Search for charged Higgs bosons in the H$^{\pm}$ $\to$ $\tau^{\pm}\nu_\tau$ decay channel in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search is presented for charged Higgs bosons in the H$^{\pm}$ $\to$ $\tau^{\pm}\nu_\tau$ decay mode in the hadronic final state and in final states with an electron or muon. The search is based on proton-proton collision data recorded by the CMS experiment in 2016 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The results agree with the background expectation from the standard model. Upper limits at 95% confidence level are set on the production cross section times branching fraction to $\tau^{\pm}\nu_\tau$ for an H$^{\pm}$ in the mass range of 80 GeV to 3 TeV, including the region near the top quark mass. The observed limit ranges from 6 pb at 80 GeV to 5 fb at 3 TeV. The limits are interpreted in the context of the minimal supersymmetric standard model $m_\mathrm{h}^\mathrm{mod-}$ scenario.


1
The dominant production mechanism of the H ± depends on its mass. Examples of leading order (LO) diagrams describing the H ± production in 2HDM in different mass regions are shown in Fig. 1. Light H ± , with a mass smaller than the mass difference between the top and the bottom quarks (m H ± < m t − m b ), are predominantly produced in decays of top quarks (doubleresonant top quark production, Fig. 1 left), whereas heavy H ± (m H ± > m t − m b ) are produced in association with a top quark as pp → tbH ± (single-resonant top quark production, Fig. 1 middle). In the intermediate region near the mass of the top quark (m H ± ∼ m t ), the nonresonant top quark production mode ( Fig. 1 right) also contributes and the full pp → H ± W ∓ bb process must be calculated in order to correctly account for all three production mechanisms and their interference [20]. In type II 2HDM, a light H ± decays almost exclusively to a tau lepton and a neutrino. For the heavy H ± , the decay into top and bottom quarks (H + → tb and H − → tb, together denoted as H ± → tb) is dominant, but since the coupling of the H ± to leptons is proportional to tan β, the branching fraction to a tau lepton and a neutrino (H + → τ + ν τ and H − → τ − ν τ , together denoted as H ± → τ ± ν τ ) remains sizable for large values of tan β. In this paper, a direct search for H ± decaying into a tau lepton and a neutrino is presented, based on data collected at a center-of-mass energy of 13 TeV by the CMS experiment in 2016, corresponding to an integrated luminosity of 35.9 fb −1 . The search is conducted in three different final states, labeled in this paper as the hadronic final state (τ h + jets, where τ h denotes a hadronically decaying tau lepton), the leptonic final state with a τ h ( + τ h ), and the leptonic final state without a τ h ( + no τ h ). For the hadronic final state, events contain a τ h , missing transverse momentum due to neutrinos, and additional hadronic jets from top quark decays and b quarks. The leptonic final state with a τ h contains a single isolated lepton (electron or muon), missing transverse momentum, hadronic jets and a τ h . The leptonic final state without a τ h is defined in a similar way, except that events with a τ h are rejected. In the leptonic final states, the lepton can originate either from the decays of the tau leptons from H ± decays, or from a W ± boson decay.
In each final state, events are further classified into different categories for statistical analysis. A transverse mass distribution is reconstructed in each category of each final state and used in a maximum likelihood fit to search for an H ± signal. The H ± mass range from 80 GeV to 3 TeV is covered in the search, including the intermediate mass range near m t .
This paper is organized as follows. The CMS detector is briefly presented in Section 2. The methods used in event simulation and reconstruction are described in Sections 3 and 4, respectively. The event selection and categorization criteria are presented in Section 5, while Section 6 details the background estimation methods used in the analysis. Systematic uncertainties included in the analysis are described in Section 7. Finally, the results are presented in Section 8 and summarized in Section 9.

The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity (η) coverage provided by the barrel and endcap detectors up to |η| = 5. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. Events of interest are selected using a two-tiered trigger system [42]. The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a time interval of less than 4 µs. The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1 kHz before data storage. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [43].

