Search for charged Higgs bosons decaying into a top and a bottom quark in the all-jet final state of pp collisions at $\sqrt{s}=$ 13 TeV

A search for charged Higgs bosons (H$^\pm$) decaying into a top and a bottom quark in the all-jet final states is presented. The analysis uses LHC proton-proton collision data recorded with the CMS detector in 2016 at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. No significant excess is observed above the expected background. Model-independent upper limits at 95% confidence level are set on the product of the H$^\pm$ production cross section and branching fraction in two scenarios. For production in association with a top quark, limits of 21.3 to 0.007 pb are obtained for H$^\pm$ masses in the range of 0.2 to 3 TeV. Combining this with data from a search in leptonic final states results in improved limits of 9.25 to 0.005 pb. The complementary $s$-channel production of an H$^\pm$ is investigated in the mass range of 0.8 to 3 TeV and the corresponding upper limits are 4.5 to 0.023 pb. These results are interpreted using different minimal supersymmetric extensions of the standard model.


Introduction
The observation of a Higgs boson [1][2][3][4][5] has motivated new areas of study at the CERN LHC, including precision measurements of its interactions with standard model (SM) particles, searches for decays to new particles [6][7][8], and studies of the Higgs boson self interactions. Often, models beyond the SM contain an extended Higgs sector. Minimal extensions known as two Higgs doublet models (2HDMs) [9][10][11][12] include a second complex Higgs doublet that leads to five physical particles: two charged Higgs bosons, H ± , two neutral scalars, h and H, and one neutral pseudoscalar, A. The 2HDMs are further classified according to the couplings of the doublets to fermions. One of the popular 2HDMs is the minimal supersymmetric standard model (MSSM) [13,14] where one doublet couples to up quarks and the other to down quarks and charged leptons (Type-II 2HDM). In these models, the lightest CP-even Higgs boson can align with the properties of the SM, while the additional Higgs bosons can appear at or below the TeV scale [15]. The production and decay of the H ± depends on its mass (m H ± ) and the ratio of the vacuum expectation values of the neutral components of the two Higgs doublets (tan β). No fundamental charged-scalar boson is present in the SM, and the discovery of such a particle would uniquely point to physics beyond the SM.
We report a search for charged Higgs bosons with mass larger than that of the top quark (heavy H ± ) decaying to a top and bottom quark-antiquark pair (H + → tb). The production of the boson in association with a top and a bottom quark can be described using either a four-(4FS) or a five-flavor (5FS) scheme [16,17], which yield consistent results. It can also be produced directly via an s-channel process. The corresponding leading order (LO) Feynman diagrams are shown in Fig. 1. Charge-conjugate processes are implied throughout this paper. Several searches for the signature H + → tb by the ATLAS and CMS Collaborations in protonproton (pp) collisions at center-of-mass energies of 8 and 13 TeV [18][19][20][21], have been interpreted in the context of 2HDMs. Results of searches for a light H ± produced in the decay t → H + b that subsequently decays to cs or cb are presented in Refs. [22,23]. Limits on the production of an H ± using the τ + ν τ decay channel have also been obtained at center-of-mass energies of 8 and 13 TeV [18,[24][25][26]. Charged-current processes from low-energy precision flavor observables, such as tauonic B meson decays and the b → sγ transition, can be affected by the presence of the charged Higgs boson. These results currently provide the best indirect lower limit on m H ± in the Type-II 2HDM [27,28]. Complementary searches for additional neutral heavy Higgs bosons decaying to a pair of third generation fermions have been performed by ATLAS and CMS at √ s = 8 and 13 TeV in tt, bb, and τ + τ − decay channels [18,24,[29][30][31][32][33][34]]. The production of H ± via vector boson fusion with subsequent decays to W and Z bosons is expected in models containing Higgs triplets [35]. These searches are discussed in Refs. [36,37].
The results presented here are based on pp collision data collected in 2016 at √ s = 13 TeV by the CMS experiment, corresponding to an integrated luminosity of 35.9 fb −1 . The search investigates all-jet events, targeting a signal containing W → qq decays, both in the charged Higgs and in the associated top quark decay chains. The all-jet final state provides the largest accessible branching fractions, ≈45% and ≈67% for the top quark associated-and the s-channel processes. In addition, all the final state objects are detected, enabling full reconstruction of the invariant mass of the H ± candidate. This analysis is the first to report results in the all-jet tb → Wbb → jjbb channel for top quark-associated and s-channel production of a charged Higgs boson.
The search targets two distinct event topologies, boosted and resolved. The boosted analysis targets H ± bosons with mass m H ± 5m top . Decay products of H ± resonances with mass of O(TeV) have average transverse momenta (p T ) of several hundred GeV. As a consequence, the objects emerging from subsequent decays of top quarks are highly collimated jets that may not be fully resolved using the standard clustering algorithm, but can be reconstructed as a single large-radius jets. We therefore use these collimated top quark-or W boson-jet candidates to distinguish signal events. The resolved analysis focuses on less boosted final states where each top quark candidate can be reconstructed from jets associated with W → jj and one jet identified as originating from the fragmentation of a b quark ("b-tagged "). Therefore a minimum of seven jets is expected for the associated production channel. The search is sensitive to any narrow resonant charged state that decays to tb.
Model-independent upper limits on the product of the H ± production cross section and branching fraction into a top and bottom quark (σB) as a function of m H ± are presented below. These limits can also be recast into model-dependent limits and interpreted in scenario-specific limits, where the underlying free parameters (e.g., m H ± , branching fractions, and tan β) are fixed by the specific scenario. Beyond the 2HDM interpretations, this decay mode is relevant in the more general context of exotic resonance searches, motivated by models of W boson production [38,39].

