Charged Higgs boson in the $W^\pm$ Higgs channel at the Large Hadron Collider

In light of the recent discovery of a neutral Higgs boson, $H_{\rm obs}$, with a mass near 125 GeV, we reassess the LHC discovery potential of a charged Higgs boson, $H^\pm$, in the $W^\pm H_{\rm obs}$ decay channel. This decay channel can be particularly important for a $H^\pm$ heavier than the top quark, when it is produced through the $pp \rightarrow tH^\pm$ process. The knowledge of the mass of $H_{\rm obs}$ provides an additional handle in the kinematic selection when reconstructing a Breit-Wigner resonance in the $H_{\rm obs} \rightarrow b\bar{b}$ decay channel. We consider some extensions of the Standard Model Higgs sector, with and without supersymmetry, and perform a dedicated signal-to-background analysis to test the scope of this channel for the LHC running at the design energy (14 TeV), for 300/fb (standard) and 3000/fb (high) integrated luminosities. We find that, while this channel does not show much promise for a supersymmetric $H^\pm$ state, significant portions of the parameter spaces of several two-Higgs doublet models are testable.


Introduction
A charged Higgs boson, H ± , is predicted in many models of new physics, with and without Supersymmetry (SUSY). The observation of a H ± at the Large Hadron Collider (LHC) is thus expected to provide concrete evidence of physics beyond the Standard Model (SM). The strategies for such searches depend on the mass, m H ± , of the charged Higgs boson. A H ± lighter than the top quark can be produced in t → H + b andt → H −b decays, where the top quarks are produced in pairs in qq annihilation and gg fusion (see [1] and references therein). When m H ± > m t − m b , bg → tH − and gg → tH −b are by far the dominant production processes. 1 As for the decays, H ± → τ ν 2 is the dominant mode as long as m H ± < m t + m b , beyond which H ± → tb becomes the leading decay channel with branching ratio (BR) approaching unity.
The Minimal Supersymmetric Standard Model (MSSM) is an example of a scenario predicting charged Higgs states. In fact, it contains a total of five physical Higgs states. Among the neutral ones are included two CP-even states, with the lighter one denoted by h and the heavier by H, a CPodd state, A, and there is also a charged pair H ± . The detection of an MSSM H ± lighter than the top quark is rather straightforward for a wide range of tan β (where tan β ≡ v 2 /v 1 , with v 1 and v 2 being the vacuum expectation values (VEVs) of the two Higgs doublet fields Φ 1 and Φ 2 ). H ± → τ ν is the dominant decay mode of such a H ± for all tan β. For m H ± > m t + m b , the large reducible and irreducible backgrounds make the search for H ± in the tb decay mode notoriously difficult [10] (see [11,12] for experimental simulations). However, some studies [13,14] concluded that the LHC discovery potential of a H ± state with mass 600 GeV is satisfactory in this decay channel, but only for very small, 1.5, or very large, 30, values of tan β. It has also been shown [15] that the H ± → τ ν decay mode can be used at the LHC even for 200 GeV < m H ± < 1 TeV provided tan β 3. In fact, if the distinctive τ -polarisation [16] is used, the H ± → τ ν channel can provide at least as good a heavy H ± signature as the H ± → tb decay mode (for the large tan β regime [17]).
At the LHC several searches have been carried out for H ± 's lighter as well as heavier than the top quark. The CMS collaboration has recently released exclusion limits [18] for a H ± lying in the 180 GeV -600 GeV mass range. That study assumes gg → tH −b production and H ± → tb and H ± → τ ν decay modes and is based on 19.7 fb −1 of data collected at √ s = 8 TeV. An earlier analysis [19] based on the same dataset provided exclusion limits in the H ± → τ ν decay channel for 80 GeV < m H ± < 160 GeV, assuming tt → H ± W ± bb production, and for 180 GeV < m H ± < 600 GeV, using the inclusive pp → tH − (b) production mode. The same production and decay modes have also been analysed by the ATLAS collaboration [20] based on 19.5 fb −1 of data at √ s = 8 TeV, providing exclusion limits for 80 GeV < m H ± < 160 GeV and 180 GeV < m H ± < 1 TeV. In an earlier ATLAS study [21] based on 4.7 fb −1 of data at √ s = 7 TeV, the H ± → cs decay channel has also been probed for H ± lying in the mass range 90 GeV -150 GeV. Note, however, that the two dominant decay channels mentioned above, i.e., tb and τ ν, leave the 1. 5 tan β 3 window virtually unexplorable for a H ± heavier than the top quark in the MSSM. Importantly, it is for such small values of tan β that the BR(H ± → W ± h) becomes sizeable, reaching the percent level. The detectability of a Supersymmetric H ± in the W ± h decay channel was studied in [22], where it was noted that a H ± with mass around 200 GeV could be detectable at the LHC with √ s = 14 TeV and L = 300 fb −1 , for tan β = 2−3. But there are two caveats. First, in these studies the mass of h was not fixed to the value eventually measured at the LHC. Second, such low values of tan β may at first glance appear to be excluded by the LEP2 Higgs boson searches [23], particularly for low m A ∼ 100 GeV. However, as discussed in [24], the LEP limit typically assumes a SUSY-breaking scale, M SUSY , in the vicinity of 1 TeV, which should be relaxed owing to the fact that SUSY remains undiscovered, implying a significantly higher breaking scale. Now, a realistic SUSY model ought to contain a Higgs boson, H obs , consistent with the one discovered at the LHC [25] and hence satisfying the 'observational constraint,' 122 GeV m H obs 128 GeV, which supersedes the LEP limit. The large allowed mass window is to take into account the theoretical uncertainties in the calculation of the H obs mass in the model. All such aspects clearly need to be re-assessed in light of the latest experimental results.