Event simulation
The signal samples for the light H ± mass values from 80 to 160 GeV are generated at nextto-leading order (NLO) with the MADGRAPH5 aMC@NLO v2.3.3 [44] generator, assuming H ± production via top quark decay (pp → H ± W ∓ bb). For the heavy H ± mass range from 180 GeV to 3 TeV, the same approach is used except that H ± production via pp → tbH ± is assumed. The simulated samples are normalized to the theoretical cross sections for the corresponding processes. For the tt background and the single top quark background in the s and t W channels, the cross sections are calculated at next-to-NLO precision [55,56]. NLO precision calculations are used for single top quark production in the t channel, and for the W +jets, Z/γ * , and diboson processes [56][57][58][59].
For all simulated samples, the NNPDF3.0 parton distribution functions (PDFs) [60] are used, and the generators are interfaced with PYTHIA 8.212 to model the parton showering, fragmentation, and the decay of the tau leptons. The PYTHIA parameters affecting the description of the underlying event are set to the CUETP8M1 tune [61] for all processes except tt, for which a customized CUETP8M2T4 tune [62] is used.
Generated events are processed through a simulation of the CMS detector based on the GEANT4 v9.4 software [63], and they are reconstructed following the same algorithms that are used for data. The effect of additional soft inelastic proton-proton (pp) interactions (pileup) is modeled by generating minimum bias collision events with PYTHIA and mixing them with the simulated hard scattering events. The effects from multiple inelastic pp collisions occurring per bunch crossing (in-time pileup), as well as the effect of inelastic collisions happening in the preceding and subsequent bunch crossings (out-of-time pileup) are taken into account. The simulated events are weighted such that the final pileup distribution matches the one observed in data.
For the data collected in 2016, an average of approximately 23 interactions per bunch crossing was measured.

Event reconstruction
Event reconstruction is based on the particle-flow (PF) algorithm [64] that aims to reconstruct and identify each individual particle in an event with an optimized combination of information from the various elements of the CMS detector. The output of the PF algorithm is a set of PF candidates, classified into muons, electrons, photons, and charged and neutral hadrons.
The collision vertices are reconstructed from particle tracks using the deterministic annealing algorithm [65]. The reconstructed vertex with the largest value of the physics-object transverse momentum squared (p 2 T ) sum is taken to be the primary p p interaction vertex. The physics objects in this case are the jets, clustered using the anti-k T jet finding algorithm [66,67] with the tracks assigned to the vertex as inputs, and the associated missing transverse momentum, calculated as the negative vector sum of the p T of those jets. All other reconstructed vertices are attributed to pileup.
Electrons are reconstructed and their momentum is estimated by combining the momentum measurement from the tracker at the interaction vertex with the energy measurement in the ECAL. The energy of the corresponding ECAL cluster and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron tracks are taken into account. The momentum resolution for electrons with p T ≈ 45 GeV from Z → ee decays ranges from 1.7% for nonshowering electrons in the barrel region to 4.5% for showering electrons in the endcaps [68]. In addition, electrons are required to pass an identification requirement based on a multivariate discriminant that combines several variables describing the shape of the energy deposits in the ECAL, as well as the direction and quality of the associated tracks [69]. A tight working point with 88% identification efficiency for tt events is used to select events with an electron, while a loose working point with 95% efficiency is used to veto events with one or several electrons, depending on the final state.
Muons are identified as tracks in the central tracker, consistent with either a track or several hits in the muon chambers, and associated with calorimeter deposits compatible with the muon hypothesis [70]. The momenta of muons are obtained from the curvatures of the corresponding tracks. Contributions from other particles misidentified as muons are suppressed with a discriminant based on the track fit quality. Two working points as defined in Ref.
[70] are used: a medium working point with 97% identification efficiency is used to select events with a muon, while a loose working point with >99% identification efficiency is used for vetoing muons.
The background contributions from nonprompt and misidentified leptons are suppressed by requiring the leptons to be isolated from hadronic activity in the event. For this purpose, an isolation discriminant is defined as the p T sum of the PF candidates in a cone around the lepton, divided by the p T of the lepton. For optimal performance across the lepton momentum range, the cone size is varied with the lepton p T as ∆R = √ (∆η) 2 + (∆φ) 2 = 10 GeV/min(max(p T , 50 GeV), 200 GeV), where ∆φ denotes a difference in azimuthal angle, leading to cone radii from 0.05 to 0.20. A tight (loose) isolation criterion with discriminant < 0.1 (0.4) is used in lepton selection (veto).
