Light charged Higgs boson with dominant decay to a charm quark and a bottom quark and its search at LEP 2 and future e + e − colliders

The possibility of a light charged Higgs boson H± that decays predominantly to cb and with a mass in the range 80 GeV ≤MH± ≤ 90 GeV is studied in the context of a 3-Higgs Doublet Model (3HDM). Searches for this decay at the Large Hadron Collider (LHC) do not have sensitivity to this mass region at present. It is shown that the searches for H± at LEP2 could be supplemented by either one or two b-tags, which would enable such large branching ratios for H± → cb to be probed in the above mass region. We comment on the possibility of this 3HDM scenario to explain a slight excess in the searches for H± at LEP2, which is best fit by MH± of around 90 GeV, and discuss the prospects for detecting H± → cb decays at future e+e− colliders. ∗Electronic address: a.g.akeroyd@soton.ac.uk †Electronic address: S.Moretti@soton.ac.uk ‡Electronic address: ms32g13@soton.ac.uk 1 ar X iv :1 90 8. 00 82 6v 1 [ he pph ] 2 A ug 2 01 9


I. INTRODUCTION
The ATLAS and CMS [1,2] collaborations at the CERN Large Hadron Collider (LHC) announced the discovery of a new particle (a spinless boson) with a mass of 125 GeV. The measurements of its properties (couplings, spin etc) are in excellent agreement with those of the Higgs boson of the Standard Model (SM), in which the Higgs boson originates from an SU (2) ⊗ U (1) scalar doublet.
It is possible that the 125 GeV boson is the first scalar to be discovered from a nonminimal Higgs sector. A (singly) electrically charged Higgs boson H ± would represent a distinctive signal of such a structure (see Ref. [3] for a recent phenomenological review) that could include additional doublets, singlets, triplets or combinations thereof. There is considerable interest in Beyond the SM (BSM) scenarios with such a framework for implementing the Higgs mechanism of Electro-Weak Symmetry Breaking (EWSM). Firstly, the SM is nonminimal in both its matter (with three fermionic generations) and gauge (with both strong and EW force mediators) sectors, and so there is no compelling reason to believe that the Higgs sector should be minimal. Secondly, in some BSM scenarios an enlarged Higgs sector is required theoretically (e.g. supersymmetry) or provides an explanation to problems that are not solved in the SM (e.g. necessity of non-zero neutrino masses, requirement of a dark matter candidate, sufficient EW baryogenesis etc).
The 2-Higgs Doublet Model (2HDM) [4,5] has attracted the most attention among models with additional scalar doublets. Two (softly-broken) discrete Z 2 symmetries are imposed in order to ensure that each fermion-type couples to no more than one scalar doublet, leading to four distinct 2HDMs that differ in their Yukawa couplings. This framework, referred to as "Natural Flavour Conservation" (NFC) [6], is invoked in order to avoid Flavour Changing Neutral Currents (FCNCs) that are mediated at tree-level by neutral scalars. More recently, 3-Higgs Doublet Models (3HDMs) have received increased attention (see, e.g. Refs. [7,8] for mini-reviews), with NFC leading to five distinct 3HDMs.
Regarding the particle content of the 3HDM there are two physical charged Higgs bosons (hereafter denoted by H ± and H ± , with M H ± < M H ± ). More parameters determine the phenomenology of the charged Higgs sector than in 2HDMs, and we make the assumption that all three Higgs doublets have a Vacuum Expectation Value (VEV). In Refs. [9][10][11][12][13], the phenomenology of H ± in 3HDMs has been studied (with decoupled H ± ) in terms of effective Yukawa couplings for the down-type quark, up-type quark and charged lepton, which are expressed as a function of four independent parameters [11] in the framework of NFC. It has been shown that a H ± can be lighter than the top quark (with H ± heavier) while satisfying constraints from B → X s γ (even for the Yukawa coupling combinations that would not permit this scenario in the 2HDM) due to the increased number of parameters in the 3HDM and the presence of two charged scalars. Moreover, it was shown in Refs. [9,10,12,14] that the decay channel H + → cb can have a large Branching Ratio (BR) (up to 80%) in a 3HDM. Although such a value for this BR is theoretically allowed in the flipped 2HDM for M H ± < m t − m b [10], the constraint M H ± > 480 GeV from B → X s γ rules out this possibility. Hence a large BR(H + → cb) is a distinctive signature of 3HDMs.