Besides the above observational constraint on the mass of the Higgs boson, the LHC measurements of its signal strengths in various production and decay channels also strongly constrain the parameter space of the MSSM wherein a H ± , potentially visible via the W ± H obs decay, can be obtained. In its singlet-extension, the Next-to-Minimal Supersymmetric Standard Model (NMSSM), the mass of the SM-like Higgs boson satisfying the mentioned mass constraint can be achieved in a more natural way, without requiring large radiative corrections from the stop sector. Such a Higgs boson, in fact, favours a lighter H ± , as we shall discuss in detail below. Moreover, in this model, which contains a total of 5 neutral Higgs states, the role of H obs can be played by the any of the two lightest CP-even Higgs bosons, H 1 or H 2 , alternatively [26].
If one leaves aside SUSY, one of the simplest non-trivial extensions of the SM is represented by a 2-Higgs doublet model (2HDM), which contains two Higgs doublets with different Yukawa assignments (see [27] for a review). Notably, this structure (albeit limited to one specific Yukawa configuration) is necessary in the MSSM, implying that the Higgs spectrum in a CP-conserving 2HDM is the same as in the MSSM, containing three neutral Higgs bosons and a charged pair. However, the absence of SUSY relations amongst the Higgs boson masses allows much more freedom to alternatively identify the discovered SM-like Higgs state with either of the two CP-even Higgs bosons of a 2HDM. Depending on the way the Higgs doublets are assigned charges under a Z 2 symmetry imposed in order to avoid large flavour-changing neutral currents (FCNCs), the 2HDMs are generally divided into four different types. In the 'aligned' 2HDM [28] (A2HDM), instead of the Z 2 symmetry, a Yukawa-alignment is enforced in order to prevent large FCNCs.
From the point of view of H ± searches, results obtained in the MSSM can be easily translated to the case of a 2HDM Type II, as long as SUSY states are very heavy, i.e., decoupled [29]. This is somewhat more involved in the case of the other three ordinary Types and the A2HDM, although still possible (see [30] and [31], respectively). Some dedicated analyses of the 2HDMs to constrain them using the latest data from the LHC have also been performed recently [32]. The key phenomenological difference in the 2HDMs from the SUSY models in general, and the MSSM and NMSSM in particular, is that there are no light SUSY particles to provide cancellations (induced by the different spin statistics between SM and SUSY states) in low energy observables, chiefly from flavour dynamics. It is in fact the latter (e.g., limits on the Z → bb and b → sγ decays) that generally produce severe constraints on the mass of H ± in the standard 2HDMs, pushing it to be larger than the top quark mass [33]. In the A2HDM, however, one can obtain m H ± < m t in a viable region of the parameter space [34].
In this article we analyse the possibility of establishing a H ± → W ± H obs signal in the next LHC run in all the models mentioned above, which are those where some relevance of such a decay has been established in the literature previously. We exploit the requirement on H obs to have a mass around 125 GeV, so that the m H ± range accessible via this signature starts at about 200 GeV and extends to nearly 500 GeV, as for heavier masses the tH ± production cross section becomes too low. We first discuss the consistency of the corresponding regions of the parameter spaces of these models with the current Higgs boson data from the LHC. We further assess the effects of imposing constraints from b-physics and, in the case of SUSY models, cold dark matter (DM) relic density measurements. We also carry out a model-independent detector-level analysis of the expected LHC sensitivity in the H ± → W ± H obs channel with √ s = 14 TeV. In doing so, we exploit the knowledge of the mass of H obs , which will result in a substantial improvement in the efficiency of previously advocated [22] kinematical selections for the extraction of the signature of concern here, which we use for guidance. We then compare the sensitivities expected for various integrated luminosities at the LHC with the cross sections obtainable for this channel in each model considered in the presence of the aforementioned experimental constraints. 3 It will be the interplay between the improved selection and the reduced parameter space available following the Higgs boson discovery (with respect to the setups assumed in earlier analyses of theH ± decay mode considered here) that will determine the actual situation at present. The article is organised as follows. In Sec. 2 we will discuss the production and decay mechanisms of the H ± considered in our analysis. In Sec. 3, we will discuss some salient features of the models analysed. In Sec. 4 we will provide some details of the scans of the parameter spaces of these models and of the experimental constraints imposed in our study. In Sec. 5 we will explain our signal-to-background analysis. In Sec. 6 we will present our results and in Sec. 7 our conclusions.

