The forgotten channels: charged Higgs boson decays to a $W^\pm$ and a non-SM-like Higgs boson

The presence of charged Higgs bosons is a generic prediction of multiplet extensions of the Standard Model (SM) Higgs sector. Focusing on the Two-Higgs-Doublet-Model (2HDM), we discuss the charged Higgs boson collider phenomenology in the theoretically and experimentally viable parameter space. While almost all existing experimental searches at the LHC target the fermionic decays of charged Higgs bosons, we point out that the bosonic decay channels -- especially the decay into a non-SM-like Higgs boson and a $W$ boson -- often dominate over the fermionic channels. Moreover, we revisit two genuine BSM effects on the properties of the discovered Higgs boson -- the charged Higgs contribution to the diphoton rate and the Higgs decay to two light Higgs bosons -- and their implication for the charged Higgs boson phenomenology. As main result of the present paper, we propose five two-dimensional benchmark scenarios with distinct phenomenological features in order to facilitate the design of dedicated LHC searches for charged Higgs bosons decaying into a $W$ boson and a light, non-SM-like Higgs boson.


Introduction
The discovery of a Higgs boson at the LHC in 2012 [1,2] has initiated the survey of the scalar sector and the concomitant mechanism of spontaneous electroweak (EW) symmetry breaking. The Higgs boson -predicted in the Standard Model (SM) to be a fundamental scalar boson h originating from a complex scalar SU(2) L doublet field with hypercharge Y = + 1 2 and vacuum expectation value (vev) v ≈ 246 GeV -is the first of its kind, and the thorough investigation of its properties is of paramount importance for the understanding of particle physics. To this end, the LHC collaborations perform detailed measurements of the signal rates of the discovered Higgs boson in various production and decay modes, from which (under certain model assumptions) the strengths of the Higgs-boson couplings to the W and Z-bosons and to the third generation fermions can be inferred. 1 By the end of Run-2 of the LHC, with ∼ 140 fb −1 of data each collected by the ATLAS and CMS experiment, the Higgs-boson rate measurements agree remarkably well with the predictions in the Standard Model (SM). Yet, with the currently achieved precision of O(10 %) in the coupling determination [4][5][6][7], it is far from certain that the scalar sector as predicted in the SM is realized in nature.
Indeed, there are many reasons to anticipate effects from beyond the SM (BSM) physics in the scalar sector. The Higgs field may interact with the dark matter (DM) sector through so-called Higgs portal interactions, or DM itself may be composed of a stable scalar particle that originates from an extension of the SM Higgs sector (see Ref. [8] for a recent review). Furthermore, a BSM scalar sector may lead to a strong first-order EW phase transition and feature new sources of CP-violation -these may enable the successful generation of the baryon asymmetry observed in the Universe (see e.g. [9][10][11][12][13][14] for recent works). BSM theories addressing the hierarchy problem, e.g. Supersymmetry (SUSY) [15][16][17][18], often modify or extend the scalar sector. Lastly, one may wonder why the scalar sector should be minimal, while we clearly have a non-minimal matter sector with three generations of fermions.
In many BSM extensions of the scalar sector, the discovered Higgs state h 125 can acquire tree-level couplings to fermions and gauge bosons identical to those predicted in the SM in the so-called alignment limit [19][20][21][22]. In this limit the physical Higgs state h 125 is aligned in field space with the direction of the vacuum expectation value v. The current LHC Higgs signal rate measurements imply that this alignment limit is at least approximately realized. However, the origin of this alignment -whether it is dynamical, by symmetry, or accidental -is unknown, and is obviously model-dependent. 2 Given the experimental observations in the Higgs signal rates, any phenomenologically viable BSM model therefore has to contain a Higgs boson with a mass around 125 GeV that is approximately "SM-like" in its coupling properties, as achieved near the alignment limit.
Extending the scalar sector also introduces additional scalar particles that could be either neutral or carry electromagnetic charge. Detecting these new states complements the precision studies of the discovered Higgs state in the quest of unraveling the details of the electroweak symmetry breaking mechanism. To this end, the ATLAS and CMS collaborations have performed searches for the direct production and decay of additional (electrically neutral and charged) Higgs bosons. The targeted collider signatures are often guided by popular BSM theories, e.g. the Minimal Supersymmetric Standard Model (MSSM), and predicted to be experimentally accessible with current detector capabilities and the current amount of accumulated data. Other experimental BSM searches look for decays of known particles (e.g. the discovered Higgs boson h 125 ) into BSM particles. A prominent example are searches for an invisibly decaying Higgs boson (see e.g. Ref. [31] and references therein). However, all these searches have not found any convincing hints for the existence of new particles yet, and have thus only produced upper limits on their possible signal cross section. Both experimental results -the Higgs-boson signal rate and mass 3 measurements and the upper limits from searches for additional Higgs bosons -give rise to important constraints on the parameters of BSM models. At the same time, they challenge the theoretical community to provide reasonable explanations for the absence of hints for BSM physics at the LHC, and to give guidance for future strategies to remedy this situation. Given the prospect of an LHC upgrade to the high-luminosity (HL) phase, with an anticipated 3 ab −1 of data per experiment, as well as recent and upcoming advances in data analysis techniques (see e.g. Refs. [33][34][35][36][37][38][39]), so-far disregarded collider signatures of additional Higgs bosons (re)gain attention (see e.g. Refs. [27,[40][41][42][43][44][45][46][47][48][49] for recent proposals).
In this work we focus on collider signatures that arise from the production of a charged Higgs boson H ± and its successive decay to a lighter neutral Higgs boson and a W boson. While this decay mode has been investigated in several phenomenological works [25,27,[50][51][52][53][54][55][56][57][58][59][60], up to now the signatures arising from this process have not been actively searched for by the LHC experiments 4 -with the notable exception of Ref. [65]. 5 Confirming earlier works we shall show in the present paper that these decays occur at sizable rates quite naturally already in minimal models that contain a charged Higgs boson, namely Two-Higgs-Doublet Models (2HDM), and, therefore, need to be explored experimentally. The purpose of this work is to motivate and initiate dedicated experimental searches by exploring the possible signal rates and providing suitable benchmark models for these studies based on the 2HDM of type-I and the lepton-specific 2HDM. We base our benchmark model definitions on the latest experimental constraints and state-of-the-art 3 The Higgs boson mass has been determined to 125.09 ± 0.21(stat) ± 0.11(syst)GeV in the combined ATLAS and CMS analysis of LHC Run-1 data [32]. 4 A possible explanation for this omission is that LHC searches for charged Higgs bosons were everso-often guided and motivated by the expectations within the MSSM Higgs sector. While MSSM parameter regions exist where the charged Higgs boson dominantly decays to a neutral Higgs and a W boson -e.g. the H ± → W ± h decays in the M 125 H scenario of Ref. [27] -these decays are absent in most of the parameter space due to an approximate mass degeneracy of the BSM Higgs bosons [19,[61][62][63][64]. 5 The CMS collaboration has searched for the process pp → H ± tb, H ± → W ± A, with the light pseudoscalar boson A decaying to µ + µ − , using 35.9 fb −1 of Run-2 data [65]. model predictions. This paper is organized as follows. We first review the coupling properties of charged Higgs bosons in multi-Higgs-doublet models in Section 2, and then discuss the charged Higgs boson phenomenology in the Two-Higgs-Doublet-Model (2HDM) in light of current experimental and theoretical constraints. In Section 3 we revisit two important BSM effects on the discovered Higgs boson h 125 that subsist even in case of exact alignmentthe charged Higgs contribution to the Higgs-to-diphoton rate and the neutral Higgs (h 125 ) decay to two lighter neutral Higgs bosons -and their implications on the charged Higgs boson phenomenology. We discuss the most relevant charged Higgs boson production and decay modes, as well as the current LHC searches in Section 4. We then elaborate on the experimentally unexplored charged Higgs boson signatures in Section 5 and present several benchmark scenarios for future searches for these signatures. We conclude in Section 6.

Charged Higgs boson phenomenology in doublet extensions of the SM
In this section we will first review the coupling structure of charged Higgs bosons in the general N -Higgs-Doublet model. 6 Afterwards, we will focus on the 2HDM. and fulfill the sum rules (see e.g. [67]) where the sum runs over all neutral Higgs bosons and h SM is a state with exactly SM-like couplings. 7 Furthermore, gauge invariance requires such that where V = W, Z.
We define the charged Higgs boson couplings to a neutral CP-even or CP-odd Higgs bosonh j and a j , respectively -and the W boson via They obey sum rules for any j where the sum runs over all charged Higgs bosons (excluding the charged Goldstone boson). This sum-rule structure leads to important correlations between constraints on the couplings c(h j V V ) and the couplings g(H ± i W ∓ h j ). In particular, in the alignment limit where one of the neutral CP-even Higgs bosons is SM-like, h j = h SM , these correlations In turn, the remaining neutral Higgs bosons h i (i = j) will have rather large couplings to the charged Higgs bosons and the W boson. In the special case of the CP-conserving Two-Higgs-Doublet Model (2HDM), which contains only two CP-even neutral Higgs bosons and a single pair of charged Higgs bosons, this implies that the coupling between the charged Higgs boson, the non-SM-like CP-even Higgs boson and the W boson is maximal in the alignment limit. We will discuss this case in more detail in Section 2.2.
Phenomenologically, these correlations have very important implications for collider searches for charged and neutral Higgs bosons. In particular, if there is a sizable difference between a charged Higgs boson mass, m H ± i , and the mass of a neutral, non-SM-like Higgs bosons, m h j , the decay modes and can have sizable rates that potentially dominate and, in turn, suppress the Higgs decay modes to SM fermions and gauge bosons. We shall focus on the first case, Eq. (14), in this work.