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, and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity (η) coverage beyond these barrel and endcap detectors. 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 [40]. The first level, composed of specialized hardware processors, uses information from the calorimeters and muon detectors, while the high-level trigger consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing. 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. [41].

Event samples and simulation
The main SM backgrounds in this analysis are multijet events produced exclusively via quantum chromodynamics (QCD) interactions and top quark-antiquark pair production. Other sources of background include single top production and tt +X processes with X = (W, Z, γ, H, or tt), and also V+jets processes (V = Z or W), dibosons (WZ, ZZ, WW, VH), and tribosons. The latter group is denoted as the "Electroweak" background below.

Object reconstruction
Events are processed using the particle-flow (PF) [78] algorithm, which aims to reconstruct and identify all particles (PF candidates) using the optimal combination of information from the tracker, calorimeters, and muon systems of the CMS detector.
Electron candidates are identified by matching clusters of energy deposits in the electromagnetic calorimeter to reconstructed charged-particle trajectories in the tracker. A number of selection criteria based on the shower shape, track-cluster matching, and consistency between the cluster energy and track momentum are then applied for the identification of electrons [79]. Muons are reconstructed by requiring consistent hit patterns in the tracker and muon systems [80]. The relative isolation variable for an electron or muon candidate is defined as the scalar sum of the transverse momenta of all PF candidates in a cone around the candidates trajectory divided by the lepton p T . The cone size depends on the lepton p T . Hadronically decaying τ leptons of p T ≥ 20 GeV, within |η| = 2.3 are reconstructed using the hadron-plus-strip algorithm [81]. The corresponding isolation variable is computed using a multivariate approach, combining identification and isolation variables with lifetime information [81,82].
The primary jet collection is formed by clustering PF candidates using the anti-k T algorithm [83,84] with a distance parameter of 0.4. Jet energies are corrected for contributions coming from event pileup [85]. Additional corrections to the jet energy scale [86] are applied to compensate for nonuniform detector response. Jets are required to have p T > 40 GeV and be contained within the tracker volume of |η| < 2.4. For the resolved analysis, the p T requirement is relaxed to 30 GeV for subleading jets ranking seventh or lower in p T . In the boosted analysis an additional large-radius jet collection is defined using a distance parameter of 0.8.
Jets consistent with originating from the decay of a b quark are identified using the combined secondary vertex (CSV) b tagging algorithm [87], at the medium or loose working points. These are defined such that the efficiency to select light-flavor quarks (u, d, or s) or gluons as b jets is about 1 or 10%, and the corresponding efficiency for tagging jets from a b (c) quark decay is about 65 or 80% (10 or 25%), respectively. For brevity we refer to jets satisfying the b tagging criteria as b jets below.
The scalar p T sum of all selected jets in an event is denoted as H T , while the missing transverse momentum vector p miss T is defined as the projection onto the plane perpendicular to the beam axis of the negative vector sum of the momenta of all reconstructed PF candidates [88]. Its magnitude is referred to as p miss T . Quality requirements are applied to remove a small fraction of events in which detector effects, such as the electronic noise, can affect the p miss T reconstruction [88]. The energy scale and resolution corrections applied to jets are propagated to the calculation of H T and p miss T .