The above scenario of a 3HDM in which there is a light H ± with a large BR to cb is the focus of this work. We consider the mass range M H ± ∼ M W ± for which detection of H ± is challenging if its BRs to hadrons are dominant. The LHC has carried out searches at √ s = 8 TeV for H ± → cb [15] and H ± → hadrons [16,17], assuming production via the mechanism t → H ± b, and the former search employs one more b-tag than the latter search. In Ref.
[18] the parameter space in the flipped 3HDM that will be excluded (or provide a signal) at upcoming searches was displayed. At present, the LHC has not set limits in the region 80 GeV ≤ M H ± ≤ 90 GeV if BR(H + → cb) or BR(H + → cs) is dominant, although limits are set for the case of H ± → τ ν being the leading decay channel. As discussed in [18], with the increased luminosity for the data taken at √ s = 13 TeV and with future data it is likely that the LHC will be able to set limits on of the region 80 GeV ≤ M H ± ≤ 90 GeV (and possibly in the case of the H + → cs channel as well). However, the production mechanism relies on the Yukawa couplings and thus such an H ± could escape detection at the LHC if these couplings are small. Consequently, it is of interest to study in more detail the CERN LEP2 searches for a hadronically decaying H ± , for which the main production mode of e + e − → H + H − depends only on gauge couplings and M H ± .
We will show that data taken at LEP2 when supplemented by b-tagging could discover or exclude a light H ± state decaying to cb pairs more efficiently than LHC searches in the region 80 GeV ≤ M H ± ≤ 90 GeV. Before the LEP2 era this possibility was pointed out for models with more than two Higgs doublets in Refs. [10,14], although the brief quantitative study in [14] (that was based on a simulation in [19]) concluded that sensitivity would not be reached in the region 80 GeV ≤ M H ± ≤ 90 GeV. Such a b-tag was never implemented in LEP2 searches for H ± states. We revisit it here in the context of the flipped 3HDM and show that by using b-quark tagging and light-quark rejection efficiencies from the LEP2 searches one can substantially improve the sensitivity to H ± → cb compared to that for H ± → hadrons, and probe the region 80 GeV ≤ M H ± ≤ 90 GeV. Attention is also given to the detection prospects for H ± → cb at future e + e − colliders operating at √ s = 240 GeV.
The plan of this paper is as follows. In section II the 3HDM is introduced. In section III the LEP2 search for H ± with the addition of b-tagging is described, with numerical results and conclusions in sections IV and V respectively.

II. THE 3HDM WITH NFC
In this section we give a brief introduction to the interactions of the lightest H ± in the 3HDM that are relevant to our analysis. We will only consider M H ± < m t and we assume that the only channels that have non-zero BRs are the decays to fermions (i.e. decays of the type H ± → W ± plus a neutral Higgs boson are forbidden by setting the masses of all the neutral Higgs bosons to be above that of the charged Higgs). For a more detailed introduction the reader is referred to [11,13].
Any extension of the SM Higgs sector is primarily constrained by two experimental facts.
Firstly, the measurement of ρ = m 2 W /(m 2 Z cos 2 θ W ) is close to 1 [4], where m W , m Z and θ W are the W, Z masses and weak mixing angle, respectively. Secondly, tree-level FCNCs that are mediated by the additional neutral scalars must be suppressed (or absent). In order for the 3HDM to comply with both of the above restrictions one requires i) no very large mass splittings between the neutral and charged scalars in order to respect ρ parameter bounds, and ii) to implement NFC [6] in order to eliminate tree-level FCNCs. Under such conditions, the part of the Yukawa Lagrangian containing the lightest charged Higgs boson interactions with the fermions can be written as follows: Here u(d) is denotes up(down)-type quarks and represents charged leptons, P L(R) is the Left(Right)-handed projector, V ud is the relevant Cabibbo-Kobayashi-Maskawa (CKM) matrix element, and v SM is the VEV of the Higgs doublet in the SM. In the 3HDM, the couplings X, Y and Z are functions of the four parameters (see below) of a unitary matrix U that connects the charged scalar interaction eigenstates to the physical mass eigenstates as follows:  Here H + , H + are physical charged scalars whereas G + is a charged Goldstone boson that will become the longitudinal component of the W ± gauge boson after EWSB. The matrix U is a 3 × 3 unitary matrix and can be parametrised as a function of four parameters, tan β, tan γ, θ, and δ. The first two parameters are defined via where v 1 , v 2 , and v 3 are the VEVs of each Higgs doublet. The parameter θ is a mixing angle between the two massive charged scalars and δ is a CP-violating phase. The explicit form of U is as follows [11]: where s(c) are represents the sine(cosine) of the respective angle.
