.Lett.B 459 (1999) 607, arXiv: hep-ph/9905542 [hep-ph].[81] ATLAS Collaboration, Measurement of τ polarization in W → τν decays with the ATLAS detector in pp collisions at √ s = 7 TeV, Eur.Phys.J. C 72 (2012) 2062, arXiv: 1204.6720[hep-ex].[82] L. Devroye, Non-Uniform Random Variate Generation, published by Springer, 1986.[83] ATLAS Collaboration, Calibration of b-tagging using dileptonic top pair events in a combinatorial likelihood approach with the ATLAS experiment, ATLAS-CONF-2014-004, 2014, : https://cds.cern.ch/record/1664335.Also at Department of Physics, California State University, Fresno CA; United States of America.m Also at Department of Physics, California State University, Sacramento CA; United States of America.n Also at Department of Physics, King's College London, London; United Kingdom.o Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg; Russia.p Also at Department of Physics, University of Fribourg, Fribourg; Switzerland.q Also at Department of Physics, University of Michigan, Ann Arbor MI; United States of America.r Also at Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa; Italy.s Also at Giresun University, Faculty of Engineering, Giresun; Turkey.t Also at Graduate School of Science, Osaka University, Osaka; Japan.u Also at Hellenic Open University, Patras; Greece.v Also at Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest; Romania.Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg; Germany.z Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen; Netherlands.aa Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest; Hungary.ab Also at Institute of Particle Physics (IPP); Canada.ac Also at Institute of Physics, Academia Sinica, Taipei; Taiwan.ad Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku; Azerbaijan.ae Also at Institute of Theoretical Physics, Ilia State University, Tbilisi; Georgia.a f Also at LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay; France.ag Also at Louisiana Tech University, Ruston LA; United States of America.ah Also at Manhattan College, New York NY; United States of America.ai Also at Moscow Institute of Physics and Technology State University, Dolgoprudny; Russia.a j Also at National Research Nuclear University MEPhI, Moscow; Russia.ak Also at Near East University, Nicosia, North Cyprus, Mersin; Turkey.al Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg; Germany.am Also at School of Physics, Sun Yat-sen University, Guangzhou; China.an Also at The City College of New York, New York NY; United States of America.ao Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing; China.
b Also at Centre for High Performance Computing, CSIR Campus, Rosebank, Cape Town; South Africa.cAlso at CERN, Geneva; Switzerland.dAlsoatCPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille; France.eAlso at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève; Switzerland.fAlsoatDepartament de Fisica de la Universitat Autonoma de Barcelona, Barcelona; Spain.gAlso at Departamento de Física Teorica y del Cosmos, Universidad de Granada, Granada (Spain);Spain.hAlso at Department of Applied Physics and Astronomy, University of Sharjah, Sharjah; United Arab Emirates.iAlso at Department of Financial and Management Engineering, University of the Aegean, Chios; Greece.jAlso at Department of Physics and Astronomy, University of Louisville, Louisville, KY; United States of America.kAlso at Department of Physics and Astronomy, University of Sheffield, Sheffield; United Kingdom.lw Also at II.Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen; Germany.xAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona; Spain.y ap Also at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny; Russia.aq Also at TRIUMF, Vancouver BC; Canada.ar Also at Universita di Napoli Parthenope, Napoli; Italy.* Deceased