Search strategy
The analysis aims to reconstruct the full event in order to search for a local enhancement in the top and bottom quark-antiquark invariant mass spectrum.
Because of the large cross section for the QCD multijet background, restrictive trigger requirements are needed to reduce the data recording rate. The data used for this search are collected with an inclusive online selection of H trig T > 900 GeV, with H trig T being defined as the scalar p T sum of small-radius jets with p trig T > 30 GeV. Events are also acquired with a dedicated largeradius jet trigger requiring p trig T > 360 GeV and a mass after jet trimming [89] of at least 30 GeV. Furthermore, events satisfying trigger requirements of H Two analyses are performed, each targeting different regions of signal parameter space. The boosted analysis targets charged Higgs bosons with high mass and utilizes collimated hadronically decaying W boson or top quark candidates to distinguish signal events. A collection of large-radius jets is used to reconstruct and identify the objects from the decays of boosted W boson and top quark. In order to discriminate against QCD multijet backgrounds, we exploit both the reconstructed jet mass, which is required to be close to the W boson or top quark mass, and the two-or three-prong jet substructure (subjets) corresponding to the W → qq or t → qq b decay. The soft-drop algorithm [90] is used to remove soft and wide-angle radiation. The use of soft-drop grooming reduces the resulting jet mass m SD for QCD multijet events where large jet masses arise from soft-gluon radiation. The W (t) jet candidates are required to have 65 < m SD < 105 GeV (135 < m SD < 220 GeV), p T > 200 (400) GeV, and |η| < 2.4. The hard substructures are identified using the N-subjettiness [91] ratios: τ 2 /τ 1 < 0.6 for the W jet and τ 3 /τ 2 < 0.67 for the t jet. Finally, because top-quark jets contain a b quark and W jets do not, additional discrimination power is achieved by applying the CSV algorithm described above to the constituent subjets. The events are categorized according to the number of b-tagged jets to separate sources of SM background and capture signals with both high and low number of b quarks.
The resolved analysis is optimized for charged Higgs bosons with lower masses that decay to moderately boosted top quarks, often identified as three separate small cone jets, one of which is b tagged and the other two jets resulting from the W boson decay. The resolved top quark candidates (t res ) are identified using a multivariate boosted decision tree with gradient boost (BDTG) classifier. This is trained on simulated top quark-antiquark pair events using the TMVA package [92]. The classifier exploits properties of the top quark and its decay products such as masses, angular separations, and other kinematic distributions. Additional input variables are quark-gluon [93], charm vs. light quark [94], and b tagging discriminator values for each of the three jets. The signal enriched region is defined by requiring the presence of seven or more jets, comprising two resolved top quark candidates and an additional b-tagged jet used to reconstruct the H ± candidate.
Both analyses veto the presence of an isolated charged lepton (e or µ) with p T ≥ 10 GeV, or an isolated hadronically decaying tau lepton with p T ≥ 20 GeV. The lepton veto ensures that leptonic final states of W bosons produced in top quark decays are not considered. These are covered by dedicated analyses [21]. To further reduce the background from semileptonic tt decays, the boosted analysis requires events to have p miss T < 200 GeV. These requirements also reduce background from any sources containing W and Z boson decays.