The interactions between the lightest charged Higgs state of the 3HDM, H ± , and the SM fermions is obtained via the U matrix as [9] where the values of d, u, and in these matrix elements are given in Tab. I and depend upon which of the five possible distinct 3HDMs is under consideration. Taking d = 1, u = 2 and = 3 means that the down-type quarks receive their mass from v 1 , the up-type quarks from v 2 and the charged leptons from v 3 . This choice is called the 'Democratic 3HDM' while the other possible choices of d, u and in a 3HDM are given the same names as the four standard types of 2HDM [5].
The experimental constraints on X, Y and Z [20,21] have been summarised in Ref. [18], to which we refer the reader. The parameter space of the 3HDM that is relevant to this work  is compliant with all such limits, the most important of which being −1.1 < Re(XY * ) < 0.7 for M H ± < 100 GeV. This is an approximate constraint that is derived from b → sγ, and neglects the contribution of the heavier H ± in a 3HDM.
In a 3HDM, the expressions for the partial widths of the decay of H ± to fermions are as follows: In the expression for Γ(H ± → ud) the running quark masses should be evaluated at the scale of m H ± , and there are QCD vertex corrections which multiply the partial widths by (1+17α s /(3π)). The first study of the fermionic BRs of H ± as a function of |X|, |Y |, and |Z| was given in [10], with further studies in [12]. In [13,18] these BRs were studied as a function of tan β, tan γ, θ, and δ, an approach which allows the BRs in the five versions of the 3HDM to be compared. For |X| |Y |, |Z| the decay channel BR(H ± → cb) dominates (which was first mentioned in [9]), and reaches a maximum of ∼ 80%. It was shown in [13,18]  with NFC the only model which contains a parameter space for a large BR(H ± → cb) with M H ± < m t is the flipped model (a possibility that was mentioned in [9,10] and studied in more detail in [22]). However, for this particular choice of 2HDM the b → sγ constraint would require M H ± > 500 GeV [23,24] for which H ± → tb would dominate.

ATLAS CMS
7 TeV (5 fb −1 ) cs [16], τ ν [26,27] τ ν [25] 8 TeV (20 fb −1 ) τ ν [28] cs [17], cb [15], τ ν [29] 13 TeV (36 fb −1 ) τ ν [31] τ ν [30]  In this paper we will focus on the case of m H ± < m t , a scenario in which production at the LHC via t → H ± b would be possible. Searches for three decays channels of H ± have been carried out (see Tab. II). The searches for H ± → τ ν constrain the product in the region 80 GeV< M H ± < 160 GeV, with the upper limit ranging from < 0.36% for M H ± = 80 GeV to < 0.08% for M H ± = 160 GeV. The searches for H ± → cs constrain the product BR(t → H ± b) × BR(H ± → cs) in the region 90 GeV< M H ± < 160 GeV, with the upper limit ranging from < 5% for M H ± = 90 GeV to < 2% for M H ± = 160 GeV. Note that this search would be sensitive to any quark decay (except t) of H ± . The search for H ± → cb (which employs one more b-tag than the search for H ± → cs) constrains the product BR(t → H ± b) × BR(H ± → cb), with the upper limit ranging from < 1.4% for M H ± = 90 GeV to < 0.5% for M H ± = 150 GeV. The searches for H ± → cs and H ± → cb do not set limits on the region 80 GeV< M H ± < 90 GeV, although this might be possible (especially for H ± → cb) with larger integrated luminosities. Earlier searches for the decay t → H ± b were carried out at the Fermilab Tevatron in [32,33].