The Two Higgs Doublet Model
The two Higgs doublet model (2HDM) (see Refs. [61,68] for reviews) is the simplest extension of the SM containing a charged Higgs state H ± , as it adds one additional Higgs doublet to the SM. In the present work, we focus on the most commonly studied version: the CP-conserving 2HDM with a softly broken Z 2 symmetry. Its scalar potential is given by with the scalar doublets It is useful to rotate to the Higgs basis (see e.g. [19]), where we introduced the abbreviations s γ ≡ sin γ and c γ ≡ cos γ for a generic angle γ. The angle β is defined via the ratio of the vacuum expectation values (vevs), t β ≡ tan β = v 2 /v 1 . In this basis, only H 1 receives a vev.
In the Higgs basis the charged Higgs field H ± and the CP-odd scalar field A are automatically mass eigenstates. To obtain the mass eigenstates h 1 and h 2 of the CPeven scalars -whose masses fulfill, by definition, m h 1 ≤ m h 2 -a further rotation is necessary, where h HB 1,2 are the CP-even scalars in the Higgs basis and α is the rotation angle relating the fields φ i of Eq. (17) to the mass eigenstates (see e.g. Ref. [19] for explicit formulas relating α to the potential parameters in Eq. (16)). In the following, we will denote the SM-like Higgs boson among h 1,2 by h 125 and the non-SM-like Higgs boson by h BSM .
The unitary matrix R is crucial for the phenomenology of the 2HDM. For instance, the couplings of the CP-even scalars to gauge bosons V ∈ {W ± , Z} are given by where R i1 is the (i1)-entry of the mixing matrix R.
In the alignment limit, where As already discussed in Section 2.1, this has important consequences for the charged Higgs boson H ± . Its coupling to a neutral Higgs boson h i and a W ± is given by In the alignment limit this coupling vanishes for h 125 and is maximized for h BSM since R is a 2 × 2 orthogonal matrix. The coupling of the charged Higgs boson to the A boson and a W ± boson, is not affected by the alignment of the SM-like Higgs boson. The Yukawa sector of the 2HDM is determined by its symmetry structure. In order to avoid tree-level flavor changing neutral currents, the Z 2 symmetry can be extended to the fermion sector resulting in four distinct types of Yukawa sectors (see Table 1): type I, type II, flipped, and lepton specific. In this work we will focus on type-I and leptonspecific models since in type II (and flipped) 2HDMs measurements of flavor observables constrain the charged Higgs boson to be very heavy [69,70]. In type-I Yukawa sectors, the SM-normalized couplings of each Higgs boson to all fermion types are equal.
Via this Yukawa interaction, also the charged Higgs boson interacts with fermions, where V CKM is the Cabibbo-Kobayashi-Maskawa matrix, and P L,R are the left-and right-handed chirality projection operators.
Type Table 1.: Assignment of the Z 2 charges to the right-handed fermions for the different types of 2HDMs. The resulting coefficients of the charged Higgs-fermion interaction are also shown.
As a consequence of the coupling dependence on the quark masses (m u i and m d i ) and the lepton masses (m l j ), the most important charged Higgs decay modes to fermions are H + → cb and H + → τ + ν for low masses below the top quark mass, and H + → tb for heavier masses.
For the rest of the paper we will work in the 2HDM framework introduced above. In many extended models, the charged Higgs boson phenomenology is very similar. Often, only the overall rates of the H ± i → W ± h j decays are expected to be lower due to the corresponding sum rules (see Eqs. (12) and (13)).

Phenomenological scan of the Two Higgs Doublet Model
We base our phenomenological study on a large parameter scan of the 2HDM type-I parameter space using the code ScannerS [71][72][73][74][75]. We require all parameter points to fulfill current theoretical and experimental constraints. These include • tree-level perturbative unitarity and boundedness from below (BfB) [68], • absolute stability 9 of the tree-level vacuum [76], • electroweak precision constraints through the oblique parameters S, T and U using the prediction of Refs. [77,78] and the fit result of Ref. [79], • flavor constraints using the results of Ref. [79], • bounds from searches for additional scalars using HiggsBounds-5.9.0 [80][81][82][83][84][85], • and agreement with the Higgs signal measurements using HiggsSignals-2.6.0 [86][87][88][89], which incorporates the combined LHC Run-1 results [4] as well as the latest Run-2 Higgs measurements by the ATLAS [90][91][92][93][94][95][96][97][98] and CMS [99][100][101][102][103][104][105][106][107][108][109][110] collaborations.   The required branching ratios of the scalars are calculated using HDECAY [111][112][113] and the neutral scalar production cross sections using SusHi [114,115]. 10 See Ref. [75] for details on the scanning procedure. We fix the mass of the h 125 boson to its observed value from the ATLAS and CMS LHC Run-1 combined analysis, m h 125 = 125.09 GeV [32], and uniformly sample the remaining model parameters within the ranges given in Table 2. For convenience, we choose the coupling c(h BSM V V ) as input parameter in order to cover the two possible cases h 1 h SM and h 2 h SM together in one scan (see Ref. [75] for details). Valid parameter points with tan β larger than the chosen upper limit are possible. However, since we are interested in scenarios where both the fermionic channels -suppressed by large tan β -and the bosonic channels -mostly independent of tan β -are potentially observable at the LHC, we focus on the low and medium tan β region and use the arbitrary upper limit of tan β < 25. In the following, we show results for a sample of 10 6 parameter points that fulfill all of the above constraints (at the 2σ level, where applicable).
As a first scan result, we investigate the well-known and important impact of the electroweak precision constraints on the Higgs mass spectrum (see e.g. Ref. [116]). Especially the constraint on the T parameter forces m H ± to be always close to one of the neutral Higgs masses. This is illustrated in Fig. 1 showing the deviation of the T parameter from the central value of the fit in Ref. [79] in the (m h BSM − m H ± , m A − m H ± ) plane. As mentioned above, only parameter points with a deviation less than 2σ are shown. It is clearly visible that either m h BSM ∼ m H ± or m A ∼ m H ± needs to be fulfilled. In the context of the charged Higgs boson decay into a W boson and a lighter Higgs boson, as discussed in Sections 2.1 and 2.2, this constraint implies that either h BSM or A -but not both -can be significantly lighter than the charged Higgs boson. As a consequence, at least one of the channels H ± → h BSM W ± or H ± → AW ± can be kinematically accessible in large parts of the parameter space. Fig. 2 shows the scan results in the plane of the two important coupling parameters c(h BSM V V ) and tan β. The Higgs signal rate measurements constrain for almost all allowed parameter points in this scan, thus the alignment limit for h 125which would mean c(h BSM V V ) = 0 -is always approximately realized. With Eq. (12) this in turn means that the H ± W ∓ h BSM coupling reaches always at least √ 1 − 0.3 2 ≈ 95 % of its maximum possible value. The color map in Fig. 2 shows the SM-normalized coupling of h BSM to fermions, which is identical for all fermions if the Yukawa sector is of type I. 11 It can clearly be seen that c(h BSM ff ) becomes small for large tan β. Furthermore, in the 2HDM there exists a so-called fermiophobic limit for each of the CP-even neutral scalars (no corresponding limit exists for the A boson), where the couplings of this particle to SM-fermions vanish. This limit is indicated for h BSM by the dashed line in Fig. 2 and is reached for It is clear from the equation and also visible in Fig. 2 that this limit is only reachable if the h 125 alignment is not exact. Trying to satisfy Eq. (26) in the case of exact alignment would require tan β → ∞.
The fermiophobic limit is phenomenologically interesting in our study because most of the direct LHC searches for h BSM rely on production and decay modes governed by its coupling to fermions, e.g. gluon fusion, which vanish in the fermiophobic limit. Only the gauge-boson mediated production channels -such as vector boson fusion (VBF) and W/Z-associated production -are non-zero, but are suppressed by the small c(h BSM V V ). Similarly, the h BSM decay modes to fermions are suppressed (or even vanish in the exact fermiophobic limit). In such a scenario, production of H ± followed by H ± → h BSM W ± could well be the most promising discovery channel for both H ± and h BSM . We come back to the discussion of the fermiophobic Higgs limit in Section 5, where we introduce a dedicated benchmark scenario that features a fermiophobic non-SM-like Higgs boson.

Genuine BSM effects on the h 125 properties
As outlined in Section 2.2, the role of the observed Higgs boson h 125 can be played by either the lighter or the heavier CP-even neutral Higgs state, h 1 or h 2 . Its tree-level couplings to fermions and gauge bosons become identical to the predictions of the SM in the alignment limit. However, through the interplay with the remaining Higgs states of the model, deviations from the SM Higgs properties can still occur in the exact alignment limit. These can either be loop-induced (effective) coupling modifications, or additional decay modes to BSM Higgs bosons. In this section we will first discuss the charged Higgs boson contribution to the h 125 → γγ decay, and then elaborate on the possibility of the decays h 125 → h BSM h BSM and h 125 → AA in case of very light h BSM and A bosons.