For each event, hadronic jets are clustered from the reconstructed PF candidates using the infrared and collinear safe anti-k T algorithm [66,67] with a distance parameter of 0.4. The jet momentum is determined as the vectorial sum of all particle momenta in the jet, and is found from simulation to be within 5 to 10% of the true momentum over the whole p T spectrum and detector acceptance. Pileup can contribute additional tracks and calorimetric energy deposits to the jet momentum. To mitigate this effect, tracks identified as originating from pileup vertices are discarded and an offset correction is applied to correct for remaining contributions. Jet energy corrections are derived from simulation to bring the measured response of jets to that of particle level jets on average. In situ measurements of the momentum balance in dijet, photon + jet, Z + jet, and multijet events are used to account for any residual differences in jet energy scale between data and simulation [71]. The jet energy resolution amounts typically to 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV [72]. Additional selection criteria are applied to each jet to remove jets potentially dominated by anomalous contributions from various subdetector components or reconstruction failures.
Jets originating from the hadronization of b quarks (b jets) are identified using the combined secondary vertex algorithm [73,74], which uses information on the decay vertices of long-lived hadrons and the impact parameters of charged particle tracks as input to a neural network discriminant. The working point is chosen such that the probability to misidentify jets originating from light-flavor quarks or gluons (c quarks) as b jets is 1% (12%), corresponding to 63% efficiency for the selection of genuine b jets in tt events. Simulated samples are corrected for differences in b jet identification and misidentification efficiency compared to the data.
The τ h are reconstructed with the hadron-plus-strips algorithm [75,76], which uses clustered anti-k T jets as seeds. The hadron-plus-strips algorithm reconstructs different τ decay modes with one charged pion and up to two neutral pions (one-prong), or three charged pions (threeprong). Since neutral pions decay promptly to a photon pair, they are reconstructed by defining strips of ECAL energy deposits in the η-φ plane. The τ h candidates are rejected if they are consistent with the hypothesis of being muons or electrons misidentified as τ h . The jets originating from the hadronization of quarks or gluons misidentified as τ h are suppressed using a multivariate discriminant [76]. It combines information on τ h isolation, based on the surrounding hadronic activity, and on its lifetime, inferred from the tracks of the τ h decay products. A loose working point is used for this discriminant, corresponding to ≈50% identification efficiency, determined from Z/γ * → τ + τ − events, and 3 × 10 −3 probability for misidentifying a jet as a τ h , determined from quantum chromodynamics (QCD) multijet events. A correction to the energy scale is derived using eτ h and µτ h final states of Z/γ * → τ + τ − events [76] and applied in simulated samples. The transverse mass is defined as where is a generic symbol used to label the electron or muon present in the leptonic final states, while the leading τ h is used in the m T in the hadronic final state.

Event selection
The search is conducted in three exclusive final states: • τ h + jets: hadronic final state (events with an electron or a muon are vetoed); • + τ h : leptonic final state with a hadronically decaying tau lepton (events with additional electrons or muons are vetoed); and • + no τ h : leptonic final state without a hadronically decaying tau lepton (events with a τ h or additional electrons or muons are vetoed).
In the low-m H ± region, below m t , the sensitivity of the hadronic final state is limited by the relatively high trigger thresholds, making the leptonic final states most sensitive for the H ± signal. In the high-m H ± region, above m t , the hadronic final state dominates the sensitivity, since the selection efficiency is higher as a result of more inclusive jet multiplicity requirements.
The event selection and categorization strategies are chosen separately for each final state to efficiently discriminate against the background events, while ensuring a sufficient signal selection efficiency.

Hadronic final state (τ h + jets)
An HLT algorithm requiring the presence of a τ h candidate and trigger-level missing transverse momentum estimated from calorimeter information (p miss,calo T ) is used to select the events for offline analysis. The trigger requires the τ h candidate to be loosely isolated with p T > 50 GeV and |η| < 2.1, and with a leading track transverse momentum p track T > 30 GeV. The p miss,calo T is required to be larger than 90 GeV.