Event categories in the boosted analysis
Events with at least one b-tagged jet and one identified top quark candidate are considered in the boosted analysis. The H ± candidate four-momentum vector is reconstructed as the sum of the four-vectors of the b jet with highest p T and the top quark candidate with mass most closely matching m top . A top quark candidate is identified as a t jet or the combination of a W jet and a b jet, excluding the b jet with highest p T . We introduce four mutually exclusive categories. The labels "t1b" and "t0b" refer to events containing a large-radius jet identified as a t jet, where at least one, or exactly zero, of the subjets satisfies the medium working point of the b tagging algorithm. In the "wbb" category the top quark candidate is formed from a W jet and an additional medium-tagged b jet. The "wbj" category relaxes the b tagging requirement on the additional jet to satisfy the loose b tagging working point.
The signal is characterized as a peak in the invariant mass distribution m tb of H ± candidates. This distribution is dominated by background contributions from QCD multijet processes. The expected shape of the H ± candidate mass distribution is dominated by the detector resolution and pairing errors, where jets are not correctly matched to the decay products of the boson. The full width at half maximum of the reconstructed MC mass distribution for correct jet assignments is used to describe the mass resolution, and events falling outside this window are used to constrain the background. The mass resolution for a charged Higgs boson of mass 1 TeV is approximately 140 GeV. The distribution of the invariant mass m tb for the t1b category is shown in Fig. 2 for the data, the expected background and for a signal of mass m H ± = 1 TeV. To enhance the expected signal to background ratio, data are selected within a window around different charged Higgs boson candidate masses in each of the categories listed above. We then   Figure 2: Data and SM background for the event sample with one t jet as a function of the charged Higgs boson candidate mass. The category t1b is shown and the background normalization is fixed to the SM expectation. The signal mass distributions for associated and schannel production of an H ± with m H ± = 1 TeV normalized with a cross section times branching fraction of 1 pbare superimposed as open histograms. The signal mass window "in" for associated production is shown together with the sidebands "below" and "above" for the mass hypothesis of 1 TeV.
search for an excess of events in the H T data distribution.
To better separate signal from background, the event categories are further subdivided to exploit differences in jet and b jet multiplicities. For signal events produced in association with a top quark, we expect at least three b quarks in the final state and a large number of extra jets not participating in the reconstruction of the H ± . Signal produced in the s channel contains two b quarks and fewer extra jets. We therefore consider different requirements on the number of b-tagged jets: exactly one, exactly two, and at least three. We also distinguish two categories based on the number of additional small-radius jets, less than three (N jets < 3) or at least three (N jets ≥ 3) such jets The signal-rich regions are analyzed together with signal-depleted regions using a binned maximum likelihood fit to the H T data distributions that simultaneously determines the contributions from signal and the major background sources.

Event selection in the resolved analysis
A multivariate analysis is employed to select top quark candidates in events containing seven or more jets. We employ a BDTG classifier that is trained using a simulated tt sample. The signal objects are considered to be three small-radius jet combinations, in which each individual jet is matched to the decay product of a top quark at the generator level. Similarly, background objects are defined as three-jet combinations in which at least one jet is not matched to a top quark decay product. The input variables used for the BDTG training (19 in total), calculated from these jet combinations, are described in detail in Ref. [95]. In the BDTG response distribution, values close to −1 are mainly populated by fake top quark candidates from QCD multijet processes, while values close to +1 are dominated by top quark candidates from tt or signal events. In this analysis we require resolved top quark candidates to have a BDTG score > 0.4, yielding a signal object efficiency of 92%, and a background object efficiency of 6%.
Events with at least three b-tagged jets passing the CSV medium working point and at least four additional jets are selected. The first top quark candidate is identified by pairing each btagged jet with all two-jet combinations and retaining the combination with the highest BDTG value. The same procedure is applied for the second candidate, using only the remaining jets as inputs. To reduce the combinatorial background, we require the combined three-jet system to have invariant mass less than 400 GeV.
The efficiency of the BDTG requirement as a function of the p T of the generated top quark in tt events is shown in Fig. 3 (left), along with the misidentification rate observed in a QCD multijet sample. At the plateau the tagging efficiency reaches 50%. The observed decrease in efficiency in the high-p T region is due to top quark decay products becoming increasingly collimated, resulting in a jet-to-parton matching inefficiency. The misidentification rate is less than 8% for the entire p T range considered.
To reconstruct the invariant mass of the H ± candidate, we use the resolved top quark candidate with the highest transverse momentum, p leading t res T , and the b-tagged jet having highest p T that is not used in the reconstruction of the two selected top quark candidates. The distribution of p leading t res T is shown in Fig. 3 (right). The invariant mass m tb of the H ± candidate is used in a binned maximum likelihood fit to extract the signal in the presence of the SM background.

Backgrounds
The dominant backgrounds arise from QCD multijet processes and top quark pair production in association with additional jets. Contributions from more rare processes, such as single top quark, tt +X, V+jets, diboson, and triboson production are found to be small.