Production and decay of H ±
The dominant production process at the LHC for a H ± heavier than the top quark is its associated production with a single top, with the relevant subprocesses being bg → tH − and gg → tbH − (plus charge conjugated channels). The division between these two subprocesses is not clear-cut. The gg amplitude can be seen as a tree-level contribution to the NLO amplitude that includes a virtual b-quark, with the bg process making the LO amplitude. In the gg process we may view the b-quarks (the virtual b and the emitted b) as resulting from a splitting of the gluon and the corresponding amplitude contains the exact kinematics of this splitting. In the bg process the b-quark instead comes from the parton distribution of the proton. The b-quark is then a collinear parton arising from a splitting in the evolution of the pdfs. This contribution to the amplitude contains a collinear approximation of the kinematics and also a resummation of large logarithms in the factorisation scale that is not present in the gg amplitude. When calculating the cross section for pp → tH ± + X the bg and gg contributions to the amplitude cannot be added naively because that would result in double counting between the two contributions. There is a correct procedure to compute the total cross section [36], but it does not generalise to the differential cross section needed for Monte Carlo (MC) simulations. In Ref. [6] a method for event generation without double counting was introduced, and an add-on, called MATCHIG, to the event generator Pythia 6 [37] was constructed. In this framework events are generated both for the bg and gg processes and for the double-counting contribution. Events corresponding to the double counting have negative weights and should be subtracted from the positive weighted bg and gg processes. We have used MATCHIG in our simulations. 4 The process pp → tH ± + X has also been calculated at NLO and has been implemented [38] in the POWHEG BOX MC framework [39], which includes matching to parton showers. At NLO the bg and gg contributions are both part of the amplitude. It has also been implemented [40] in the MC@NLO framework [41]. In [38] it was shown that the MATCHIG program produces very similar kinematical distributions to the POWHEG implementation except at very large transverse momentum, p T > 200 GeV of the tH ± pair. The overall normalisation is, however, larger for the NLO calculations. The ratio between the total cross sections at NLO and LO depends on the model parameters via the mass spectrum, but for an example choice of 2HDMs it was found to be around a factor 2 for the Tevatron energies and a factor 1.4 for the LHC energies [38]. We do not consider this NLO enhancement of the signal in this paper for consistency, as we are only able to simulate the backgrounds at LO, but one should bear in mind that our quoted sensitivities may be somewhat stronger if NLO effects were systematically taken into account.
The spin/colour summed/averaged squared amplitude for the gb → tH − production process is given by [42] where g s and g 2 are the SU (3) C and SU (2) L gauge couplings, N C = 3 is the number of colours and V tb is the relevant CKM matrix element. See Refs. [14] and [43] for the gg → tH −b amplitudes and graphs. The total cross section is proportional to the coupling g 2 qH ± , as noted in the equation above, which is the only model dependent factor for a given m H ± . This factor depends on the masses, m t and m b , of the t and b quarks, respectively, as well as the parameter tan β, and will be discussed in the next section for each model considered here. As shown in [6], the total cross section for a charged Higgs mass above m t is actually well-approximated by the bg cross section. However, since the bg and the gg contributions lead to different kinematical distributions in the MC simulations, as noted above, we included both these contributions in our MC simulations.
Finally, as noted in the Introduction, this study aims to exploit the H ± → W ± H obs decay channel at the LHC. Of relevance for this particular process is the coupling of H ± to a generic neutral Higgs boson, H i , and the W boson, given by where S i1 and S i2 are the elements of the mixing matrix that diagonalises the CP-even Higgs mass matrix in the model. It is clear that this coupling depends strongly on tan β, both explicitly and through the elements S i1 and S i2 , (except in the A2HDM, as will be explained later) making the H ± → W ± H obs decay process highly sensitive to this parameter.

3
The models

Supersymmetric models
The Supersymmetric models considered here contain two Higgs doublets, Φ 1 and Φ 2 , which make the scalar components of the superfields H d and H u , respectively. The field Φ 1 is needed for generating the masses of the d-type quarks and leptons and Φ 2 those of the u-type quarks. The coupling of the charged Higgs boson to the quarks, defined in Eq. (1) as the factor g 2 qH ± , is given in these models as Thus the amplitude for the gb → tH − process is maximal for either small or large tan β.