Charged Higgs boson contribution to h 125 → γγ
The h 125 → γγ decay channel is currently measured with an accuracy at the level of ∼ 10 % [6,117], which is expected to improve to 3 % at the HL-LHC [3]. The charged Higgs boson induces deviations from the SM prediction at the leading order, as depicted in Fig. 3. These corrections do not vanish in the alignment limit in which all treelevel couplings of h 125 are exactly equal to the respective SM values. Interestingly, these corrections also do not necessarily vanish if the charged Higgs boson is much heavier than the electroweak scale. This non-decoupling effect (described in detail in Refs. [21,22,[118][119][120][121][122]) opens the possibility to indirectly probe the charged Higgs boson via precision h 125 → γγ measurement.
The relevant couplings of the CP-even Higgs bosons h i (i = 1, 2) to a pair of charged Higgs boson are given by where m 2 = m 2 12 /(s β c β ) and R is the unitary mixing matrix defined in Eq. (19). In the alignment limit, in which one of the h i becomes SM-like (implying that R i1 → 1), we obtain In the m H ± v limit, the terms involving m 2 H ± can compensate the suppression arising through the loop integrals which scale proportional to v 2 /m H ± . Consequently, the charged Higgs boson contribution to the di-photon decay rate can reach a constant value even if m H ± v. While the h 1 = h 125 and h 2 = h 125 cases appear to be very similar, they actually have a distinct phenomenology. This is illustrated in Fig. 4 showing the di-photon signal strength of h 125 as a function of m H ± for the parameter scan described in Section 2.3. For the blue points, the lighter CP-even Higgs boson is SM-like (h 1 = h 125 ); for the orange points, the heavier CP-even Higgs boson is SM-like (h 2 = h 125 ). Scan points for which m h 1 , m h 2 ∈ [120, 130] GeV are not shown in order to allow for a clear distinction of these cases.
In case of h 1 = h 125 , the di-photon rate can deviate from the SM value by up to ±17 % for m H ± 200 GeV. For m H ± 300 GeV, positive deviations from the SM of up to ∼ 5 % and negative deviations of up to ∼ 15 % are possible. If the di-photon rate is close to the SM value, the term proportional to m 2 compensates the remaining terms in Eq. (28). This is exactly what happens in the decoupling limit of the 2HDM [19], where 12 v 2 and this contribution vanishes as expected. This is not possible in the case of h 2 = h 125 . If m h 1 , m h 2 m H ± , constraints arising from perturbative unitarity (and perturbativity) force m 2 ∼ O(v 2 ) and the term proportional to m 2  an approximately constant value for m H ± 200 GeV with a negative deviation from the SM by ∼ 9 − 15 %. Perturbative unitarity also implies that m H ± can not reach values above ∼ 700 GeV if h 2 = h 125 . Given these observations, we may optimistically argue that the h 2 = h 125 scenario in the 2HDM can completely be covered experimentally at the HL-LHC, using two complementary probes: in the heavy H ± regime, m H ± 200 GeV, the deviations from the SM in the h 125 → γγ rate will be probed with corresponding precision measurements. In contrast, the light H ± regime, m H ± < 200 GeV, may be probed experimentally with direct H ± searches due rather large production cross sections. In this endeavor, though, all possible H ± collider signatures have to be searched for, including, in particular, the signatures arising from the H ± → W ± h BSM decay, as proposed in this work. The charged Higgs contribution to the h 125 di-photon rate also affects the selection of the benchmark scenarios to be discussed in Section 5 (see also the discussion in Appendix A).

The h 125 → h BSM h BSM and h 125 → AA decay modes
The parameter space with a very light non-SM-like neutral Higgs boson h BSM or A, with a mass ∼ O(few 10 GeV), is interesting for the charged Higgs boson phenomenology for two reasons: First, it kinematically enables the decay H ± → W ± h BSM or H ± → W ± A, respectively, even in case that the charged Higgs boson is very light, e.g., below the top quark mass (m H ± m t ). This, in turn, can lead to a sizable charged Higgs boson production cross section. Second, very light BSM Higgs bosons in the final state can lead to distinct kinematics, e.g., boosted and collimated BSM Higgs decay products, warranting the design of specific analysis techniques in the experimental searches. However, scenar-ios with a light non-SM-like neutral Higgs boson with mass below m h 125 /2 ≈ 62.5 GeV have to obey stringent constraints, as the additional decay mode h 125 → h BSM h BSM or h 125 → AA is kinematically allowed. In the 2HDM, direct searches for such decays, e.g. Refs. [123][124][125][126][127][128][129], are currently weaker than the indirect constraints arising from the 125 GeV Higgs boson precision rate measurements (see e.g. Ref. [43]). In this section we therefore investigate these decays in detail and discuss under which circumstances the constraints can be evaded by suppressing the corresponding decay rate.
The triple scalar couplings governing these decay modes are given by Even in the alignment limit h 125 → h SM , the resulting couplings can lead to decays of h 125 → h BSM h BSM , AA if kinematically allowed. Even for BSM Higgs masses above m h 125 /2, the off-shell branching ratios into these final states can be substantial.
For the purpose of studying charged Higgs phenomenology for m h BSM /A < 62.5 GeV it is useful to define scenarios where the h 125 → h BSM h BSM , AA decays are not the most sensitive observables (in order to not be experimentally excluded by these channels). This can be accomplished by choosing m 2 and thus m 2 12 such that the respective triple scalar couplings are zero, For the benchmark scenarios to be discussed in Section 5, we only consider the case of a light CP-even Higgs boson for simplicity (we expect the case of light A boson to be very similar phenomenologically). In this context, we find that g h 1 h 1 h 2 = 0 is not possible in the exact h 2 = h 125 → h SM alignment limit without violating theoretical constraints and therefore consider scenarios that deviate slightly from alignment (see also Appendix C).

Searching for charged Higgs bosons at the LHC
In this section we will discuss in detail the various LHC production and decay modes of the charged Higgs boson and give an overview of current LHC searches focusing on the 2HDM structure introduced in Section 2.2

Charged Higgs boson production at the LHC
At the LHC there are three main channels for direct charged Higgs boson production (see e.g. Refs. [55,63] for other comprehensive reviews): The charged Higgs boson can be produced in association with a top and a bottom quark, in association with a neutral Higgs boson, and in association with a W boson. These production modes will be discussed in more detail below. In addition to these channels, charged Higgs bosons can also be produced in pairs (see e.g. Ref. [63]), albeit at a very small rate, or in vector-boson fusion, if the charged Higgs boson originates from a SU (2) Higgs triplet.
All used cross-section values (except of pp → H ± tb production) are available as data tables in the form of ancillary files accompanying the present paper. The cross section calculations in these channels use the MMHT2014 pdf set [130].
Charged Higgs boson production in association with a top and a bottom quark can be calculated either in the four-flavor scheme (4FS) as shown in Fig. 5a -corresponding to the process gg →tbH + -or in the five-flavor scheme (5FS) as shown in Fig. 5b -corresponding to the process gb →tH + . While the calculation in the 5FS is more precise in the collinear region of phase space in which the transverse momentum of the b quark is small, the 4FS yields more accurate results if the transverse momentum of the b quark is large. To obtain a prediction precise for all phase space regions, both calculations have been matched by identifying terms which would be double-counted if both calculations would be summed naively [131].
A related issue appears for low charged Higgs boson masses, m ± H , well below the top-quark mass, m t . In this regime a charged Higgs boson can be produced via the decay of a top quark. This process can be conveniently calculated in the narrow-width approximation. If the mass of the charged Higgs boson is, however, close to the topquark mass, the narrow-width approximation becomes invalid and all contributions to the process pp → H ± tb have to be taken into account (see Refs. [131][132][133] for LO calculations).
NLO corrections for charged Higgs boson production in association with a top and a bottom quark in the regime of m H ± > m t have been calculated in Refs. [134][135][136][137][138][139][140][141][142]. In the regime m H ± < m t , NLO corrections have been derived in Refs. [143][144][145][146][147][148][149][150][151][152][153]. The intermediate mass regime of m H ± ∼ m t has been addressed at the NLO level in Refs. [137, 200 300 400 500 600 700 800 900 1000  [142,154]. For our present study, we use the tabulated NLO results of Refs. [142,154] for m H ± > 145 GeV. We refer to those references for details on the calculation, the 4FS/5FS matching procedure, and the input parameters. Figure 6 shows the corresponding numerical prediction for the 2HDM type-I (and the lepton-specific 2HDM) with tan β = 1. The cross section for other tan β values can be obtained by dividing by tan 2 β. For lower charged Higgs masses, we multiply the 13 TeV LHC σ(pp → tt) cross section of ∼ 803 pb [155] by the appropriate branching fraction obtained from HDECAY [111,113]. While σ(pp → H ± tb) can reach values of more than 100 pb for m H ± < m t , the cross section is substantially smaller above the t-threshold with values of 6 pb at m H ± = 200 GeV decreasing to ∼ 0.1 pb at 800 GeV.
Another important production channel is charged Higgs production in association with a neutral Higgs boson [156][157][158][159][160][161], see Fig. 7 for the dominant LO s-channel diagram. The contribution from this diagram is proportional to the H ± W ∓ h i coupling, which is  For the pp → H ± h BSM process, no dedicated calculation beyond the LO exists. While NLO-QCD corrections could easily be derived using automated NLO tools, we estimate the impact of higher-order corrections to the pp → H + h BSM cross section by comparing it to the SM pp → W + h process. Since the only colored states in both processes are the incoming quarks, QCD corrections arise only as initial state radiation and as virtual corrections to the W ± qq vertex, which are identical in both processes. Since the different couplings in the second vertex cancel out in the K-factor, the only remaining difference between the two process is the different mass of the final state particles, and the resulting differences in phase space and scale. We use this analogy by employing the NNLO-QCD pp → W + h calculation implemented in the code vh@nnlo-2.1 [162,163] adjusted to account for the changed final state masses 12 in order to derive a mass-dependent Kfactor, which is defined as the ratio of the NNLO cross section over the LO cross section. We then use this K-factor to rescale the LO pp → H + h BSM cross section obtained with MadGraph5-2.8.0 [164]. Both calculations are performed in the 4FS, as is appropriate for an s-channel W ± -exchange process, where b-quark contributions are negligible.
The left panel of Fig. 8 shows the 13 TeV LHC LO cross section as a function of m H ± and m h BSM , assuming exact alignment of h 125 . The right panel displays the LO cross section multiplied with the NNLO K-factor. The K-factor only varies slightly within the considered mass plane with a range between 1.34 for low masses and 1.37 for high masses. Both plots show the cross section summed over both possible charges of Figure 9.: Leading-order Feynman diagrams for pp → H ± W ∓ production.