At LEP2 the production process σ(e + e − → γ * , Z * → H + H − ) was used, which depends on only one unknown parameter, M H ± . Searches were carried out at all four experiments [34][35][36][37] at energies in the range √ s = 183 GeV to √ s = 209 GeV, each with an integrated luminosity of roughly 0.6 fb −1 . The LEP working group [38] combined these individual searches, resulting in a cumulative integrated luminosity of 2.6 fb −1 . Dedicated searches for the decay mode H ± → A 0 W * were also carried out in [34,37], but in this work we are assuming that this channel is absent or very suppressed. From the combination of the searches for fermionic decays, and with the assumption that BR( is obtained in [38]. For M H ± < 80 GeV the whole range 0 ≤ BR(H ± → τ ν) ≤ 100% is excluded. For 80 GeV ≤ M H ± < 90 GeV, most of the region is not excluded for BR(H ± → τ ν) < 80% (i.e. for BR(H ± → cs) > 20%). We will focus on this region of 80 GeV ≤ M H ± < 90 GeV and the case of a large hadronic BR for H ± , which is not being probed by the LHC at present.

III. SEARCH FOR H ± AT LEP2
At LEP2 it was assumed that the dominant decay channels were H ± → cs and H ± → τ ν, which leads to the following three signatures from H + H − production: cscs, csτ ν, τ ντ ν. The decay of H ± → cb was not explicitly searched for at LEP2 [34][35][36][37]. It is the searches in the hadronic channels cscs and csτ ν that are relevant for the decay H ± → cb, and these are discussed in more detail below.
i) 4-jet channel: This signature arises when H + and H − both decay into quarks, giving four quarks that will usually be detected as 4 jets. For H ± in the kinematical range of LEP2 (i.e. M H ± < √ s/2 ≈ 100 GeV) there are six possible hadronic decay channels of H ± . Decays involving the t quark (e.g. H ± → t * b) are extremely suppressed due to the t quark being very off-shell, and can be neglected. In the LEP searches it was assumed that H ± → cs is the dominant hadronic decay mode, which is true in most 2HDMs, and the experimental limits on BR(H ± → hadrons) were interpreted as limits on BR(H ± → cs). However, the 4-jet search as carried out by three of the LEP collaborations (OPAL [34], ALEPH [35], L3 [36]) was sensitive to any of the allowed six decay channels into quarks. In contrast, the search by the DELPHI collaboration [37] used c-tagging to discriminate against lighter quarks and b quarks. Consequently, this search strategy would be less sensitive to the decay H ± → cb than the searches by the other three collaborations.
ii) 2-jet+τ ν channel: This signature arises when one H ± decays into quarks and the other H ± decays into a τ lepton and a neutrino. Again, it was assumed that H ± → cs is the dominant hadronic decay mode, and the DELPHI collaboration alone used c-tagging.
In this work we quantify the effect of applying one (or more) b-tags to both of the above search strategies in order to increase the sensitivity to the decay H ± → cb, which can have a large BR in the flipped and democratic 3HDMs. In the 4-jet channel the separate cases of exactly one tagged b-jet and exactly two tagged b-jets will be considered. In the 2-jet+τ ν channel the case of exactly one tagged b-jet will be considered. A b-tag requirement usually involves a cut on the impact parameter of a jet [39]. Due to the longer lifetime of the b quark, a jet that has originated from a b quark will (on average) have a larger impact parameter than a jet that originated from a lighter quark. Additional discriminating variables are sometimes used in the full b-tag requirement. The three dominant decay channels of H ± in the 3HDMs that we study are BR(H ± → cb), BR(H ± → cs) and BR(H ± → τ ν). These will be denoted below by BR cb , BR cs , and BR τ ν respectively.

A.
Signal for H ± → cb with b-tags at LEP2 The number of e + e − → H + H − events (with no b-tag requirement) in the LEP2 searches in the 4-jet and 2-jet+τ ν channels are denoted by S 4jnobtag and S 2jτ nobtag respectively, and are given as follows: Note that BR cb and BR cs are summed, because the search strategy does not apply a b-tag.