• MSSM
The MSSM Superpotential, from which the scalar potential is derived, is given as where Q, U c R , D R , L and E R are the quark and lepton superfields and h u , h d and h e are the corresponding Yukawa couplings. In this model, the mass of H ± is given at LO as where m W is the mass of the W boson. In order to allow the H ± → W ± H obs decay, one requires m H ± > m H obs + m W , which translates into the requirement m A 190 GeV. In the MSSM, under such a condition, the tree-level mass of the SM-like Higgs boson, H SM , has an upper limit where m Z is the mass of the Z boson. Therefore, if the H SM is identified with the H obs and hence required to have a mass close to 125 GeV in accordance with the LHC measurement, a large value of tan β is necessary. Furthermore, the absence of any significant deviations of the signal strengths of the H obs from the SM expectations so far [44] seems to be pushing the MSSM towards the so-called 'decoupling regime'. This regime corresponds to m A 150 GeV for tan β 10 and yields SM-like couplings of the H SM , in addition to a maximal tree-level mass, as noted above. The net effect of all these observations is that a H ± with mass greater than 200 GeV and a H SM with the correct mass and SM-like couplings can be obtained simultaneously only for large tan β. However, according to Eqs. (2) and (3), tan β ∼ 10 not only diminishes the BR(H ± → W ± H SM ) but also the gb → tH − cross section. The complete MSSM contains more than 120 free parameters in addition to those of the SM. In its phenomenological version, the pMSSM, one assumes the matrices for the sfermion masses and for the trilinear scalar couplings to be diagonal, which reduces the parameter space of the model considerably. Here, since we are mainly concerned with the Higgs sector of the model, we further impose the following mSUGRA-inspired (where mSUGRA stands for minimal supergravity) universality conditions: where M Q 1,2,3 , M U 1,2,3 , M D 1,2,3 , M L 1,2,3 and M E 1,2,3 are the soft masses of the sfermions, M 1,2,3 those of the gauginos and A t,b,τ the soft trilinear couplings. This leaves us with a total of six free parameters, namely m 0 , m 1/2 , A 0 , m A , tan β and the Higgs-higgsino mass parameter µ.

• NMSSM
The NMSSM [45,46,47] (see, e.g., [48,49] for reviews) contains a singlet Higgs field in addition to the two doublet fields of the MSSM. The scale-invariant Superpotential of the NMSSM is written as where S is the additional Higgs singlet Superfield and λ and κ are dimensionless Yukawa couplings. The introduction of the new singlet field results in a total of five neutral Higgs mass eigenstates and a H ± pair, after rotating away the Goldstone bosons. In the NMSSM, the MSSM upper limit on the tree-level mass of the SM-like Higgs boson, given in Eq. (6), gets modified as where v ≡ v 2 1 + v 2 2 = 246 GeV, s is the VEV of the singlet field and A λ is the soft SUSY-breaking parameter corresponding to the coupling λ. Clearly, for large values of λ and small tan β, the second term in the above equation gives a significant positive contribution to the H SM mass.
The mass expression for H ± in the NMSSM is given as where m 2 A is, in contrast with the MSSM, the diagonal entry [M 2 A ] 11 of the pseudoscalar mass matrix M 2 A of the model, given by Again, for a given value of tan β, the negative third term in Eq. (10) results in a smaller m 2 H ± in the NMSSM compared to that in the MSSM, where it is given by the first two terms only. This negative contribution increases with the size of λ.
A crucial observation here is that a large λ, necessary to obtain sufficiently small m H ± , has the dual advantage of enhancing also the tree-level mass of H SM , as noted above. Such a scenario is therefore more natural than the one with a very MSSM-like H SM , since a much smaller amount of fine-tuning is required to achieve the correct Higgs boson mass via radiative corrections. But large λ also implies a substantial singlet component in H SM , which could result in significantly reducing its couplings to fermions and gauge bosons compared to those of the SM Higgs boson. However, recent studies [26] have shown that, for large λ and small tan β, the H SM of the model, which can correspond to either H 1 or H 2 , can still be consistent with the LHC Higgs boson data. The signal strength of H SM in the γγ decay channel in such a scenario can in fact be much larger than that of a SM-like Higgs boson, owing to a reduction in the BR(H SM → bb) compared to the true SM case. We point out here that, as in the MSSM, the H SM in the NMSSM will also be identified with H obs , since it is assumed to be the Higgs boson observed at the LHC.
The phenomenological version of the NMSSM that we study here contains three new parameters in addition to those of the pMSSM, mentioned earlier, with µ replaced by µ eff (≡ λs) and m A traded for A λ . These include λ, κ and A κ , the latter being a dimensionful coupling originating in the SUSY-breaking part of the Higgs potential.