Background estimations in events with boosted W boson and top quark candidates
We estimate the QCD multijet and top quark backgrounds using a method that exploits a number of background-rich control regions (CRs) in data. These control regions are included in a simultaneous fit with the signal enriched regions to determine the normalization and the shape of the background distributions.
Because the cross section for QCD multijet production is large, this background can produce many events satisfying the signal selection requirements. The distribution of m SD for signal peaks around the W boson or the top quark mass for large-radius jets corresponding to their hadronic decays, while the QCD multijet background spectrum is peaked at lower m SD . This background is estimated from simulation and corrected to match data using a CR enriched with jets arising from the hadronization of single quarks or gluons. The CR is defined by inverting the N-subjettiness requirements used to identify the t and W jets. The normalization is determined for each event category using sideband regions around the signal mass windows in the invariant mass spectrum of the top and bottom quark pair. We validate this correction by applying the technique in an orthogonal CR defined by requiring that no b-tagged jets are identified. The shapes of the N-subjettiness distributions and kinematics of jets having m SD consistent with either a t or W jet are found to be consistent with events passing the signal selection.
The contribution from the tt process arises from all-jet final states or states with a leptonic decay of a W boson where the charged lepton is outside the kinematic acceptance of the CMS detector or evades identification by the dedicated lepton vetoes. Such events contain a pair of b quarks and boosted W and t jets. The tt background is estimated from simulation and normalized using a control region in data. A lepton enriched set of events is used to describe the kinematics for the top quark pair production and the normalization is allowed to vary unconstrained in the final fit. The CR is defined by requiring a lepton (e, µ) with 10 < p T < 35 GeV, p miss T > 100 GeV and at least one b-tagged jet. This ensures orthogonality with the searches for charged Higgs bosons in the leptonic channels [21].

Background estimations in events with resolved top quarks
The main backgrounds for the resolved analysis can be decomposed into events containing either genuine b jets or events with at least one light quark or gluon jet erroneously tagged as a b jet. We refer to the latter as misidentified b jets. Background containing genuine b jets is modeled using simulation. The background due to misidentified b jets is measured with a datadriven technique using control regions that are defined by inverting the BDTG requirement, the b jet selection, or both.
The shape of the H ± candidate mass distribution in the background is obtained from events that are separated from the signal region (SR) by requiring that only two (of at least three) b jets pass the CSV medium working point, and the remaining jets only pass the loose CSV working point. This region is referred to as the application region (AR). In order to compensate for the different selection efficiencies between these two regions, transfer factors are used to normalize the AR to the SR. These transfer factors are determined by taking the ratio of events in two additional CRs that are orthogonal to each other and to both the AR and SR. The first CR, CR1, is obtained by requiring one t res candidate plus a second top quark candidate failing the BDTG requirement, and the second CR, CR2, is obtained by also altering the b jet selection as described above for the AR. In order to minimize the effect of kinematic differences between the loose and medium working points, the background from misidentified b jets is evaluated separately in p T and η bins of the b-tagged jet used in the reconstruction of the invariant mass of the H ± candidate.
Because the SR and associated CRs are mutually exclusive, the expected yield of misidentified b jet events passing the signal selections can be predicted as: where CR1(2) refers to the first (second) control region and the index i runs over all p T and η bins of the aforementioned leading in p T b-tagged jet.