Here σ is the cross-section for pair production of H + H − at a particular centre-of-mass energy √ s, and L is integrated luminosity at that energy. The searches for H + H − at LEP2 were carried out using data taken at eight different values of √ s, each with a unique value of integrated luminosity L. Hence the product σL is actually a sum 8 i=1 σ i L i where each i denotes a specific value of √ s. The parameters 4jnobtag and 2jτ nobtag are the selection efficiencies for the cuts as used in the LEP searches for the 4-jet signature and the 2-jet+τ ν signature respectively. For the magnitude of these efficiencies we will use the numerical values obtained in the search by OPAL (similar values were obtained by the other three collaborations). We now discuss in turn three proposed search strategies for the decay H ± → cb that make use of b-tagging.

Signal in 4-jet channel with exactly two b-tagged jets
A maximum of two b quarks can be produced when both charged scalars decay via H ± → cb. However, lighter quarks (u, d, s, c) can fake b quarks, and so up to four jets could be recorded as b-jets by a detector. In the numerical analysis for LEP2 the b-tag efficiency ( b ) is taken to be b = 0.7, while the fake b-tag efficiencies for charm quarks ( c ) and u, d, s quarks ( j ) are c = 0.06 and j = 0.01 respectively. These numbers are roughly similar (although slightly optimistic for b ) to those in the OPAL measurement of R b in [40] for √ s = 183 GeV to 209 GeV. Due to c and j being small we will not consider the signatures of three or four tagged b-jets, in which one or two non-b quarks have been mistagged as b quarks. We first consider the channel in which exactly two of the four jets are tagged as b jets. The number of such events is denoted by S 4j2btag , and is given by the following expression: The factor of 2 accounts for the cbcs andcbcs signatures. This expression for S 4j2btag is obtained from the expression for S 4jnobtag , with the effect of the b-tagging requirement contained in the parameters cbcb 4j2btag , cbcs 4j2btag and cscs 4j2btag that are given explicitly as follows: Inserting the above values for b , c and j gives numerical values of roughly 0.48, 0.04 and 0.004 for cbcb 4j2btag , cbcs 4j2btag and cscs 4j2btag respectively. Note that the three terms in cbcb 4j2btag correspond to the cases of the two tagged b-jets originating from i) two real b quarks, ii) one real b quark and one fake b quark (i.e. a mistagged c quark), and iii) two fake b quarks.
In cbcs 4j2btag the first two terms correspond to the case of the two tagged b-jets originating from one real b quark and one fake b quark, and the last two terms are for the case of two fake b quarks. In cscs 4j2btag the only contributing terms are from two fake b quarks. Factors of 2 or 4 in these expressions account for the various combinations that contribute (e.g. cs andcs being the fake b-tags in the third term in cbcs 4j2btag , leading to a factor of 2).

Signal in 4-jet channel with exactly one b-tagged jet
The number of 4-jet events in which exactly one of the jets is tagged as a b quark is denoted by S 4j1btag , and is given by the following expression: The explicit expressions for cbcb 4j1btag , cbcs 4j1btag and cscs 4j1btag (which are different to those for the two b-tag case) are as follows: Inserting the values for b , c and j gives numerical values of roughly 0.38, 0.64 and 0.13 for cbcb 4j1btag , cbcs 4j1btag and cscs 4j1btag respectively.

Signal in 2-jet plus τ ν channel with exactly one b-tagged jet
The number of 2-jet + τ ν events in which exactly one of the jets is tagged as a b quark is denoted by S 2jτ 1btag , and is given by the following expression: The explicit expressions for cbτ ν 2jτ 1btag and csτ ν 2jτ 1btag are as follows: The numerical values of cbτ ν 2jτ 1btag and csτ ν 2jτ 1btag are roughly 0.68 and 0.07 respectively.
B. Background to H ± → cb decay The backgrounds for the above three channels are denoted by B 4j2btag , B 4j1btag and B 2j+τ 1btag respectively. The main contributions to B 4j2btag and B 4j1btag are from 4 fermion production (mainly W + W − production, with a smaller contribution from ZZ) which we neglect) and from 2-fermion production (e.g. e + e − → γ * , Z * → qqgg), which can give four jets. The main contribution to B 2jτ 1btag is from W + W − production.