Cross sections for pp
The pp → AH ± cross sections are independent of all other model parameters.
Let us consider this production mode in conjunction with the subsequent decay of the charged Higgs boson into a W boson and the non-SM-like Higgs boson, pp → This final state can also arise from double-Higgsstrahlung, or Higgsstrahlung followed by an h BSM → h BSM h BSM splitting. These could contribute and may even interfere with our signal process. However, both of these processes involve the coupling c(h BSM V V ) which is strongly suppressed in the alignment limit. Using MadGraph5-2.8.0 we have verified that the total cross sections for the exclusive subprocess pp → H + h BSM → W + h BSM h BSM and the inclusive pp → W + h BSM h BSM process agree within less than 3 % for all benchmark scenarios defined in Section 5. Thus, the alternative processes can be safely neglected.
In the used approximation, the cross section for the production of the charged Higgs boson in association with an A boson is identical to the pp → H ± h BSM cross section.
At the leading order, four different subprocesses contribute to the production of a charged Higgs boson in association with a W boson: the bb-initiated non-resonant channel (see Fig. 9a), the bb-initiated resonant channel (see Fig. 9b), the gg-initiated non-resonant channel (see Fig. 9c), and the gg-initiated resonant channel mediated by any of the three neutral Higgs bosons (see Fig. 9d).
The cross section for this process has been calculated at the leading order in Refs. [165][166][167][168][169]. Higher-order corrections have been derived in Refs. [170][171][172][173]. Studies focusing on the collider phenomenology of H ± W ∓ production can be found in Refs. [174][175][176][177][178][179]. For our present study in the 2HDM type-I, we have derived the 13 TeV LHC cross section for charged Higgs production in association with a W boson using MadGraph assuming exact alignment limit and tan β = 1. We work in the 5FS, as is appropriate for the dominant bb-initiated channel, for which we take into account approximate NNLO (aNNLO) corrections by multiplying with the given K-factors derived in Ref. [173]. The blue curves in Fig. 10 show the cross section of the bb-initiated channel at LO (solid curve) as well as at aNNLO (dashed curved). 13 While the cross section of the bb-initiated channel only depends on m H ± in the given approximation and scales with tan −2 β, the cross section of the gg-initiated channels additionally depend on m h BSM and m A . We quantify this dependence by varying them in the interval 10 GeV to 500 GeV, which results in the greenpoints for the gg-initiated contributions. As a simple criterion to differentiate the non-resonant and the resonant case, we regard points for which m A < m H ± + m W and m h BSM < m H ± + m W as dominated by the non-resonant process -since neither h BSM nor A can be on-shell 14 -and color them dark-green. All other points are considered to be dominated by resonant production and are shown in lightgreen.
For m H ± 450 GeV, the bb → H + W − subprocess dominates. For lower charged Higgs boson masses the non-resonant gg-initiated contribution remains smaller than the bb initiated cross section by a factor between 2.2 and 30. In this region, the resonant gginitiated channel can, however, yield a significant contribution to the total cross section potentially exceeding the contribution of the bb-initiated channel by a factor of ∼ 30 for m H ± = 100 GeV.
For our benchmark scenarios defined below, we will always assume that either m m H ± or m h BSM = m H ± in order to satisfy the constraints from electroweak precision observables (see discussion in Section 2.3). Additionally, the second non-SM-like neutral Higgs boson is assumed to be lighter in order to kinematically allow the H ± → h BSM W ± or the H ± → AW ± decay processes. For this mass setting, the gg-initiated channel is always significantly smaller than the bb-initiated channel. Therefore, we approximate the total cross section for charged Higgs boson production in association with a W boson used in our numerical analysis by only taking into account the bb-initiated channel, which we rescale by a factor of tan −2 β if tan β = 1.

Charged Higgs boson decay modes
The coupling structure of the charged Higgs boson (see Section 2.2) allows charged Higgs boson decays into SM fermions as well as into a W boson and a neutral Higgs boson. Among the fermionic decay channels, the H + → tb as well as the H + → τ +ν τ decays are phenomenologically most important due to the comparatively large respective couplings, followed by the H + → cs decay. In the 2HDM of type-I, the partial widths for the fermionic decays are proportional to cot 2 β, and thus become small for large tan β.
In contrast, as discussed in Sections 2.1 and 2.2, the charged Higgs coupling to a W boson and a non-SM-like Higgs boson becomes maximal in the alignment limit. Therefore, if kinematically allowed, the decay H ± → W ± h BSM can easily become the dominant decay mode. In order to assess this statement more quantitatively, we show in In the kinematically allowed region for the on-shell decay, the minimal branching ratio often reaches values of above 60 %. As expected, the branching ratio is especially large for low masses of the non-SM-like Higgs boson. The H ± → W ± h BSM decay mode is, however, also important in the off-shell region if m h BSM is below ∼ 150 GeV and the H ± → tb decay is suppressed because m H ± < m t . The right panel of Fig. 11 shows that in almost the entire parameter region of these two kinematical regimes, i.e. in the on-shell region and in the off-shell region with m h BSM 150 GeV, the H ± → W ± h BSM decay can reach branching ratios very close to 100 %. The right panel also shows that the BR can reach 100 % in the off-shell region even for larger m h BSM , as long as m H ± < m t .
Besides the H ± → W ± h BSM decay also the H ± → W ± A can be phenomenologically relevant. The minimal and maximal branching ratios for this decay are shown in the left and right panel of Fig. 12 in the (m A , m H ± ) plane, respectively. While the overall behavior is quite similar to the previously discussed H ± → W ± h BSM decay, the minimal BR(H ± → W ± A) tends to be smaller than BR(H ± → W ± h BSM ).
In the parameter regions in which BR(H ± → W ± h BSM ) and BR(H ± → W ± A) are both small, the charged Higgs boson decays predominantly into a top and bottom quark, if kinematically allowed. This is apparent in the left and right panels of Fig. 13 which display the minimal and maximal value, respectively, of BR(H ± → tb) in the (min(m h BSM , m A ), m H ± ) plane. If the decays H ± → W ± h BSM /A are kinematically suppressed (i.e., below the dashed line), the charged Higgs boson decays almost always to ∼ 100 % to a top and a bottom quark. 15 We observe a steep rise of the maximal BR(H ± → tb) for min(m h BSM , m A ) greater than ∼ 350 GeV, which corresponds to the decrease in the minimal value of BR(H ± → W ± h BSM ) and BR(H ± → W ± A), seen in the left panels of Figs At this mass value -corresponding to ∼ 2m t -the decays of the h BSM and A bosons to a pair of top quarks become kinematically accessible suppressing the branching ratio of all other decays. Since the di-top final state is experimentally challenging, only rather weak bounds exist for scalars decaying dominantly to tt. Consequently, lower values of tan β -and thereby higher values of BR(H ± → tb) -remain allowed by current direct searches.
It is interesting to note that BR(H ± → tb) can be small even if the decay channel is open and neither of the competing H ± → W ± h BSM /A decays is kinematically allowed. This is visible in the left plot of Fig. 13 in which the minimal BR(H ± → tb) is only ∼ 30 % for most of region below the dashed line as long as m H ± 220 GeV. For these points, the alignment limit is only approximately realized resulting in a non-zero H ± W ∓ h 125 coupling (see Section 2.2). In addition, tan β is comparably high and therefore BR(H ± → tb) is rather small. As a consequence, for these points the charged Higgs boson decays dominantly into a the SM-like Higgs boson and a W boson. This parameter region can therefore also be probed by searches for a bosonically decaying charged Higgs boson. The exception is the mass region m H ± ≈ m t + m b , where the H ± → tb decay is resonant and always dominates the decay width if the H ± → W ± A/h BSM decay modes are not accessible. This is the origin of the yellow region in Fig. 13 (left).