2HDMs
A generic non-Supersymmetric 2HDM is defined by its scalar potential and its Yukawa couplings. The two Higgs doublets in such a model are written in terms of their VEVs and the physical Higgs states as where α is the mixing angle of the two CP-even Higgs bosons, tan β has been defined earlier and G and G + are the Goldstone bosons. The most general, CP-conserving potential for two Higgs doublets reads Through the minimisation conditions of the Higgs potential above, m 2 11 and m 2 22 can be traded for the VEVs v 1 and v 2 , respectively. Furthermore, the tree-level mass relations allow the quartic coupling λ 1−5 in Eq. (14) to be substituted by the four physical Higgs boson masses and the neutral sector mixing parameter sin(β − α). Thus, in contrast with the SUSY models, in the 2HDMs the masses of the Higgs bosons are free input parameters, along with λ 6 , λ 7 , m 2 12 , sin(β − α) and tan β. In the 2HDMs, the Yukawa couplings of the fermions are also a priori free parameters. However, depending on how the two Higgs doublets couple to the fermions, FCNCs can be mediated by scalars at the tree level. The requirement of no large FCNCs thus puts very strong restrictions on the coupling matrices. There are two general approaches for avoiding large FCNCs. One way is to impose a Z 2 symmetry so that each type of fermion only couples to one of the doublets ("natural flavour conservation") [50,51]. The same symmetry then holds also in the scalar potential (forcing λ 6 = λ 7 = 0), up to the soft breaking terms with parameter m 2 12 , thus further reducing the number of free parameters.
As noted in the Introduction, there are four ways of assigning the Z 2 charges, giving 2HDMs of Types I, II, X and Y. One defines as Type I the model where only the doublet Φ 2 couples to all fermions; Type II is the scenario similar to the MSSM, where Φ 2 couples to up-type quarks and Φ 1 couples to down-type quarks and leptons; in a Type X (or Type IV or 'lepton-specific') model Φ 2 couples to all quarks and Φ 1 couples to all leptons; and a Type Y (or Type III or 'flipped') model is built such that Φ 2 couples to up-type quarks and to leptons and Φ 1 couples to down-type quarks. The Type X and Type Y models have a similar phenomenology to Type I and II, respectively, especially in the context of this study. Specifically, g 2 qH ± is the same in the Type I and Type X models. Similarly, the Type Y model has a similar Yukawa structure, and consequently g 2 qH ± , as Type II, except for the leptons which couple to a different Higgs doublet in either of the two models. This, incidentally, implies that there is no tan β-enhancement in the Type Y model to affect the BR(H ± → τ ν). We therefore consider only the Type I and Type II models, referred to as 2HDM-I and 2HDM-II, respectively, which are the most well-known ones.
Another way to achieve small FCNCs without imposing natural flavour conservation is to postulate that the Yukawa coupling matrices of the two Higgs doublets are proportional to each other, i.e., they are aligned. This approach has been adopted in the aforementioned A2HDM [28], where both scalar doublets (Φ 1 and Φ 2 ) couple to all types of fermions. In the Z 2 -symmetric 2HDMs discussed above the Yukawa couplings are determined solely by the parameter tan β, while the CP-conserving A2HDM instead has separate parameters for the up-type quarks, the down-type quarks and the leptons, usually denoted by β U , β D and β L . In the A2HDM there is no specific basis singled out by the fermionic sector due to the absence of the Z 2 symmetry. For this study we choose the basis where only one doublet acquires a VEV, called the 'Higgs basis'. In this basis the input parameters include sin α (where α is the angle that diagonalises the CP-even Higgs-sector), λ 2 , λ 3 , λ 7 and the above-mentioned alignment angles β U,D,L , in addition to the physical Higgs boson masses.
The expressions for g 2 qH ± in Eq. (1) for the different 2HDMs (including the A2HDM) are given in Table 1. It should be noted that g 2 qH ± in the 2HDM-II is identical to the one in the SUSY models.

Model scans and experimental constraints
We have performed scans of the parameter spaces of all the models considered here, requiring m H ± to lie in the 200 GeV -500 GeV range. For each scenario except the MSSM, we carried out two separate scans for the cases with H 1 and H 2 alternatively playing the role of H obs , i.e., having mass near 125 GeV and SM-like signal rates in the γγ and ZZ decay channels. We point out here that in the MSSM it is not possible to obtain a H with a mass around 125 GeV while also requiring m H ± 200 GeV, as their masses lie very close to each other by theoretical construction. In the case of the SUSY models, since the masses of the scalar Higgs bosons are derived and not input parameters, we used the nested sampling package MultiNest-v2.18 [52] for efficiently scanning their parameter spaces.
The mass spectra and Higgs boson decay BRs for each scanned point of the MSSM, the NMSSM and the 2HDMs were computed using the public packages SUSY-HIT-v1.3 [53], NMSSMTools-v4.2.1 [54] and 2HDMC [55], respectively. For a point to be accepted in a given scan, it had to pass the condition 122 GeV ≤ m H obs ≤ 128 GeV for the SUSY models and 123 GeV ≤ m H obs ≤ 127 GeV in the 2HDMs. This is to take into account the experimental as well theoretical uncertainties (which are understandably larger in the presence of SUSY) in m H obs predicted in the two scenarios. As for the b-physics observables, the points for which their theoretically evaluated values did not lie in the following ranges were rejected during the scans for the NMSSM and the A2HDM.
These 95% confidence level ranges are the ones suggested in the manual of the package SuperIso-v3.4 [56], which was used for the theoretical evaluation of these observables. Additionally, the scan points were also required to satisfy the constraint ∆M B d = (0.507 ± 0.004) ps −1 , which is based on [57]. In the case of the Z 2 -symmetric 2HDMs, their parameter spaces consistent with the b-physics constraints were adopted directly from [57], so that these constraints were not tested against during the scans. Moreover, for SUSY models the (lightest) neutralino DM relic density was calculated for every point using the package MicrOMEGAs-v2.4.5 [58]. Only points with Ω χ h 2 < 0.131, assuming a +10% theoretical error on the central value of 0.119 measured by the PLANCK collaboration [59], were retained.
Finally, we used the public package HiggsBounds-v4.1.3 [60] to test the neutral Higgs bosons other than the H obs in a given case for each model against the exclusion limits from the Large Electron-Positron (LEP) collider, the Tevatron and the LHC. This program also takes care of the exclusion constraints on H ± from the various LHC searches mentioned in the Introduction. Finally, the magnitude of a possible Higgs boson signal at the LHC is characterised by the signal strength modifier, defined as where X denotes the decay channel under consideration and h SM denotes a 125 GeV SM Higgs boson. The theoretical counterparts of µ X , which we refer to as R X here, were obtained from the program HiggsSignals-v1.20 [61] for X = γγ, ZZ. 5 In our analysis below, while we will show all the good points from our scans, we will highlight the points for which R γγ,ZZ are consistent with the measured µ γγ,ZZ at the LHC. The latest publicly available measurements read µ γγ = 1.13 ± 0.24 and µ ZZ = 1.0 ± 0.29 (16) at CMS [62] and µ γγ = 1.57 +0.33 −0.28 and µ ZZ = 1.44 +0.40 −0.35 (17) at ATLAS [63]. 6