To evaluate the background before imposing b-tagging we again use the numbers in the OPAL search paper. For simplicity we assume a diagonal CKM matrix, and take BR(W ± → cs) = BR(W ± → ud) = 35%. OPAL had around 1100 4-jet events after all cuts, of which 90% are expected to be from 4-fermion events. With the assumption of a diagonal CKM matrix this background would be composed of 250 cscs events, 250 udud events and 500 csud events. Given these numbers, it turns out that the contributions to the background from W ± → cb decays can be neglected because its branching ratio is about 600 times smaller than that of W ± → cs. The contribution of W + W − → cbcb to the background would be much less than one event (= 250/600 2 ), and the contributions from W + W − → cbcs and W + W − → cbud would each be less than one event (= 500/600), before b-tagging is imposed.

Background to 4-jet channel with exactly two b-tagged jets
The 4-fermion background to the 4-jet signal with two tagged b quarks is given by: The explicit expressions for W cscs 4j2btag , W csud 4j2btag and W udud 4j2btag are as follows: The numerical values of W cscs 4j2btag , W csud 4j2btag and W udud 4j2btag are 0.006, 0.002 and 0.0004 respectively, giving B 4f ermion 4j2btag ≈ 2.
OPAL had around 100 4-jet events that originated from 2-fermion events. Around 15 of these would be bb events, due to σ(e + e − → bb)/σ(e + e − → uū, dd, ss, cc, bb) being roughly 0.15 at √ s = 200 GeV. We estimate the 2-fermion background to the 4-jet signal with two tagged b quarks to be: This is around 7 events. The contribution to the 2-fermion background from cc events would be around 15 2 c and is much smaller than one event. The total background (B 4j2btag ) to the signal with 4-jets and two tagged b quarks (S 4j2btag ) is: Since B 4f ermion 4j2btag is around 2 events, then the dominant background is from the 2-fermion events.
2. Background to 4-jet channel with exactly one b-tagged jet The 4-fermion background to the 4-jet signal with one tagged b-jet is given by: The explicit expressions for W cscs 4j1btag , W csud 4j1btag and W udud 4j1btag are as follows: The numerical values of W cscs 4j1btag , W csud 4j1btag and W udud 4j1btag are 0.13,0.08 and 0.04 respectively. We estimate the 2-fermion background (from bb production) to the 4-jet signal with one tagged b quark to be: This is about 6 events, but is much less than the 4-fermion background, which is of the order of 90 events. We neglect the contribution to the 2-fermion background from cc events, which would be 30 c (1 − c ) and equal to around 1.7 events. Similar to before, one has: 3. Background to 2-jet plus τ ν channel with exactly one b-tagged jet The background to the 2-jet plus τ ν channel with exactly one b-tagged jet is dominantly from 4-fermion production, and is given by: The explicit expressions for W csτ ν 2jτ 1btag and W udτ ν 2jτ 1btag are as follows: The numerical values of W csτ ν 2jτ 1btag and W udτ ν 2jτ 1btag are 0.07 and 0.02 respectively.

IV. NUMERICAL RESULTS
We now present our results for the statistical significances of a signal for H ± → cb at  A. Enhancing the detection prospects for H ± → cb at LEP2 by using b-tags The BRs of H ± as functions of the four parameters (tan β, tan γ, θ, δ) have been studied in detail in [18], and the parameter space for a dominant BR(H ± → cb) > 50% was displayed.
In Fig. 1 [18]. This parameter choice for θ and δ will be used in Fig. 1 to Fig. 7, with all these plots being shown in the plane [tan γ, tan β]. In Fig. 1 Fig. 1 (left panel) are permissible.
In Fig. 2 (left panel) and Fig. 2 (right panel) contours of BR(H ± → cs) and BR(H ± → τ ν) (respectively) are displayed. For this choice of θ = − π 2.1 and δ = 0 one can see that BR(H ± → cs) ≈ 35% and BR(H ± → τ ν) ≈ 65% when BR(H ± → cb) is small (corresponding to small tan β and tan γ). In Fig. 3 the sums and products of BRs of H ± are displayed, which will  aid the understanding of the statistical significances that are displayed in Fig. 4 to Fig. 7. In shown. Note that BR(H ± → cb) × BR(H ± → τ ν) is maximised (taking a value of around 0.14) in a band that is away from the region of both tan β and tan γ being small or large.