Current LHC searches for a charged Higgs boson
Existing LHC searches for a charged Higgs boson (as listed in Table 3) have mainly focused on the charged Higgs boson decays into SM fermions. One exception are searches for a charged Higgs boson produced in a vector-boson-fusion process and decaying to a Production process Higgs decay processes Final state particles Exp. searches Refs. [180][181][182][183][184] pp → H ± tb H ± → tb tbtb Refs. [181,[185][186][187] Refs. [189,190] Refs. [191][192][193]  W and a Z boson, but these production and decay channels are only possible in highermultiplet extensions of the SM (e.g. Higgs triplet models). Another exception is the search for a light charged Higgs boson decaying to a W boson and an A boson, with the A boson decaying to a µ + µ − pair [65]. While this search is the first experimental attempt to target the decay signatures discussed in this paper at the LHC, its results are only of very limited use, as the experimental limit has not been released for the two-dimensional mass plane (m H ± , m A ), but only for one-dimensional slices of the twodimensional parameter space, assuming either m H ± = m A + 85 GeV or m H ± = 160 GeV.
We illustrate the impact of the current LHC searches for a charged Higgs boson on our phenomenological 2HDM scan in Fig. 14. In the left panel we show the branching ratio BR(H ± → τ ν τ ) normalized by t 2 β as a function of m H ± . This normalization is chosen as it allows us to show limits from the different LHC charged Higgs production modes that are relevant in this mass range on the same scale. The gray points are allowed by all constraints listed in Section 2.3. For charged Higgs boson masses below ∼ 80 GeV, no points in our scan pass all constraints. The most important constraints in this region are set by combined LEP searches for charged Higgs pair production [194]. 16 Above the kinematic reach of the LEP searches, m H ± 90 GeV, the LHC searches for a charged Higgs boson decaying into τ ν and produced either from top quark decays, t → H ± b, or through pp → tbH ± [183] become relevant (blue and orange curves in Fig. 14 (left)). 17 They limit BR(H ± → τ ν τ )/t 2 β to be below ∼ 10 −2 . These searches loose sensitivity above the kinematic threshold for the H ± → tb decay at m H ± ∼ m t +m b , where BR(H ± → τ ν τ ) becomes small due to the large partial width of the H ± → tb decay, as can be seen from the distribution of gray points in this mass range in the left panel of Fig. 14.
The impact of LHC searches for a charged Higgs boson decaying into a top and a bottom quark is shown in the right panel of Fig. 14  The gray points pass all relevant constraints. In the left plot, we include the observed (solid line) and expected (dashed line) limits from the most sensitive t → H ± b, H ± → τ ν τ (blue) and pp → H ± tb, H ± → τ ν τ (orange) searches [183]. In the right panel, the limit from the latest pp → H ± tb, H ± → tb search [186] is shown (green).
section pp → tbH ± → tbtb as a function of m H ± . While this channel has a comparatively large cross section of up to ∼ 1 pb, the tb final state is experimentally hard to disentangle from SM background processes. Therefore, the most recent experimental search [186] constrains the parameter space only slightly within the region m H ± ∼ 500 − 700 GeV. From the discussion of the charged Higgs boson decay rates in Section 4.2 we know that many of our scan points in fact exhibit a large H ± → W ± h BSM and/or H ± → W ± A decay rate, which in turn suppresses the decay modes with fermionic final states. This is also evident from the large swath of gray points in Fig. 14 that are far below the current limits from the discussed LHC searches. These observations strongly motivate experimental efforts to complement the existing searches by probing the H ± → W ± h BSM and H ± → W ± A decay modes directly. In the upcoming section we focus on the collider signatures arising from these decays and present suitable benchmark scenarios for the design of such dedicated experimental searches.

Unexplored LHC signatures and benchmark models
As discussed above, vast parts of the phenomenologically viable parameter space of the 2HDM of type-I feature a charged Higgs boson that dominantly decays into a W boson and a non-SM like neutral Higgs boson (h BSM or A). However, the collider signatures Production process

Higgs decay processes
Final state particles Table 4.: LHC signatures arising from the charged Higgs boson decay H ± → W ± φ, with a neutral non-SM-like Higgs boson, φ = h BSM , A, for the most relevant production (first column) and decay (second column) processes. The resulting final state particles are given in the third column (further decays of the SM particles are not explicitly shown). The "⊗" symbol in the center right cell indicates that any combination of the final states within the square brackets can occur due to the independent decays of the two neutral Higgs bosons.
arising from these decays are to a large extent not covered by LHC searches. We summarize the most relevant LHC signatures in Table 4. These arise from charged Higgs production via one of the three main LHC production modes discussed in Section 4.1, and the successive decay of the charged Higgs boson into a W boson and a neutral Higgs boson φ, which can either be the h BSM boson or the A boson. For the neutral Higgs boson decays we include the bb, τ τ , W W , ZZ and γγ final states, as these are typically the most frequent (bb, τ τ ) or experimentally cleanest (W W , ZZ, γγ) channels. The corresponding rates are model-dependent and will be discussed in more detail below in the context of benchmark scenarios. Besides the final states included in Table 4, the experimentally more challenging decays φ → cc and φ → gg may also become relevant in certain scenarios (see e.g. Refs. [195][196][197] for related searches and studies for the h 125 ). We shall therefore also include their rates in the following discussions if relevant.
While a detailed analysis of the LHC discovery potential of the various collider signatures must be postponed to future work, we briefly want to comment on a few features that may be exploited in collider searches, and the most important SM backgrounds. For the pp → tbH ± production process -which is typically the dominant charged Higgs boson production mode, see Section 4.1 -inclusive SM processes with pairs of top quarks, tt(+X) and tth 125 , are inevitably a major background, almost irrespective of how the neutral non-SM-like Higgs boson φ of the signal process decays (see also discussion in Ref. [58]). For the experimentally clean signature arising from the decay φ → γγ, we expect that a good signal-background separation can be achieved by using similar techniques as in the tth 125 , h 125 → γγ analyses [109,198]. However, as the signal rate is typically very low -except for specific scenarios with a very light and/or fermiophobic φ (see below) -sensitivity may only be reached with a very large amount of data. Hence, we expect that for the more conventional 2HDM scenarios near the alignment limit the signal processes from φ → bb and φ → τ τ provide a more promising avenue (see also Refs. [52,53]). Moreover, under the additional model-assumption on the relative size of BR(φ → bb) and BR(φ → τ τ ) as predicted in the 2HDM, search results from the two signatures may be combined to maximize the sensitivity to the 2HDM parameter space.
For the pp → H ± φ → W ± φφ process a multitude of signatures arises because the two φ bosons decay independently. As the production rate is already comparatively small, we also expect the typically more frequent decay modes φ → bb and φ → τ τ to exhibit the highest sensitivity in most of the 2HDM parameter space. In this case, a leptonically decaying W boson provides a triggerable isolated lepton. Moreover, dedicated signal regions for resolved, semi-boosted and fully-boosted bb/τ τ pairs can be defined to enhance the sensitivity. Again, the main SM background to these signatures arises from (semi-leptonic) top quark pair production.
For the third process, pp → H ± W ∓ → W ± W ∓ φ, we again expect the semi-leptonic analysis to be the most sensitive selection (see also Ref. [51]). SM backgrounds arise from inclusive electroweak boson production, W + W − + X and top quark pair production. Note, however, that the signal cross section scales with cot 2 β, and is therefore typically smaller than the cross section of the previous processes. We therefore expect this production channel to be not as sensitive as the pp → tbH ± and pp → H ± φ channels.
2HDM scenarios with large decay rates for H ± → W ± φ typically feature a concomitant signature in the neutral Higgs sector -the A → Zh BSM (if φ = h BSM ) or h BSM → ZA (if φ = A) decay -with a sizable rate. This can be ascribed to the EW precision measurements discussed in Section 2.3 which constrain the mass of one of the neutral Higgs bosons to be close to the charged Higgs boson mass. Consequently, these scenarios are simultaneously probed by searches for pp → A → Zh BSM or pp → h BSM → ZA, and current limits from these searches constrain parts of the relevant parameter space [199,200] (see also discussion of benchmark scenarios below). Yet, direct charged Higgs boson searches for the H ± → W ± φ decay signatures are highly warranted, as they are able to directly probe the charged Higgs sector independently of the (model-dependent) correlation between neutral and charged Higgs boson masses enforced by the EW precision constraints. In particular, in the optimistic case of a discovery in either of these channels, the model correlations would strongly suggest to look for a corresponding signal in the complementary channel as well.
Another related channel is of course the inverse decay φ → H ± W ± if the mass hierarchy of H ± and φ is reversed. This decay is governed by the same coupling as the H ± → W ± φ decay, and is therefore also maximized in the alignment limit of h 125 . However, through the mass correlation imposed by the EW precision measurements, this channel is even more strongly related to the h BSM /A → ZA/h BSM channels, since it also shares the initial production mode of the neutral scalar. We expect the W ± H ∓ final state to be experimentally more challenging than the Zφ final state, regardless of the successive H ± and φ decay. As a result, the 2HDM parameter region where searches for pp → φ → H ± W ∓ are competitive with pp → A/h BSM → Zh BSM /A searches is limited to the small mass region where the Zφ decay is kinematically suppressed, while the H ± W ∓ decay is not. We stress that this decay channel is nevertheless very interesting to search for, since the mass correlations imposed by the EW precision constraints are model-dependent. We will further comment on this channel below, whenever our benchmark scenarios include parameter regions where it can appear.
In order to facilitate future searches for the H ± → W ± φ signatures, we present in the following five benchmark scenarios, which are parametrized in the (m H ± , m φ ) plane: m ± H > m h BSM in most of the parameter plane. We assume the exact alignment limit and take a very small value tan β = 3, which maximizes the H ± → W ± h BSM decay rate and the pp → tbH ± production rate, respectively. The light non-SM-like Higgs boson h BSM mainly decays to SM fermions (bb, τ τ ) and gluons (gg); • cH(W A) scenario with large BR(H ± → W ± A): We choose m H ± = m h BSM , and m ± H > m A in most of the parameter plane. Analogous to the previous scenario, we assume the exact alignment limit and take a very small value tan β = 3 to obtain a large pp → tbH ± production rate. The A boson predominantly decays to bb, gg and τ τ .
• cH(W h fphob BSM ) scenario with fermiophobic h BSM : The charged Higgs boson and the A boson are chosen to be mass degenerate, m H ± = m A , and h BSM is lighter in most of the parameter space. We depart slightly from the exact alignment limit, c(h BSM V V ) = 0.2, and chose tan β to fulfill the fermiophobic Higgs condition, Eq. (26) Each of these scenarios features a distinct collider phenomenology and shows the importance of the H ± → W ± h BSM or W ± A decay mode. While the first two "standard" scenarios, cH(W h BSM ) and cH(W A), aim to maximize the signal rate in the pp → tbH ± → tbW ± φ (φ = h BSM , A, respectively) channel, the latter three "specialized" scenarios highlight exceptional phenomena (fermiophobic, leptophilic, or very light h BSM ) that may occur for specific parameter choices, and lead to very different collider signatures. A significant part of the parameter planes evade all current constraints evaluated as specified in Section 2.3.
In order to evade constraints from electroweak precision observables (see Section 2.3), we set the mass of the other Higgs boson, A or h BSM , respectively, equal to the charged Higgs boson mass, as described above. The other neutral CP-even Higgs boson is considered to be the discovered Higgs boson h 125 with a mass fixed to 125.09 GeV. The values for the remaining 2HDM input parameters are given in Table 5. Their choices are explained in the description of the respective benchmark scenarios. We provide the full data tables for all benchmark scenarios as ancillary files.
While we aimed to pick typical and illustrative scenarios, different choices of the fixed parameters could have led to different phenomenology and different parameter regions excluded by existing constraints. When designing experimental searches for these signatures, the search ranges should therefore never be constrained to the allowed region in the targeted benchmark scenario, but chosen as large as possible for the experimental analysis.
It is also possible to define similar scenarios in the type-II or flipped 2HDM. As discussed in Section 2.2, the light H ± region in these models is tightly constrained by flavor constraints. As a consequence, the charged Higgs boson mass would have to be significantly higherm H ± 580 GeV [69] -resulting in smaller signal cross sections for charged Higgs bosons decaying to a W and a non-SM like neutral Higgs boson.