Signal and background analysis
In addition to constraining the parameter spaces of the new physics models, knowledge of the mass of H obs also provides an additional handle in identifying the H ± → W ± H obs decay. We focus here on the decay H obs → bb, as it generally has a substantial BR and allows for a full reconstruction of H obs . 7 In particular, we look for the production channel pp → t(b)H ± → W ∓ b(b)W ± H obs , which, after semi-leptonic decays of the two W bosons and H obs → bb, gives a final state of bbb(b)jjℓν ℓ . The main background for this process is tt production, and here we consider all processes pp → t(b)W ± bb, where the extra pair of b-quarks can come from the emission of a gluon, a Higgs boson, or a Z. In this section we describe our method for reconstructing the H ± signal and separating it from the background events to give an estimate of the sensitivities that could be achieved at the 14 TeV LHC. We generate the hard process for the signal using the MATCHIG package [6] with Pythia 6.4.28 [37], thus including the bg and gg contributions and subtracting the correct double-counting term to get proper b-jet momentum distributions. MadGraph5 aMC@NLO [65] is used to generate the backgrounds. Parton showers and hadronisation for both signal and background are performed with Pythia 8 [66], followed by detector simulation with DELPHES 3 [67] using experimental parameters calibrated to the ATLAS experiment with modified b-tagging efficiencies. 8 For reconstruction and background reduction, we roughly follow the procedures of previous analyses [22], with the addition of a top veto (described below) to further suppress the background. 3. Reconstruct a leptonically decaying W using the lepton and the missing energy, by assuming that the missing energy comes entirely from the single neutrino and imposing the invariant mass constraint m ℓν = m W . Because this is a quadratic constraint, there is a two-fold ambiguity in the solution for the longitudinal momentum of the neutrino. If the solutions are real, both are kept, and if they are complex, the real part is kept as a single solution.
4. Apply top veto for high mass searches ("veto first").  which are able to pass our requirement of providing an SM-like Higgs candidate do so by combining a b-jet coming from a top decay with another b-tagged jet, so the background will be most reduced if a top veto is applied before the Higgs reconstruction, Veto first: Using reconstructed W 's and all remaining jets, veto event if two top quarks can be reconstructed, both with |m W j − m t | ≤ 20 GeV.

Find a Higgs boson
We also wish to avoid unnecessarily cutting signal events. When a charged Higgs boson with m H ± ≥ m t undergoes the decay H ± → W ± H obs → W ± bb, it is kinematically possible for one of the b-jets from the H obs decay to combine with the W to give an invariant mass close to the top mass. Indeed, this effect occurs in large regions of the available phase space for charged Higgs bosons with masses just above the threshold for W ± H obs decays. In this case, we wish to identify the bb pair from the H obs decay before applying a top veto, Veto second: After identifying two b-jets which reconstruct H obs , using reconstructed W s and all remaining jets, veto event if two top quarks can be reconstructed, both with |m W j − m t | ≤ 20 GeV. Fig. 1(a) and (b) show the signal and background m W H obs distributions for m H ± = 220, 300, 400 GeV and the two types of top veto. The "veto first" scenario clearly reduces the background more effectively, but at the expense of a reduced signal. However, for larger m H ± , the signal is less likely to fake an additional top, so there is less difference between the two vetoes in the higher mass signal distributions. It is also clear from Fig. 1 that the H ± resonance can be reconstructed well enough to further separate it from the background. For each mass, we select a window in the reconstructed m W H obs range which maximises the statistical significance S/ √ B of the signal. 9 We additionally choose the top veto which maximises S/ √ B for each mass, and find that "veto second" is most effective at lower masses, m H ± 350 GeV, whereas "veto first" is preferable above this mass range. 10 In Fig. 2 we show how this signal and background translate into sensitivities at the 14 TeV LHC for different values of the product σ(pp → tH ± ) × BR(H ± → W ± H obs ) × BR(H obs → bb), which we henceforth refer to as the signal cross section. We see that we can probe σ × BR ∼ O(100 fb) with an integrated luminosity of 300 fb −1 , but require higher luminosities to see O(10 fb) signals. These sensitivities can be compared to the model-dependent cross sections and BRs in various scenarios, which we discuss in the following section.
6 Results and discussion 6.1 MSSM In Fig. 3(a) we show the mass of h as a function of m H ± in the MSSM, with the heat map corresponding to tan β. The ranges of the MSSM input parameters scanned to obtain these points are shown in Table 2(a). One sees in the figure that for the selected m H ± range, m H SM lying between 122 GeV -128 GeV can only be obtained for tan β 6. As noted earlier, such intermediate values of tan β bring down not only the pp → tH ± cross section but also the BR(H ± → W ± H obs ). The product of these two quantities, only for points in the narrow strip corresponding to m H SM > 122 GeV and consequently to highest allowed tan β in Fig. 3(a), is shown in Fig. 3(b). This product hardly exceeds 4 fb, and that too only for points very close to the lower limit imposed on m H SM . The heat map in the figure shows the BR(H obs → bb), which grows as the H obs becomes more and more SM-like due to falling m A , and hence m H ± , given the intermediate value of tan β.