In Fig. 8  is used for illustration, and is larger than the maximum value of this product in Fig. 3 (bottom panel) with θ = −π/2.1 and δ = 0. Again, one sees a roughly linear dependence on M H ± . In Fig. 10 in [34] we estimate that such a cut could reduce the 2-fermion background by a factor of 2, while preserving the majority of the signal events of an H ± with a mass between 80 GeV and 89 GeV. In Fig. 11 the effect of the invariant mass cut efficiency ( mass ) on S √ B in  experiments [38].   and BR(H ± → τ ν) = 35%, and in our earlier work [13,18] we suggested the possibility of this being due to an H ± of a 3HDM. If such an excess is genuine, and if a large fraction of the hadronic BR is from H ± → cb decays, then b-tagging would increase the significance.
In Tab if the excess is genuine then its significance could be significantly increased in the 4j2b and 2j1b channels, assuming that BR(H ± → cb) is large. As discussed in [18] [42] and FCC-ee [43] at CERN. These colliders would produce a large number of H + H − events with a mass of up to M H ± = 120 GeV. The integrated luminosity at this energy is expected to be of the order of a few ab −1 , which is roughly a thousand times larger than the total integrated luminosity taken at a single LEP2 experiment (0.6 fb −1 ). Two linear e + e − colliders are also being   discussed, the International Linear Collider (ILC) [44] and the Compact Linear Collider (CLIC) [45], which will both offer the possibility of energies much higher than √ s = 240 GeV. In this work we will consider the detection prospects of the decay channel H ± → cb In Fig. 12  GeV could be probed at LEP2 by adding one or more b-tags to the existing search strategy.
We evaluated the significances (S/ √ B) for H ± → cb decays in three channels by taking the selection efficiencies and backgrounds from the OPAL searches, and applying realistic b-tagging and fake b-tagging efficiencies. In the optimum scenario of BR(H ± → cb) = 80% (BR(H ± → cb) = 40% for 2-jets), it was shown that S/ √ B as large as 7, 3 and 4 could be obtained for M H ± = 80 GeV in the three channels i) 4-jet plus two b-tags, ii) 4-jet plus one btag, and iii) 2-jets plus one b-tag, respectively. These significances decrease to roughly 3, 1.4 and 1.7 respectively for M H ± = 89 GeV, but would be increased by combining all four experiments. Consequently, LEP2 has the capability to exclude or discover a H ± with a large BR(H ± → cb), and with a mass in the region 80 GeV ≤ M H ± ≤ 90 GeV. We commented on a > 2σ excess at around M H ± = 89 GeV and BR(H ± → hadrons) ≈ 65% in the LEP working group combination. Under the assumption that such an excess is genuine and has a large BR(H ± → cb), it was shown that its significance could be increased significantly in two of the three channels with b-tagging. We encourage an updated LEP2 search for H ± that includes b-tagging as suggested above. This would become especially important if the LHC eventually obtains evidence for an H ± with 80 GeV ≤ M H ± ≤ 90 GeV and a large BR(H ± → cb).
In contrast to hadron colliders, the cross-section for H ± at LEP2 does not depend on the magnitude of the Yukawa couplings. Hence a light H ± with small Yukawa couplings could escape detection at the LHC, but be discovered at LEP2 or at future e + e − colliders. Even if a light H ± is discovered at the LHC, future e + e − colliders would be able to measure its BRs much more precisely in order to shed light on the underlying Higgs structure. We evaluated S/ √ B for H ± → cb decays at a proposed e + e − collider (CEPC/FCC-ee) of √ s = 240 GeV and found that BR(H ± → cb) = 1% (which is possible in all 2HDMs/3HDMs) would give a clear signal. In the context of 3HDMs, the flipped and democratic structures are the only ones which can have BR(H ± → cb) significantly greater than 1%, and so precise measurements of this channel could provide evidence for these models.