Systematic uncertainties
The systematic uncertainties are divided into two categories: those that affect the estimation of the background from the SM processes, and those that affect the expected signal distributions and yields.
The events used in this search are largely collected with a trigger efficiency close to 100%. The trigger efficiency is extracted from data and the uncertainties in trigger correction factors applied to the simulation are less than 5%.
The uncertainty from pileup modeling is estimated by varying the total inelastic pp cross section of 69.2 mb by 5% [96]. The uncertainty in the integrated luminosity is estimated to be 2.5% [97].
Uncertainties in the background prediction that also affect the signal arise from the jet energy scale [98], from the scale factors correcting the efficiency and misidentification rate for b tagging [87], and from the reconstruction and identification efficiencies of the leptons. In addition, uncertainties arising from the simulation-to-data corrections for boosted t and W tagging and the BDTG response are applied in the boosted and resolved analyses, respectively. The variations in the jet selection and jet energy scale are propagated to the H T , p miss T , and H ± candidate yields and invariant mass.
For the boosted analysis a normalization uncertainty of 50% is applied for the QCD multijet background. This uncertainty is treated as uncorrelated among the boosted t-and W-tagged event categories and it is 100% correlated within each category and across the signal regions and the side bands. An additional uncertainty to account for shape variations in modeling the H T observable is parametrized linearly as a function of H T and reaches 30% for an H T of 1 TeV. These uncertainties are then constrained by studying the CR used to correct the simulation and the resulting variation in expected QCD multijet background yield is approximately 28%.
The systematic uncertainties affecting the misidentified b jet background measurement in the resolved analysis can be divided into three components. The first component consists of events containing jets from b quark decays that fail the b tagging requirement and is subtracted from the CRs used in the measurement. The uncertainty on the normalization of this component is estimated by propagating all the uncertainties related to the simulation of electroweak and top quark processes. The other two components account for the statistical and systematic uncertainties in determining the transfer factors applied in the normalization of the AR. Statistical fluctuations in the value of the transfer factors can result in rate and shape differences in the predicted invariant mass distribution. Similarly, the definition of the CR affects the individual transfer factors and subsequently the invariant mass shape in the AR. The aforementioned contributions affect the expected event yield by approximately 4%.
For tt and single top quark processes, the effect of the top quark mass on the cross sections is estimated by varying the top quark mass by ±1.0 GeV around the nominal value of 172.5 GeV. Uncertainties due to the choice of factorization and renormalization scales in the inclusive cross sections are estimated for each simulated process by varying the scales independently and together by factors of 0.5 and 2 with respect to the default values. The event yields are then calculated for each of the six variations and the maximum variation with respect to nominal is taken as the systematic uncertainty. The PDF uncertainties are treated as fully correlated for all processes that share the same dominant partons in the initial state of the matrix element calculations (i.e., gg, gq, or qq) [99].
Finally, the limited number of simulated background and signal events leads to statistical fluctuations in the nominal predictions. The effects are considered in the limit calculations using a Barlow-Beeston lite approach [100,101], which assigns the combined statistical uncertainty in each bin to the overall background yield in that bin.
Tables 1 and 2 summarize the various sources of systematic uncertainty and their impact on signal yield and the expected background in data, for the boosted and resolved analyses, respectively. Table 1: The systematic uncertainties affecting signal and background for the boosted analysis, evaluated after fitting to data, summed over all final states and categories. The numbers are given in percentage and describe the effect of each nuisance parameter on the overall normalization of each event category. Nuisance parameters with a check mark also affect the shape of the H T spectrum. Sources that do not apply in a given process are marked with dashes. For the H ± signal, the values for m H ± = 1 TeV and for associated production are shown.