NMSSM
Our initial scans for the NMSSM covered very wide ranges of the nine input parameters mentioned in Sec. 3. These scans revealed only a small region of the NMSSM-specific parameters where m H obs and m H ± both lied within the desired ranges. Two subsequent scans of this narrow region, for the MSSM parameter Range m 0 (GeV) 500 -4000 100 -500 tan β 1 -6 NMSSM parameter Range m 0 (GeV) 500 -3000 cases with H obs = H 1 and with H obs = H 2 each, yielded a much larger density of interesting points. The corresponding parameter ranges are given in Table 2(b). In Fig. 4(a) we show the BR(H ± → W ± H obs ) as a function of m H ± for the points obtained in the scan requiring H 1 to be the H obs . In Fig. 4(b) the corresponding points for the case with H obs = H 2 are shown. The heat maps in the two figures show the distribution of the σ(pp → tH ± ). We see in the figures that while the BR(H ± → W ± H obs ) in the H 1 = H obs (H 2 = H obs ) case can reach up to ∼ 23% (∼ 28%), its maximum reachable value drops slowly with decreasing m H ± and, in fact, for m H ± < 250 GeV it falls below 5%. This behaviour of the BR(H ± → W ± H obs ) is thus in conflict with that of the σ(pp → tH ± ), which clearly rises with decreasing m H ± and is in fact maximal for points with the lowest BR(H ± → W ± H obs ) observed.
In Fig. 5(a) we show the signal cross section for the case with H obs = H 1 . The points in green are the ones fulfilling only the b-physics constraints and we note for these points that, as a result of the tension between the BR(H ± → W ± H obs ) and the σ(pp → tH ± ), the total cross section barely exceeds 10 fb. The points in red and blue in the figure are the ones for which R γγ/ZZ are consistent with the CMS and ATLAS ranges of µ γγ/ZZ , respectively. Evidently, imposing these constraints further reduces the maximum signal cross section obtainable to below 5 fb. For the case with H obs = H 2 the signal cross section, shown in Fig. 5(b), can reach slightly higher to around 20 pb, for the green points. This is owing to the somewhat larger BR(H ± → W ± H obs ) obtainable for low m H ± in this case compared to the H obs = H 1 case. However, again the overall signal cross section is highly diminished for points observing the ATLAS or CMS signal rate constraints. Also shown in the Figs. 5(a) and (b) are the 2σ (exclusion), 3σ (evidence) and 5σ (discovery) sensitivity curves for 3000 fb −1 accumulated luminosity at the LHC 14 TeV run. All the good points from the scans lie well below the lowest (2σ) curve, implying that none of them has a signal cross section large enough to be testable even at such a high luminosity.

2HDM Types I and II
The scanned ranges of the parameters in these two models are shown in Table 3. Note that in the 2HDM-II, m H ± 320 GeV is excluded for all values of tan β by the constraint on BR B → X s γ , while tan β 1.5 is ruled out for m H ± up to 500 GeV or so by the ∆M B d constraint, according to [57]. We therefore reduced the input range of m H ± instead of imposing these constraints during   the scans for this model. The BR(H ± → W ± H obs ) for 2HDM-I with the H obs = h case, shown in Fig. 6(a), can be as high as ∼ 95% for a fairly large number of points. Moreover, compared to the NMSSM, while the maximum σ(pp → tH ± ) reachable is much lower here, the BR(H ± → W ± H obs ) grows much more sharply with increasing m H ± . As a result, there are plenty of low m H ± points where both the BR(H ± → W ± H obs ) as well as the σ(pp → tH ± ), shown by the heat map, can be significant. In Fig. 6(b) are shown the corresponding quantities for the H obs = H case in the 2HDM-I. In this case a very large BR(H ± → W ± H obs ) is obtainable for a comparatively much smaller number of points and it mostly stays below 40%.
In Fig. 7(a)  135 -500 320 -500 tan β  generally obtainable in this model compared to the NMSSM, the total cross section can reach as high as about 100 fb. A small portion of the green points with m H ± > 400 GeV lies above the 2σ sensitivity curve corresponding to L = 300 fb −1 and should thus be reachable at the LHC. The picture, however, becomes grim when the LHC signal rate constraints are imposed. Points consistent with the CMS constraints have a maximum possible cross section of around 20 fb, while none of the points obtained in the scans are able to satisfy the ATLAS constraints.
Turning to the 2HDM-II, for the H obs = h case one sees in Fig. 8(a) that in this model both the BR(H ± → W ± H obs ) and the σ(pp → tH ± ) show a similar behaviour as noted in the 2HDM-I above, being significantly large simultaneously for a number of points with m H ± up to ∼ 400 GeV. The maximum obtainable values of both these quantities are also similar to those in the 2HDM-I. In the H obs = H case the BR(H ± → W ± H obs ) struggles to reach high values generally and in fact stays close to 0 for a vast majority of the points, as seen in Fig. 8(b). In Figs. 9(a) and (b) we show the signal cross sections for the H obs = h and H obs = H cases, respectively, in the 2HDM-II. In the former case, not only do a large number of points observing only the b-physics constraints lie above the 5σ sensitivity curve for L = 3000 fb −1 , but also some of the points consistent with the CMS constraints can have a signal cross section in excess of 30 fb and should thus be accessible at the  LHC. In the H obs = H case, however, the maximum reachable cross section for points consistent with the CMS and ATLAS signal rate constraints barely exceeds 10 fb and 1.5 fb, respectively, only when m H ± is below 350 GeV or so.