The trigger efficiencies for the τ h and p miss,calo T requirements are measured separately. The efficiency of the τ h part of the trigger is determined with the tag-and-probe technique [78], using Z/γ * → τ + τ − events with one hadronic and one muonic tau lepton decay. The efficiency is found to vary between 50 and 100%, as a function of p T and η of the τ h . The efficiency of the p miss,calo T part of the trigger is measured from events with a signal-like topology selected with a single-τ h trigger, resulting in efficiencies between 10 and 100%, depending on the value of the p miss T . The simulated events are corrected to match the trigger efficiencies measured in the data. In the offline selection, low thresholds for the p T of the reconstructed τ h and p miss T are needed to maximize the sensitivity for light H ± . Thus selection criteria identical to those in the HLT are applied to the reconstructed τ h candidate and to the p miss T . The one-prong τ h candidates, corresponding to τ decays into a charged pion and up to two neutral pions, are selected for further analysis. Events are required to contain at least three jets with p T > 30 GeV and |η| < 4.7, separated from the reconstructed τ h by ∆R > 0.5. At least one of the jets is required to pass the b jet identification with |η| < 2.4. Any event with isolated electrons (muons) with p T > 15(10) GeV, |η| < 2.5, and passing the loose identification and isolation criteria is rejected.
To suppress the background from QCD multijet events with a jet misidentified as a τ h , an additional selection based on ∆φ(τ h , p miss T ) and ∆φ(jet n , p miss T ) is applied, where the index n runs over the three highest p T jets (jet n ) in the event. QCD multijet events passing the previous selection steps typically contain a hadronic jet misidentified as a τ h , another hadronic jet recoiling in the opposite direction, and p miss T arising from the mismeasurement of the jet momenta. These events can be suppressed with an angular discriminant defined as The selected events are required to have R min bb > 40 • . The distribution of the R min bb variable after all other selections is shown in Fig. 2 (left).
The selected events are classified into two categories based on the value of the variable R τ = p track T /p τ h T , reflecting the helicity correlations emerging from the opposite polarization states of the tau leptons originating from W ± and H ± decays [79]. The distribution of the R τ variable is shown in Fig. 2 (right). After all other selections, most of the signal events have a large value of R τ , and the high-R τ category provides a good signal-to-background ratio. For large m H ± values, the signal events are more evenly distributed between the two categories, so inclusion of the background-dominated low-R τ category in the statistical analysis further improves the sensitivity for the heavy H ± . Separating the two categories at R τ = 0.75 maximizes the signal sensitivity across the m H ± range.

Leptonic final state with a hadronically decaying tau lepton ( + τ h )
Single-lepton trigger algorithms are used for the online selection of events with isolated electrons or muons. Several HLT algorithms for electron (muon) selection with different thresholds starting from 27 (24) GeV, with |η| < 2.1 (2.4) and with different isolation criteria, are used in or combination to maximize the efficiency across the lepton p T range.
In the offline selection, electrons (muons) are required to have p T > 35(30) GeV and |η| < 2.1(2.4) because of trigger constraints. Electrons (muons) are required to pass the tight (medium) identification and tight isolation requirements. Events with any additional electrons (muons) with p T > 10 GeV and |η| < 2.1(2.4) that pass the loose identification and isolation criteria are vetoed. Efficiencies for online and offline identification of leptons are measured, and the simulated events are corrected to match the efficiencies observed in data. The presence of a τ h is required, with p T > 20 GeV, |η| < 2.3, and with a ∆R separation of at least 0.5 with respect to the lepton.
One, two, or three jets are required with p T > 30 GeV and |η| < 2.4, separated from the lepton and the τ h by ∆R > 0.5. At least one of the jets is required to pass the b jet identification. To suppress the background from jets misidentified as τ h , the p miss T is required to be at least 70 GeV. The background contribution from events with muons originating from b hadron decays is suppressed by requiring ∆φ( , p miss T ) to exceed 0.5.
The selected events are classified into several categories for statistical analysis. Three categories are defined based on the jet multiplicity and the number of jets passing the b jet identification: 1j1b (one jet that is also identified as a b jet), ≥2j1b, and ≥2j≥2b. A second categorization is performed in bins of p miss T : 70-100, 100-150, and >150 GeV. Together with the separate electron and muon final states, this results in 18 categories.