Results and interpretation
The expected SM event yields from a background-only fit to the data are shown in Fig. 4 and Table 3 for the boosted and resolved analyses, respectively. For the boosted analysis, the background predictions are broken down into various categories of signal-and backgroundenriched regions and in total 98 distributions are fitted. The shape of the H T distribution in the boosted analysis and the invariant mass of the H ± in the resolved analysis are used to assess the agreement with the background-only hypothesis or the presence of the signal in a global binned maximum likelihood fit incorporating all the systematic uncertainties described in section 7 as nuisance parameters. The fitted distributions for the background only hypothesis are shown in Fig. 5 (left) for one category of the boosted analysis (t1b, 2b, N jets ≥ 3) and in Fig. 5 (right) for the resolved analysis. The contribution of a hypothetical charged Higgs boson with a mass of 0.8 or 1 TeV and σB = 1 pb, assuming the associated production mechanism, is also displayed.
The observed data agree with the predicted SM background processes. The results of the search are interpreted to set upper limits on the product of the charged Higgs boson production cross section and branching fraction into a top and bottom quark-antiquark pair. The upper limits are calculated at 95% confidence level (CL) using the CL s criterion [102,103]. An asymptotic approximation is applied for the test statistic [104,105], ln L µ /L max , where L max is the maximum likelihood determined by allowing all fitted parameters, including the signal strength, µ, to vary, and L µ is the maximum likelihood for a fixed signal strength. Results are shown for the associated production model in Fig. 6 (left). The reported limit at each mass value is determined by choosing the analysis strategy (resolved or boosted) with the best expected sensitivity. The data in the boosted analysis are also evaluated in the context of the s-channel model and the resulting limits are shown in Fig. 6 (right).
Exclusion limits are placed on the production cross section of the H ± associated with a top and a bottom quark, σ H ± t(b) B(H ± → tb) = σ pp→H + t (b) B(H + → tb ) + σ pp→H − t(b ) B(H − → tb), for masses from 0.2 to 3 TeV in the range 21.3 to 0.007 pb. The boosted analysis has the best sensi-    Fig. 2 for a H ± with mass 1 TeV in each of the signal categories used with the associated production model. The 11 categories on the left contain low jet multiplicity (N jets < 3), while categories on the right have high jet multiplicity (N jets ≥ 3). The yields observed in data (black markers) are overlaid. The dashed lines represent the yields for an H ± with a mass of 1 TeV and σB = 1 pb for associated production. The background distributions result from the global fit described in the text for the background-only hypothesis. Similar categories are fitted for the s-channel production.  Model-dependent upper limits are obtained by comparing the observed limit with theoretical predictions. The hMSSM benchmark scenario [106][107][108][109] assumes that the discovered Higgs boson is the light Higgs boson in the 2HDM and that the SUSY particles have masses too large to be directly observed at the LHC. The M 125 h ( χ) scenario [110] is characterized by significant mixing between higgsinos and gauginos, a compressed electroweakino mass spectrum, and with a phenomenology that resembles the Type-II 2HDM with MSSM-inspired Higgs couplings compatible with m h ≈ 125 GeV for large masses of the m A boson. Figure 7 shows the excluded parameter space in the MSSM scenarios. In the hMSSM scenario the maximum tan β value excluded is 0.88 for m H ± values between 0.20 and 0.55 TeV. In the M 125 h ( χ) scenario the maximum tan β value excluded is 0.86 for m H ± values between 0.20 and 0.57 TeV.

Combination with the leptonic final states
In Ref.
[21] a search is presented for an H ± with mass greater than the top quark and decaying into a top and bottom quark-antiquark pair in the complementary leptonic final states. Events are selected by the presence of a single isolated charged lepton (e or µ) or an opposite-sign dilepton pair (ee, µµ, eµ). These are categorized according to the jet multiplicity and number of b-tagged jets and multivariate techniques are used to enhance the signal and background discrimination in each category. The search is based on the same pp collision data collected by the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb −1 .
These results are combined with those from the all-jet channel analyses to calculate the 95% CL combined upper limits on the product of the cross section and the branching fraction as function of the m H ± for the process σ H ± t(b) B(H ± → tb). The limits are shown in Fig. 8 and Table 4. The common experimental and theoretical nuisance parameters between final states sharing the same production mechanism are correlated, while the uncertainties from different sources described in Section 7 are assumed to be uncorrelated. The single-lepton final state has the best sensitivity in the whole m H ± range from 0.2 to 3 TeV, while the dilepton channel contributes in the low m H ± regime, i.e., ≤ 1.5 TeV, and the all-jet channel improves the overall sensitivity by 20-25% at larger values of m H ± .

Summary
Results are presented from a search for charged Higgs bosons (H ± ) that decay to a top and a bottom quark in the all-jet final state. The search considers two distinct event topologies. The H ± is reconstructed from a b-tagged jet in combination with a top quark candidate, either resolved as two jets from qq decays of a W boson and an additional b-tagged jet, or, for highly boosted decay products, reconstructed as a single top-flavored jet or a W jet paired with an additional b-tagged jet. The analysis uses data collected with the CMS detector in 2016 at a center-of-mass energy of √ s = 13 TeV, corresponding to an integrated luminosity of 35.9 fb −1 . No significant deviation is observed above the expected standard model background. Modelindependent upper limits at 95% confidence level are set on the product of the H ± production cross section and branching fraction. For production in association with a top quark, limits of 21.3 to 0.007 pb are set for H ± masses in the range 0.2 to 3 TeV. Combining these results with data from a search in leptonic final states of W bosons sets improved limits of 9.25 to 0.005 pb. The complementary s-channel production of an H ± is investigated in the mass range 0.8 to 3 TeV and the corresponding upper limits are set at 4.5 to 0.023 pb. Exclusion regions are also presented in the parameter space of the minimal supersymmetric standard model hMSSM and M 125 h ( χ) benchmark scenarios.   [28] Belle-II Collaboration, "The Belle II physics book", (2018). arXiv:1808.10567.