cH(W h BSM ) scenario with large BR(H ± → W ± h BSM )
With our first benchmark scenario, the cH(W h BSM ) scenario, we aim to provide a reference model that maximizes the rates of the H ± → W ± h BSM decay and pp → tbH ± production mode. The h BSM boson decays predominantly to bb, τ τ and gg. This "standard" scenario exhibits a collider phenomenology that is found in large parts of the viable parameter space, without the need of tuning specific parameters.
We assume the exact alignment limit, c(h BSM V V ) = 0, and set m A = m H ± . The scenario is parametrized in the (m H ± , m h BSM ) plane, with m h BSM < m H ± in most of the parameter plane. As a consequence, the decay H ± → W ± h BSM is one of the most important decay channels of the charged Higgs boson. The parameter tan β is chosen as low as possible without violating flavor constraints for light H ± , which maximizes the rates in the pp → tbH ± production mode. The charged Higgs boson phenomenology is not significantly affected by the choice of the parameter m 2 12 (see Table 5). With the m 2 12 value chosen here theoretical constraints are successfully evaded. Similar scenarios in the exact aligment limit can easily be defined for larger values of tan β. In that case all fermionic production and decay modes would be suppressedsince the fermionic couplings scale with 1/ tan β -while the pp → H ± h BSM production cross section would be unaffected, and the H ± → W ± h BSM branching ratio would be enhanced -due to the suppressed fermion decays. Therefore, this low tan β scenario is intentionally chosen as a worst case scenario for searches targeting pp → H ± h BSM → W ± h BSM h BSM , while showing the complementarity with searches in fermionic channels.
The branching ratio BR(H ± → W ± h BSM ) is shown in the upper left panel of Fig. 15 in the (m H ± , m h BSM ) parameter plane (colored contour lines). The colored regions are excluded by the following LHC searches: experimental searches for pp → A → Zh BSM [199][200][201] (orange region) exclude the upper left part of the parameter plane, pp → A/h BSM → τ + τ − searches [202] (green region) constrain the central right part of the parameter plane, and searches for pp → tbH ± , H ± → τ ± ν τ [183] (blue region) exclude the lower right part of the parameter plane. In the remaining unconstrained parameter region, BR(H ± → W ± h BSM ) can reach values above 99 % (for m H ± ∼ 170 GeV and m h BSM ∼ 70 GeV) rendering the H ± → W ± h BSM decay a prime target for future searches in this part of the parameter space. The branching ratio decreases for increasing m h BSM due to the decreasing phase space. All of the LHC searches that exclude parts of the scenario rely on fermionic production modes. Therefore, at larger tan β the existing experimental constraints would become significantly weaker.
The total signal cross sections for the three main charged Higgs production modes (as discussed in Section 4.1) with the subsequent H ± decay into a W boson and an h BSM boson are shown in the remaining three panels of Fig. 15. In the unconstrained parameter region, the signal cross section can maximally reach about 13 pb for tb-associated charged Higgs production, 340 fb for h BSM -associated charged Higgs boson production, and HiggsBounds95 fb for W -associated charged Higgs boson production. All of these maximal cross sections are reached for the lowest considered masses. Figure 16 shows the branching ratios of h BSM for the most important decay modes as a function of m h BSM . This completes the rate information required for designing experi- , and pp → W ∓ H ± → W ± W ∓ h BSM (bottom-right) channels in the remaining panels. The colored regions of parameter space are excluded by current constraints from searches in the pp → A → Zh BSM [199][200][201], pp → A/h BSM → τ + τ − [202] and pp → tbH ± , H ± → τ ± ν τ [183] channels, as denoted by the labels.
mental searches to probe this benchmark scenario. Since the decay modes depend on the mass of H ± directly or indirectly through the total width, the ranges of BRs within the m H ± range of the scenario are shown. The cH(W h BSM ) scenario is defined in the exact alignment limit, therefore h BSM does not couple to massive vector bosons. Accordingly, h BSM decays dominantly to two bottom quarks (bb, blue curve) with branching ratios of up to 80 % (70 %) for low (high) masses. The decay into gluons (gg, green curve) becomes increasingly important for rising m h BSM , reaching decay rates of up to ∼ 25 %. The branching ratios for h BSM decays to a pair of tau leptons (τ + τ − , orange curve) and a pair of charm quarks (cc, red curve) are approximately constant reaching values of This decay rate is anti-correlated with all other decay rates, leading to the filled regions and declining slopes of the minimal decay rates for other decay modes. As discussed above, this illustrates that the h BSM → W ± H ∓ decay can become equally large as the H ± → W ± h BSM decay.
Finally, the charged Higgs boson contribution to the di-photon decay mode (see Section 3.1) also induces deviations in the h 125 di-photon rate of up to 13 % from the SM (see Appendix A for more details).

cH(W A) scenario with large BR(H ± → W ± A)
Our second benchmark model, the cH(W A) scenario, is designed to feature a maximal rate for the H ± → W ± A decay and a dominant production through the pp → tbH ± process. In analogy with the previous scenario, we choose m h BSM = m H ± , and m A is allowed to vary. A small value of tan β = 3 is chosen to obtain a large pp → tbH ± production cross section. The choice of m 2 12 (see Table 5) has no significant impact on the charged Higgs boson phenomenology but is chosen differently from the cH(W h BSM ) scenario in order to satisfy theoretical constraints that depend differently on the CP-even and CP-odd Higgs masses. As in the cH(W h BSM ) scenario, the low value for tan β is an intentionally chosen worst case scenario for the bosonic production and decay channels  [199][200][201], pp → A/h BSM → τ + τ − [202] and pp → tbH ± , H ± → τ ± ν τ [183] channel. Theoretical constraints from perturbative unitarity (gray region) also impact cH(W A).
of H ± compared to the fermionic channels. We display the branching ratio of the H ± → W ± A decay in the upper left plot of Fig. 17. The BR values are identical to those found in the cH(W h BSM ) scenario (shown in the upper left plot of Fig. 15) under the exchange A ↔ h BSM . The pp → h BSM → ZA searches [199][200][201] (orange region) cover a significantly smaller parameter region than the pp → A → Zh BSM searches in the cH(W h BSM ) scenario due to the lower gg → h BSM production cross section. The pp → A/h BSM → τ + τ − search [202] excludes parts of the parameter region with m A 180 GeV. The region excluded by pp → tbH ± , H ± → τ ± ν τ searches [183] is identical to the corresponding region in the cH(W h BSM ) scenario. As an additional constraint in the cH(W A) scenario, charged Higgs boson masses above ∼ 270 GeV are excluded by perturbative unitarity. As for the cH(W h BSM ) scenario, the maximal BR(H ± → W ± A) reaches values above 99 %. In the cH(W A) scenario, however, larger parts of the parameter space with BR(H ± → W ± A) 65 % at large m H ± values are still unconstrained making this scenario a very interesting target scenario for future H ± → W ± A searches. As in the cH(W h BSM ) scenario, the existing searches all rely on fermionic production modes and quickly loose sensitivity for larger values of tan β.
The future potential of this channel becomes even more apparent from the 13 TeV LHC signal cross section values, as shown in the remaining plots of Fig. 17. These are the same as in the cH(W h BSM ) scenario under the exchange A ↔ h BSM , however, the experimental and theoretical constraints differ. Large cross section are possible in particular in the mass region of m A 120 GeV, which is now unexcluded compared to the cH(W h BSM ) scenario. Through most of this region the cross section for tb-associated charged Higgs boson production, σ(pp → tbH ± , H ± → W ± A) lies above ∼ 200 fb and the cross section for charged Higgs boson production in association with an A (W ) boson lies above 20 fb HiggsBounds(10 fb).
Analogous to Fig. 16 for the previous scenario, we show the branching ratios of the A boson in the cH(W A) scenario in Fig. 18. The overall behavior of the branching ratios is similar to those of the h BSM boson in the previous scenario (see Fig. 16). As a consequence of the A boson being a CP-odd scalar, the decays of the A boson into two gluons and two photons are enhanced in comparison to the decays of the h BSM boson in the cH(W h BSM ) scenario. For m A ∼ 200 GeV, BR(A → gg) and BR(A → γγ) reach values of 47 % and 0.1 %, respectively.
In the cH(W A) scenario, the charged Higgs boson contribution to the di-photon decay width (see Section 3.1) induces deviations of the h 125 di-photon rate with respect to the SM of up to 9 % (see Appendix A for more details).