The signal-to-background ratio in different categories varies with H ± mass, as jet categories with two jets and high p miss T become more sensitive for higher m H ± values. The backgroundenriched categories allow a precise determination of the background yields with a fit to data and extrapolation of this information to signal regions. The categorization is found to improve the expected sensitivity significantly, especially in the low-m H ± region, where efficient discrimination against backgrounds is essential.

Leptonic final state without a hadronically decaying tau lepton ( + no τ h )
The event selection criteria for the + no τ h final state are identical to those described in Section 5.2 for the + τ h final state, except for the following requirements. An event is vetoed if it contains a τ h with p T > 20 GeV, |η| < 2.3, and with a ∆R separation of at least 0.5 with respect to the lepton. Two or three jets are required, each jet separated from the lepton by ∆R > 0.5. Higher jet multiplicities are not selected, because they are expected to be more sensitive in searches for other H ± decay modes, such as H ± → tb. At least one of the jets is required to pass the b jet identification.
The number of QCD multijet events with jets misidentified as leptons is reduced to a negligible level by requiring a high p miss T of >100 GeV and by applying the following angular selections: where jet n refers to any of the selected jets in the events. The first criterion is identical to the one applied in the + τ h final state against muons from b hadron decays whereas the second discriminates efficiently against the QCD multijet background. The last requirement is designed to reject background events where all the jets are back-to-back with respect to the selected lepton. Table 1: A summary of the event selection criteria applied in each final state. The electrons, muons, τ h candidates and jets are required to be separated from each other by ∆R > 0.5 in all final states. The † symbol means that the selection is identical between + τ h and + no τ h final states. In all final states, events with additional electrons or muons are vetoed as detailed in Section 5. In this table, "b jets" refers to all jets passing the b jet identification, and jet n refers to any of the selected jets.
∆φ(leading jet, p miss T ) > 0.5, min(∆φ( , jet n )) < π − 0.5 To further enhance the signal sensitivity and to constrain the backgrounds, a similar categorization as in the + τ h final state is established. Four categories are used based on jet multiplicity and the number of jets passing the b jet identification: 2j1b, 2j2b, 3j1b, and 3j≥2b, followed by two categories in p miss T : 100-150 and >150 GeV. Together with the separate electron and muon final states, this results in 16 categories.
An overview of the event selection criteria in all three final states is shown in Table 1.

Background estimation
The dominant background processes in the hadronic final state are QCD multijet and tt production. Other backgrounds are single top quark production, W boson production in association with jets, Z/γ * processes, and diboson production. We refer to tt and single top quark events as "top events", and to W +jets, Z/γ * , and diboson events as "electroweak events". The backgrounds from events containing either a genuine τ h or an electron or a muon misidentified as a τ h are estimated from simulation, while the background from jets misidentified as a τ h is estimated from data. The correct identification or misidentification of a τ h is determined by requiring a generator-level tau lepton to match with the reconstructed τ h within a ∆R cone of 0.1.
In the events where a jet is misidentified as a τ h (denoted as jet → τ h ), QCD multijet production is the dominant process. The jet → τ h background is estimated using a control sample enriched in jets misidentified as τ h , obtained by inverting the offline τ h isolation requirement used for signal selection. The contamination of the control region from electroweak/top events with a genuine τ h or a lepton misidentified as a τ h is estimated from the simulation and subtracted from the control sample. The difference in selection efficiency between signal and control re-gions is corrected by normalizing the control sample with fake factors, calculated at an early stage of event selection (i.e. before applying b jet identification, offline selection on p miss T or the angular selections), where a possible signal does not stand out from the large background yield. To account for the correlation between the p T of the τ h and p miss T as well as geometrical differences in detector response, the measurement is performed in bins of p T and |η| of the τ h .