A2HDM
The scanned ranges of the A2HDM parameters are given in Table 4 and have been adopted from [69]. In Fig. 10(a) we show the BR(H ± → W ± H obs ) for the H obs = h case, which can reach unity over the entire desired mass range of H ± . Also, the σ(pp → tH ± ), illustrated by the heat map in the figure, can reach the pb level, but it is maximal only for points for which the BR(H ± → W ± H obs ) is relatively small, 40%. On the other hand, Fig. 10(b) shows that in the H obs = H case the BR(H ± → W ± H obs ) mostly stays below ∼ 35%.    Table 4: Ranges of the input parameters scanned for the A2HDM.
In Fig. 11(a) the signal cross section for the H obs = h case is shown. This cross section can reach much higher, ∼ 700 fb, than in the ordinary 2HDMs, when the constraints from the LHC Higgs boson searches are not imposed. Points with such a high cross section lie above even the 5σ sensitivity curve for the LHC with L = 300 fb −1 . This implies that the H ± in this model could be discoverable at the standard luminosity LHC over almost the entire mass range analysed for this channel. However, as in the other models above, points satisfying the LHC constraints have a much smaller signal cross section generally. Still, unlike in any of the other models considered here, a small number of points consistent with the CMS constraints lies above the 5σ sensitivity curve for L = 3000 fb −1 and could thus be visible at the high luminosity LHC. The same is not true though for the H obs = H case, seen in Fig. 11(b), where only a couple of points consistent with the CMS constraints appear to be testable at the high luminosity LHC.

Conclusions
In this article we have analysed the detectability of H ± in the W H obs decay mode in some minimal extensions of the SM, at the upcoming Run 2 of the LHC with √ s = 14 TeV. We have discussed some important features of the models of our interest, in particular the coupling parameters governing the production of H ± in pp collisions as well as the H ± → W H obs decay process. We have performed dedicated scans of the parameter spaces of these models to search for their regions where a H ± with a mass lying in the 200 GeV -500 GeV range can be obtained and its production cross section can be maximised. These scans were subject to the most relevant constraints from b-physics, from the LHC Higgs boson searches and, in the case of SUSY models, from relic density measurements. Moreover, in the NMSSM as well as in the 2HDMs we considered both the possibilities of the observed Higgs boson being the lightest or the next-to-lightest CP-even scalar of the model.
We then reconstructed the signal and the background in the bbb(b)jjℓν ℓ final state and, through a dedicated detector-level analysis, estimated the signal significance for various accumulated luminosities at the LHC. We found that, through a judicious choice of selection criteria, including a veto on tt events and the requirement of a reconstructed 125 GeV Higgs boson from a pair of b-tagged jets, we were able to significantly reduce the backgrounds. The semi-leptonic channel provides enough kinematic information to reconstruct the m H ± peak and identify signals with σ(pp → tH ± ) × BR(H ± → W ± H obs ) × BR(H obs → bb) ∼ O(100 fb) with an integrated luminosity of 300 fb −1 , with even better sensitivity at high luminosities.
We have concluded that in the SUSY models studied here, the H ± → W H obs decay channel does not carry as much promise for the identification of a H ± as has been envisaged in some earlier studies. This is due to the fact that the pp → H ± production process and the subsequent H ± → W H obs decay process generally show contrasting dependence on the various parameters involved. The situation looks a bit better in the Z 2 -symmetric 2HDMs, as long as the constraints from the LHC measurements of the Higgs boson signal rates are ignored. Imposing these constraints leaves an insignificant number of points in the 2HDM-II visible at only the high luminosity (∼ 3000 fb −1 ) LHC, implying that the Higgs boson assumed to be the one observed at the LHC in these scenarios deviates substantially from SM-like properties. In the case of the A2HDM, a fairly large portion of the parameter space could in general be tested even at the standard luminosity (∼ 300 fb −1 ) LHC. However, again if the measurements of the observed Higgs boson signal rates do not fluctuate much from the current ones, only a few parameter space points lie within the reach of the LHC at this luminosity.