cH(W h fphob BSM ) scenario with fermiphobic h BSM
As a first benchmark model specialized on a rather exceptional parameter region with a very distinct collider phenomenology, we discuss the cH(W h fphob BSM ) scenario. We again choose m A = m H ± , and m h BSM is allowed to vary. In this scenario we depart from the exact alignment limit by setting the coupling of h BSM to the massive vector bosons to one fifth of the respective SM Higgs couplings. By choosing tan β according to Eq. (26) (taking a value of ∼ 4.9), we realize the fermiophobic limit for h BSM , which implies that h BSM does not couple to fermions. Note that the realization of the fermiophobic limit very sensitively depends on the chosen tan β value. Already small deviations from Eq. (26) result in substantial couplings of h BSM to fermions. This is discussed in more detail in Appendix B. In contrast, the choice of m 2 12 (see Table 5) only has a minor impact on the phenomenology of the cH(W h fphob BSM ) scenario but is important to satisfy the theoretical constraints. Earlier studies of scenarios with a fermiophobic Higgs boson can be found in Refs. [57,157,[203][204][205][206]. This choice of parameters can be considered very fine-tuned from a theoretical perspective. Nevertheless, the collider signatures of this scenario are strikingly different from the scenarios discussed above and should not remain unexplored.
The branching ratio BR(H ± → W ± h BSM ) for the cH(W h fphob BSM ) scenario is shown in the top-left panel of Fig. 19. As before, the results are displayed in the (m H ± , m h BSM ) parameter plane with current experimental and theoretical constraints shown as colored areas. Theoretical constraints in the cH(W h fphob BSM ) scenario are the boundedness from below (BfB) requirement on the Higgs potential (dark magenta) -excluding m H ± 76 GeV -and perturbative unitarity (gray) -excluding m H ± 160 GeV. Experimental constraints arise from searches for pp → h BSM → γγ [207][208][209] (purple) -excluding m h BSM 95 GeV except for a narrow region around the Z-boson mass -, searches for pp → A → Zh BSM [200] (orange) -excluding an otherwise unexcluded small patch around m H ± ∼ 230 GeV and m h BSM ∼ 155 GeV -, as well as searches for pp → tbH ± , H ± → τ ± ν τ [183] (blue) -excluding a small region around m H ± ∼ 150 GeV and m h BSM 120 GeV. In the remaining allowed parameter region, BR(H ± → W ± h BSM ) values of up to ∼ 90 % are possible. Especially the region of low m h BSM and high m H ± features large branching fractions.
The corresponding signal cross sections, shown in the remaining panels of Fig. 19, have a slightly different behavior. Since the production cross sections for a charged Higgs boson decrease with rising m H ± , also the cross sections for charged Higgs boson production with the subsequent H ± → W h BSM decay tend to decrease for rising m H ± . The cross section for pp → tbH ± , H ± → W ± h BSM , shown in the top-right panel of Fig. 19, reaches values almost 5 pb. For pp → H ± h BSM → W ± h BSM h BSM production, shown in the bottom-left panel of Fig. 19, the maximal cross section is ∼ 200 fb. The  [200], pp → h BSM → γγ [207][208][209] and pp → tbH ± , H ± → τ ± ν τ [183] channels. Theoretical constraints from perturbative unitarity and boundedness from below (BfB) are also relevant.
pp → H ± W ∓ → W ± W ∓ h BSM production cross section, displayed in the bottom-right panel of Fig. 19, reaches values HiggsBounds35 fb.
Due to fermiophobic character of the h BSM boson, its decays shown in Fig. 20 are very different from the ones in the cH(W h BSM ) scenario. For m h BSM 90 GeV, the h BSM boson decays dominantly to a pair of photons reaching a maximal branching ratio of ∼ 90 %. 18 For m h BSM 90 GeV, the (off-shell) decays into a pair of W or Z bosons become increasingly important with branching ratios of ∼ 90 % and ∼ 10 %, respectively. Note that the decay modes into massive vector bosons are possible as the alignment of This departure from alignment, together with the charged Higgs boson effects, leads to deviations of the h 125 di-photon decay rate from the SM by up to 14 % (see Appendix A for more details) in the cH(W h fphob BSM ) scenario.

cH(W h light BSM ) scenario with light h BSM
The second rather specialized benchmark model is the cH(W h light BSM ) scenario which features a light h BSM with m h BSM ≤ 62.5 GeV. Similar to the other scenarios we choose again m A = m H ± . In order to suppress the h 125 → h BSM h BSM decay channel we choose m 2 12 according to Eq. (33). As already mentioned in Section 3.2, unitarity and absolute vacuum stability requirements enforce a strong correlation between c(h BSM V V ) and tan β. For tan β values consistent with flavor constraints, tan β 3, we need to slightly depart from the exact alignment limit. We therefore choose c(h BSM V V ) = −0.062 in this scenario, and we set tan β to 16.6 in order to fulfill the unitarity and vacuum stability requirements. See Appendix C for more details on these parameter choices showing that this kind of scenario in the 2HDM clearly requires significant tuning of the parameters. However, similar phenomenology may be far easier to achieve in more complex models, for which this scenario can serve as a simple benchmark.
Due to the low m h BSM values and the relatively high tan β, BR(H ± → W ± h BSM ) is larger than 98 % in the entire benchmark plane. The signal cross section for tbassociated charged Higgs boson production with a subsequent H ± → W h BSM decay is shown in the left panel of Fig. 21   by requiring boundedness from below (BfB) of the scalar potential (red), and the region of m H ± 49 GeV is excluded by perturbative unitarity (gray). The signal cross section σ(p → tbH ± , H ± → W ± h BSM ) strongly depends on m H ± but it is nearly independent of m h BSM . It ranges from around 10 fb at m H ± = 300 GeV to above 2 pb at m H ± ∼ 100 GeV. We find similar cross-section values for charged Higgs boson production in association with a h BSM boson and the subsequent H ± → W h BSM decay, shown in the right panel of Fig. 21. Also for this production mode, cross-section values above 1 pb can be reached for m H ± ∼ 100 GeV. At H ± masses above ∼ 150 GeV the cross section for the pp → H ± h BSM channel even surpasses the one for the pp → tbH ± channel. The cross section for charged Higgs boson production in association with a W boson (not shown) is negligible in the cH(W h light BSM ) scenario, reaching values of only HiggsBounds 6 fb. The branching ratios of the h BSM decays are displayed in the left panel of Fig. 22. For very low masses, m h BSM ∼ 10 GeV, h BSM decays with almost equal probabilities to b quarks, c quarks, and τ leptons. For masses in the intermediate range, 10 GeV < m h BSM 40 GeV, the h BSM → bb decay dominates with a branching ratio of ∼ 80 − 90 %. For higher mass values, it is possible that h BSM decays to two photons with a branching ratio of up to 25 % in the allowed region. In the same region, the branching ratio of h BSM decaying to two photons can, however, also be very close to zero.
This large variation originates from the varying charged Higgs mass. This dependence is shown in more detail in the right panel of Fig. 22 Table 5), however, instead of type-I, the cH(W h phil BSM ) scenario is defined in the lepton-specific 2HDM (see Section 2.2). As a direct consequence, h BSM decays almost exclusively to tau leptons (with a branching ratio above 99 %). Therefore, in contrast to the cH(W h light BSM ) scenario, LHC searches need to focus on the h BSM → τ + τ − decay (following the charged Higgs boson decay H ± → W ± h BSM ) in order to probe this scenario. The HL-LHC sensitivity to a phenomenologically similar scenario has previously been studied in Ref. [59].
As for the cH(W h light BSM ) scenario, m h BSM ≤ 62.5 GeV is required. While it is in principle possible to define benchmark scenario within the lepton-specific 2HDM analogously to the cH(W h BSM ) or cH(W A) scenarios, we found that such scenarios are completely excluded experimentally by searches for a neutral Higgs decaying to tau leptons. These searches do, however, not cover the region m h BSM ≤ 62.5 GeV.
The   Table 5. The colored contours indicate BR(H ± → W ± h BSM ) in the left panel and the 13 TeV LHC cross sections for the search processes pp → tbH ± , H ± → W ± h BSM (center ) and pp → H ± h BSM → W ± h BSM h BSM (right). The shaded regions are excluded by perturbative unitarity, boundedness from below, and LEP searches for di-Higgs production in the 4τ final state [211].
left panel of Fig. 23 in the (m H ± , m h BSM ) parameter plane. The colored areas are excluded by the following constraints: as for the cH(W h light BSM ) scenario, the region of m h BSM 21 GeV is excluded by requiring boundedness from below (red) and the region of m h BSM 50 GeV by unitarity constraints (gray). While no experimental search constrains the cH(W h light BSM ) scenario, the region of m H ± 140 GeV is excluded in the cH(W h phil BSM ) scenario by LEP searches for e + e − → Ah BSM → 4τ (green). In the remaining unexcluded parameter space, BR(H ± → W ± h BSM ) is always above 50 %, and reaches almost 100 % for m H ± ∼ 300 GeV. BR(H ± → W ± h BSM ) is smaller than in the cH(W h light BSM ) scenario due to the fact that the competing BR(H ± → τ ±ν τ ) decay is enhanced by the large tan β value in the lepton-specific 2HDM.
The signal cross section for charged Higgs boson production in association with a top and a bottom quark and its subsequent decay to a W boson and a h BSM boson is shown in the center panel of Fig. 23. In the allowed parameter space, σ(p → tbH ± , H ± → W ± h BSM ) can reach almost 500 fb for m H ± ∼ 150 GeV. For higher values of m H ± the cross section quickly drops below 100 fb. In this region, σ(p → H ± h BSM , H ± → W ± h BSM h BSM ) -shown in the right panel of Fig. 23 -exceeds σ(p → tbH ± , H ± → W ± h BSM ), still reaching e.g. 200 fb for m H ± ∼ 200 GeV and m h BSM ∼ 30 GeV. Note in particular, that -since BR(h BSM → τ + τ − ) ≈ 1 -the signal cross sections for the tbW ± τ + τ − and W ± τ + τ − τ + τ − final states are almost as large as the corresponding cross sections without the h BSM decays. Charged Higgs production in association with a W boson is negligible in the cH(W h phil BSM ) scenario. In the cH(W h phil BSM ) scenario, the h 125 di-photon decay rate deviates from the SM by up to 7 % (see Appendix A for more details).