The jet → τ h background consists of two components: the QCD multijet events and electroweak/top events with jets misidentified as τ h . The jets in these two background components have different quark and gluon composition implying different tau fake factors. Thus the fake factors for misidentified τ h from the QCD multijet events and for misidentified τ h from electroweak/top events are estimated separately. The fake factor for the QCD multijet events is defined as the ratio of the QCD multijet event yields in signal and control regions. The QCD multijet event yield in the control region is estimated by subtracting the simulated electroweak/top contribution (both genuine and non-genuine τ h events) from data. To estimate the contribution of the QCD multijet events in the signal region, a binned maximum likelihood fit of p miss T templates to data is performed, using the fraction of the QCD multijet events as a fit parameter. The templates describe the expected shape of the p miss T distribution for each background component prior to the fit. The p miss T shape of the QCD multijet events is assumed to be similar in the signal and control regions, so the shape observed in the control region is used as the fit template. The template for electroweak/top events is obtained directly from simulation. The fake factor for electroweak/top events is also estimated from simulation as the ratio of event yields in signal and control regions. Finally, the overall normalization factor of the control sample (as a function of the p T and |η| of the τ h ) is determined as a weighted sum of the two fake factors, where the weight corresponds to the relative fractions of the QCD multijet and electroweak/top events in the control region after all selections. A closure test is performed by comparing the background predictions obtained with the above method to data in a signal-depleted validation region. The validation region is defined similarly to the signal region, except that events with jets passing the b jet identification are vetoed.
In the leptonic final states, the dominant background is tt production in which the semileptonic tt decays are dominant in the + no τ h final state and the dilepton tt decays are dominant in the + τ h final state. Minor backgrounds include single top quark, W +jets, Z/γ * , and diboson production. The QCD multijet background is suppressed to a negligible level with tight angular selections and p miss T requirements. All backgrounds in the two leptonic final states are estimated from simulation.

Systematic uncertainties
A summary of uncertainties incorporated in the analysis is given in Table 2, where the effects of the different uncertainties on the final event yields are shown. For the uncertainties common to all final states, the variations in the yields are similar across the final states. Some of them affect only the final event yield for a given signal or background process, whereas others also modify the shape of the final m T distributions. The uncertainties from different sources are assumed to be uncorrelated. Each uncertainty is treated as 100% correlated among the signal and background processes, except for the few special cases mentioned in the following.
The simulated events are corrected to match the online and offline selection efficiencies measured in data. For the trigger used in the τ h + jets final state, the correction depends on the p T of the τ h and p miss T , so the corresponding uncertainty is taken into account as a shape uncertainty. In the + τ h and + no τ h final states, the online selection with single-lepton triggers is in- corporated into the overall lepton selection efficiency and the corresponding normalization uncertainty.
The systematic uncertainties in identification and isolation efficiencies for τ h , electron, and muon candidates are taken into account. The agreement of the τ h identification efficiency between data and simulated samples is measured using the tag-and-probe technique [76]. The uncertainty in the measurement is 5%. It is incorporated as a normalization uncertainty for all events with genuine tau leptons, and anticorrelated between the + no τ h final state and the final states with a τ h . For the τ h with large p T , an additional uncertainty of +5 −35 %p T / TeV is applied in the hadronic final state as a shape uncertainty to account for possible differences arising in the extrapolation of the measured efficiencies to the high-p T range. Simulated events with an electron or a muon misidentified as a τ h are weighted to obtain the misidentification rates measured in data. The corrections are applied as a function of η and the corresponding uncertainties are propagated to m T distributions and incorporated as shape uncertainties.
For the selection of electrons (muons), the combined uncertainty in online selection and offline identification is 3 (4)%. For leptons vetoed with loose identification and isolation criteria the effect of this uncertainty in the final event yield is typically only 0.3%. Both effects are included as normalization uncertainties.
The systematic uncertainties related to the calibration of energy measurement for jets, τ h and p miss T are considered as shape uncertainties. The uncertainties in the jet energy scale and jet energy resolution are specified as a function of jet p T and η. The uncertainty in the τ h energy scale is ±1.2% for p T < 400 GeV and ±3% otherwise [76]. The variations of the jet and τ h energy scales are propagated to p miss T , for which the uncertainties arising from the unclustered energy deposits in the detector are also included. The uncertainty in the lepton energy scale is negligible for this analysis. Correcting the b jet identification and misidentification efficiencies in simulated samples affects the final m T shapes, so the related uncertainties are considered as shape uncertainties [74].
The systematic uncertainty due to the pileup modeling is obtained by shifting the mean of the total inelastic pp production cross section by ±5% around its nominal value [80], and propagating the difference to the final m T distributions as a shape uncertainty.
The uncertainty in the measurement of the integrated luminosity is 2.5% [81].
The uncertainties related to the jet → τ h background measurement in the hadronic final state are included. The statistical uncertainties in the data and simulated samples used to determine the fake factors are propagated into the final m T distributions as a normalization uncertainty. The limited statistical precision of samples in the signal and control region after all selections can lead to a difference in m T shapes between the two regions. This effect is estimated and incorporated as a shape uncertainty. As the jet → τ h background is estimated by subtracting simulated events (electroweak/top contribution) from the control data sample, all uncertainties related to the simulated samples are propagated to this background. These uncertainties are scaled to correspond to the contribution from simulated events in the control region after all selections, and anticorrelated between the jet → τ h background and the other background processes.
The reference cross sections used to normalize each simulated background process are varied within their theoretical uncertainties related to the choice of renormalization and factorization (RF) scales and PDFs [82]. For tt and single top quark processes, the effect of m t on the cross sections is considered by varying m t by 1.0 GeV around the nominal value of 172.5 GeV. Theoretical uncertainties in the acceptance of signal and background events are determined by varying the RF scales and PDFs [82]. For the RF uncertainties, the RF scales are varied by factors of 0.5 and 2, excluding the extreme variations where one scale is varied by 0.5 and the other one by 2. The envelope of the six variations is used to determine the total uncertainty. The cross section and acceptance uncertainties are uncorrelated between different background processes.
The uncertainty arising from the parton shower modeling is included for the dominant tt background in the leptonic final states. Four parton showering variations are included by perturbing the initial-and final-state parameters [83], the matching of jets from matrix element calculations and from parton shower, and the underlying event tune [62]. The parton shower uncertainties are derived in each category and are applied as normalization uncertainties, uncorrelated between categories. The leptonic final states are sensitive to the parton shower modeling due to the event categorization based on the jet multiplicity. In the hadronic final state, the event selection is inclusive in jet multiplicity and thus this uncertainty is neglected.
For the intermediate-mass signal samples, an additional normalization uncertainty is assigned to incorporate the statistical uncertainties of the samples used in the calculation of the LO-to-NLO correction factors.
The statistical uncertainties related to the finite number of events in the final m T distributions are taken into account using the Barlow-Beeston method [84].

Results
A simultaneous binned maximum likelihood fit is performed over all the categories in the three final states. In total, 36 m T distributions (two from the τ h + jets final state, 18 from the + τ h final state, and 16 from the + no τ h final state) are fitted. The distributions are binned according to the statistical precision of the samples, separately for each category. This leads to wider bins in the tail of the distributions, such that the last bin extends to 5 TeV. The systematic uncertainties are incorporated as nuisance parameters in the likelihood. They are profiled in the fit according to their probability density functions, taking correlations into account. For normalization uncertainties, log-normal probability density functions are used as priors. For shape uncertainties, polynomial interpolation is used to derive continuous prior distributions from the nominal and varied m T shape templates. The expected event yields after a background-only fit to the data and the observed yields are summarized in Table 3.
The distributions of m T after a background-only fit to the data are shown in Fig. 3 for both categories in the τ h + jets final state, in Fig. 4 for two categories with high signal sensitivity in the + τ h final state, and in Fig. 5 for two high-sensitivity categories in the + no τ h final state. No significant excess is observed in any of the categories, and the result of the simultaneous fit is found to agree with the SM prediction.
The modified frequentist CL s criterion [85,86] based on the profile likelihood ratio test statistic [87] is applied to determine the 95% confidence level (CL) limit for the product of the H ± production cross section and the branching fraction B(H ± → τ ± ν τ ). The asymptotic approximation [88] is used throughout the analysis. Pseudo-experiments are performed for selected signal mass hypotheses to verify the validity of the asymptotic approximation. For the H ± mass range up to 165 GeV, the limit on B(t → bH ± )B(H ± → τ ± ν τ ) is calculated, scaling down the tt background component consistently with the B(t → bH ± ) signal hypothesis, and the result is interpreted as a limit on σ H ± B(H ± → τ ± ν τ ) by assuming σ H ± = 2σ tt B(t → bH ± )(1 − B(t → bH ± )), where the tt production cross section σ tt is assumed unmodified by the presence of H ± and the value of 831.76 pb is used [55,56]. For the H ± mass range from 170 GeV to 3 TeV, the limit on σ H ± B(H ± → τ ± ν τ ) is calculated without assuming a specific production mode.