Conclusions
The presence of charged Higgs bosons is a generic prediction of multiplet extensions of the SM Higgs sector. Collider searches for charged Higgs bosons are, therefore, an important puzzle piece in the search for new physics in the Higgs sector. While many LHC searches for charged Higgs bosons decaying to SM fermions exist, the bosonic decay modes of charged Higgs bosons have so far received much less attention.
Focussing on the 2HDM, we discussed the charged Higgs boson phenomenology taking into account all applicable constraints of theoretical as well as experimental nature. We considered type I and lepton specific Yukawa sectors, where light charged Higgs bosons are not excluded by flavor observables. We revisited two genuine BSM effects on the discovered SM-like Higgs boson -the non-decoupling charged Higgs boson contribution to the SM-like Higgs boson decay into two photons, as well as the decay of the SM-like Higgs boson into two non-SM-like Higgs bosons -and their impact on the charged Higgs boson phenomenology. These effects even appear in the alignment limit, in which the SM-like Higgs boson has exactly SM-like couplings.
We then investigated in detail the production and decay modes of the charged Higgs bosons. We demonstrated that the charged Higgs boson decays predominantly to a W boson and a neutral non-SM-like Higgs state (which could be either CP-even or CPodd) in large parts of the allowed parameter space. This decay mode is especially large close to the observationally-favored alignment limit, in which the charged Higgs boson coupling to a non-SM-like Higgs boson and a W boson is maximized.
We discussed current experimental searches for charged Higgs bosons at the LHC and pointed out the so-far unexplored decay signatures that arise from the above-mentioned decay to a W boson and a neutral non-SM-like Higgs state. In order to facilitate future searches for these signatures, and as the main result of this work, we introduced five benchmark scenarios, each featuring a distinct phenomenology: the cH(W h BSM ) scenario, the cH(W A) scenario, the cH(W h fphob BSM ) scenario, the cH(W h light BSM ) scenario, and the cH(W h phil BSM ) scenario. All scenarios exhibit a large decay rate of the charged Higgs boson to a W boson and a neutral non-SM-like Higgs boson. The scenarios are defined in a 2HDM of type I, except for cH(W h phil BSM ) where the Yukawa sector is chosen to be lepton specific.
In the cH(W h BSM ) scenario, the charged Higgs boson decays dominantly to a non-SMlike CP-even Higgs boson and a W boson. The signal cross section for the production of the charged Higgs boson in association with a top and a bottom quark and its subsequent decay reaches up to 5 pb in significant parts of the yet-unconstrained parameter space. The experimentally most interesting decay modes of the non-SM-like Higgs boson in this scenario are the decay into bottom quarks and the decay into tau leptons.
In contrast to the cH(W h BSM ) scenario, the charged Higgs boson decays dominantly to a CP-odd A boson and a W boson in the cH(W A) scenario, while the h BSM boson has the same mass as the charged Higgs boson. Also in this scenario, signal cross sections of up to 5 pb can be reached in large parts of unconstrained parameter space. Due to the CP-odd nature of the A boson, its decay width into two photons is enhanced with respect to the corresponding decay width of the h BSM boson in the cH(W h BSM ) scenario.
As in the cH(W h BSM ) scenario, the charged Higgs boson decays dominantly to a non-SM-like CP-even Higgs boson and a W boson in the cH(W h fphob BSM ) scenario reaching signal cross sections of up to 1 pb. In contrast to the previous scenarios, the non-SM-like CP-even Higgs boson is fermiophobic in the cH(W h fphob BSM ) scenario, which results in large branching ratios of the h BSM decays into massive vector bosons and photons.
In the cH(W h light BSM ) scenario the non-SM-like CP-even Higgs boson is much lighter than the SM-like Higgs boson, allowing in principle for decays of the SM-like Higgs boson into two light non-SM-like CP-even Higgs bosons. We, however, showed that this decay mode can be suppressed by suitable parameter choices. In that case, strong constraints on additional decay modes of the SM-like Higgs boson arising from precision rate measurements can be avoided. LHC searches for the charged Higgs boson decay into a light, non-SM-like CP-even Higgs boson and a W boson therefore would provide an important complementary probe of such scenarios. In this scenario, the branching ratio of h BSM to two photons can become quite large, i.e. up to 25 % within the allowed parameter region.
For the cH(W h phil BSM ) scenario, we use the same parameters as in the cH(W h light BSM ) scenario. However, in contrast to all other benchmark scenarios, which are defined in the 2HDM type-I, the cH(W h phil BSM ) scenario is defined in the lepton-specific 2HDM. Consequently, the h BSM boson almost exclusively decays to tau leptons, while the remaining phenomenology is very similar to the cH(W h light BSM ) scenario. We hope that the presented work and in particular the five benchmark scenarios serve as an encouragement as well as an useful set of tools for future experimental searches for bosonic charged Higgs boson decays at the LHC.  [117], the shaded region is the corresponding 1σ uncertainty and the displayed µ h 125 →γγ range corresponds to the 2σ uncertainty region (assuming a Gaussian uncertainty).
A. Benchmark scenarios: di-photon rate of h 125 As discussed in Section 3.1, the presence of the charged Higgs boson can result in deviations of the h 125 di-photon rate even in the exact alignment limit. Fig. 24 shows these deviations for the various benchmark scenarios defined in Section 5: the cH(W h BSM ) scenario (blue), the cH(W A) scenario (orange), the cH(W h fphob BSM ) scenario (green), the cH(W h light BSM ) scenario (dark red), and the cH(W h phil BSM ) scenario (purple). For all these scenarios the di-photon rate of h 125 is suppressed with respect to the SM with the deviations ranging from ∼ 5 % (for the cH(W h phil BSM ) scenario) to ∼ 14 % (for the cH(W h fphob BSM ) scenario). While the deviation is entirely caused by the charged Higgs effects in the cH(W h BSM ) and cH(W A) scenarios, which are defined in the exact alignment limit, the deviations in the other scenarios are also slightly affected by the departure from exact alignment. In the cH(W h fphob BSM ) scenario, c(h 125 tt) ≈ 1.02 and c(h 125 V V ) ≈ 0.98, while the misalignment is even smaller in the cH(W h light BSM ) and cH(W h phil BSM ) scenarios with c(h 125 tt) ≈ 1.002 and c(h 125 V V ) ≈ 0.998.
This suggests that large parts of the considered parameter space can be probed by future Higgs precision measurements (e.g. at the HL-LHC [3]). The deviation of the di-photon rate, however, strongly depends on the value of m 2 12 . Correspondingly, it is possible to define phenomenologically similar benchmark scenarios with smaller (or even positive) deviations of the di-photon rate with respect to the SM.

B. Realizing the fermiophobic limit
The cH(W h fphob BSM ) scenario is defined as a (m h BSM , m H ± ) parameter plane with tan β ∼ 4.9 and cos(β−α) = 0.2 taking fixed values (see Section 5). In order to motivate the choice of tan β and cos(β −α), we show BR(h BSM →f f ) as a function of tan β as well as cos(β −α) for m h BSM = 150 GeV and m H ± = 200 GeV in Fig. 25. All other parameters are chosen as in the cH(W h fphob BSM ) scenario. The shaded regions are excluded by boundedness from below (brown) -excluding the region of tan β 18 -, perturbative unitarity (gray)excluding the region of 6 tan β 17 -, searches for pp → A/h BSM → τ + τ − [202,212] (green) -excluding the region of tan β 2.5 -, searches for pp → h BSM → ZZ [213] -excluding the region of cos(β − α) −0.15 and cos(β − α) 0.25 -as well as h 125 measurements -excluding the region of large | cos(β − α)| and low tan β.
In the still unconstrained parameter region, the fermiophobic limit (see Section 2.3) can be realized either for tan β ∼ 5 or tan β ∼ 17.5. While choosing tan β ∼ 17.5 would allow to approach the alignment more closely, the high tan β value would result in a relatively low charged Higgs production cross section (see Section 4.1). Therefore, we choose tan β ∼ 4.9 for the definition of the cH(W h fphob BSM ) scenario (as marked by the cross in Fig. 25).