The model-independent upper limit with all final states and categories combined is shown on the left side of Fig. 6. The numerical values are listed in Table 4. The observed limit ranges from 6 pb at 80 GeV to 5 fb at 3 TeV. For the light H ± mass range of 80-160 GeV, the limit corresponds to B(t → bH ± )B(H ± → τ ± ν τ ) values between 0.36% (at 80 GeV) and 0.08% (at 160 GeV). In the light H ± mass range, this is the most stringent limit on B(t → bH ± )B(H ± → τ ± ν τ ) to date set by the CMS Collaboration, with a factor of 1.5-3.0 improvement with respect to Ref.
[28], depending on m H ± . In the intermediate mass range of 165-175 GeV, this is the first limit on σ H ± B(H ± → τ ± ν τ ) set by the CMS Collaboration. The drop in the expected and observed limits in the intermediate region is not predicted from theory [20] but is rather an experimental feature explained by the fact that in this region LO signal samples are used instead of NLO. This dip is mitigated but not completely cancelled by the LO-to-NLO corrections extrapolated from the surrounding mass regions. In the heavy mass range from 180 GeV, this result extends the search region up to m H ± = 3 TeV, compared to 600 GeV in Ref. [28].
In the light and intermediate H ± mass regions all three final states contribute significantly to the sensitivity, and the combined limits are on average ≈40% lower compared to the τ h + jets final state alone. In the heavy H ± mass region, the sensitivity of the leptonic final states decreases, and the τ h + jets final state starts to dominate the limit as m H ± increases. Above m H ± = 500 GeV the combined limit is solely driven by the τ h + jets final state.
The limit is interpreted in the MSSM m modh benchmark scenario [89] by comparing the observed limit on the H ± cross section to the theoretical cross sections predicted in this scenario [20, [90][91][92][93][94]. The MSSM m modh scenario is specified using low-energy MSSM parameters and is designed to give a mass of approximately 125 GeV for the light CP-even Higgs boson over a wide region of the parameter space. The limit for the MSSM m modh scenario in the m H ± -tan β plane is shown on the right side of Fig. 6. Based on the observed limit, all values of the parameter tan β from 1 to 60 are excluded for m H ± values up to 160 GeV. The limit extends to m H ± = 500 GeV. For m H ± = 200 (400) GeV, the observed limit excludes all tan β values above 26 (40), compared to 45 (56) excluded in Ref. [28].

Summary
A search is presented for charged Higgs bosons decaying as H ± → τ ± ν τ , using events recorded by the CMS experiment in 2016 at a center-of-mass energy of 13 TeV. Transverse mass distributions are reconstructed in hadronic and leptonic final states and are found to agree with the standard model expectation. Upper limits for the product of the H ± production cross section and the branching fraction to τ ± ν τ are set at 95% confidence level for an H ± mass ranging from 80 GeV to 3 TeV, including the range close to the top quark mass. The observed limit ranges from 6 pb at 80 GeV to 5 fb at 3 TeV. The results are interpreted as constraints in the parameter space of the minimal supersymmetric standard model m modh benchmark scenario. In this scenario, all tan β values from 1 to 60 are excluded for charged Higgs boson masses up to 160 GeV.

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses.   Figure 6: The observed 95% CL exclusion limits on σ H ± B(H ± → τ ± ν τ ) (solid black points), compared to the expected limit assuming only standard model processes (dashed line) for the H ± mass range from 80 GeV to 3 TeV (left), and the same limit interpreted in the m modh benchmark scenario (right). The green (yellow) bands represent one (two) standard deviations from the expected limit. On the left, the horizontal axis is linear from 80 to 180 GeV and logarithmic for larger m H ± values. On the right, the region below the red line is excluded assuming that the observed neutral Higgs boson is the light CP-even 2HDM Higgs boson with a mass of 125 ± 3 GeV, where the uncertainty is the theoretical uncertainty in the mass calculation.      [67] M. Cacciari, G. P. Salam, and G. Soyez, "FastJet user manual", Eur. Phys. J. C 72 (2012) 1896, doi:10.1140/epjc/s10052-012-1896-2, arXiv:1111.6097.