Let there be light from a second light Higgs doublet

In this article, we demonstrate that the unexpected peak at around $95 \, {\rm GeV}$ as seen recently by CMS in the di-photon final state can be explained within the type-I~two-Higgs-doublet model by means of a moderately-to-strongly fermiophobic CP-even Higgs $H$. Depending on the Higgs mass spectrum, the production of such~a~$H$ arises dominantly from vector boson fusion or through a cascade in either $pp \to t \bar t$ with $\overset{(-)}{t} \to H^{\pm} \overset{(-)}{b} \to W^{\pm \, \ast} H \overset{(-)}{b}$ or $pp \to A$ with $A \to W^{\mp} H^{\pm} \to W^{\mp} W^{\pm} H$ or via $pp \to W^{\pm \, \ast} \to H^\pm H$. In this context, we also discuss other Higgs anomalies such as the LEP excess in Higgsstrahlung and the observation of enhanced rates in $t \bar t h$ at both the Tevatron and the LHC, showing that parameters capable of explaining the CMS di-photon signal can address the latter deviations as well. The Higgs spectra that we explore comprise masses between $80 \, {\rm GeV}$ and $350\, {\rm GeV}$. While at present all constraints from direct and indirect searches for spin-0 resonances can be shown to be satisfied for such light Higgses, future LHC data will be able to probe the parameter space that leads to a simultaneous explanation of the discussed anomalies.

cascade decays of charged Higgses H ± or neutral CP-odd states A and associated H ± H production, with gg → H always accounting only for a subleading part of the total rate. Also the decays of the H and the other spin-0 states turn out to have unfamiliar features, which we illustrate by discussing four different benchmark scenarios. These benchmark scenarios all have in common that they feature a light spectrum of Higgses with masses not exceeding 350 GeV. We explicitly show that in all four cases the chosen parameters are compatible with the existing direct and indirect constraints on the type-I 2HDM parameter space. While this study was ongoing, a similar investigation of the CMS di-photon excess in the context of the type-I 2HDM has been presented in [15]. Whenever indicated we will highlight the similarities and differences between this and our work.
The outline of this article is as follows. In Section 2 we first recall briefly the structure of the type-I 2HDM and then discuss in Section 3 four benchmark scenarios that render consistent explanations of the recent CMS di-photon excess as well as some of the LEP, Tevatron and the other LHC anomalies mentioned above. For each benchmark scenario we also discuss strategies of how-to test it at future LHC runs. Our conclusions are presented in Section 4.

Type-I 2HDM in a nutshell
The 2HDM scalar potential that we will consider throughout this work is given by the following expression (see for example [16,17] for a review) Here we have imposed a Z 2 symmetry under which H 1 → H 1 and H 2 → −H 2 . The parameters µ 1,2 and λ 1,2,3,4 are real, while µ 3 and λ 5 are in general complex. To avoid possible issues with electric dipole moments, we assume in what follows that µ 3 and λ 5 have no imaginary parts. This automatically ensures that the potential is CP conserving, i.e. the mass eigenstates have definite CP properties. In addition, by appropriately charging the right-handed fermions, the Z 2 symmetry can also be used to obtain one of the four 2HDMs with natural flavour conservation, eliminating phenomenologically dangerous tree-level flavour-changing neutral currents. The discrete symmetry is however softly broken by the term µ 3 H † 1 H 2 + h.c. The vacuum expectation values (VEVs) of the Higgs doublets are given by 246 GeV the electroweak VEV and we define tan β = v 2 /v 1 .
The potential (2.1) gives rise to five physical spin-0 states: two neutral CP-even ones (h and H), one neutral CP-odd state (A), and the remaining two carry electric charge of ±1 and are degenerate in mass (H ± ). We identify the 125 GeV resonance discovered at the LHC with the CP-even Higgs h while the masses of the other scalars are free parameters. The angle that mixes the neutral CP-even weak eigenstates into the mass eigenstates h and H will be denoted by α. Diagonalising the masssquared matrices of the scalars leads to relations between the fundamental parameters of V H and the physical masses and mixing angles. This allows one to trade the parameters µ 1 , µ 2 , µ 3 , λ 1 , λ 2 , λ 4 , λ 5 for α, β, M h , M H , M A , M H + and v. The only remaining free parameter of the original Higgs potential entering our calculations is λ 3 . We will use it together with the latter parameters as input in our numerical analysis.  Figure 1. Exotic H production channels through cascades or in association with a charged Higgs. The left Feynman diagram shows the process gg → tt followed by t → H + b (H + → W + H), the middle graph illustrates the reaction gg → A with A → W − H + (H + → W + H), while the diagram on the right corresponds to the transition qq → W + → H + H.
In all 2HDMs with CP conservation the tree-level couplings of the CP-even Higgs mass eigenstates to gauge bosons are given relative to the coupling of the SM Higgs by where V = W, Z. The fermion couplings to h, H, A and H + instead depend on the specific realisation of the Yukawa sector. In the type-I 2HDM the neutral Higgs couplings are relative to the SM and the couplings of the charged Higgses to fermions resemble those of the CP-odd Higgs. Notice that the interactions of h become SM-like, i.e. κ h f → 1, in the limit α → 0 and β → π/2. Furthermore, the CP-even Higgs H does not couple to fermions (i.e. fermiophobic) for α = 0, while it does not couple to gauge bosons (i.e. gaugephobic) for α = β ± π/2.

Numerical analysis
In the following, we will show that the type-I 2HDM provides an economic explanation of the small CMS excess in the di-photon mass spectrum at around 95 GeV [13,14] in terms of a moderately-tostrongly fermiophobic H, i.e. models with small values of α. We find that depending on the choice of mixing angles α and β as well as the masses M A and M H + , the production of such a H proceeds dominantly either via the vector boson fusion (VBF) and associated (WH and ZH) channels [18] or through a cascade in either pp → tt with If the charged Higgs is very light associated H production via pp → W ± * → H ± H [20,21] can also be the most important production mode. Gluon fusion (ggH) instead accounts only for a subleading fraction of the total H production in all cases. Examples of Feynman graphs that can give rise to H production in 2HDMs via a cascade or in association with a charged Higgs are displayed in Figure 1. We emphasise that while the first two aforementioned production mechanism have been discussed in [15], the third and fourth channel has not been considered in the latter paper -the possible importance of cascades and associated H ± H production in 2HDMs has however been stressed before in the literature [19][20][21][22][23][24][25][26]. In order to illustrate the four production mechanism and the resulting phenomenology, we discuss a specific benchmark scenario in each case. The discussed type-I 2HDM benchmarks are tailored to provide explanation of other small anomalies as seen at LEP, the Tevatron and the LHC, while being consistent with a plethora of null results.

Diamond benchmark scenario
The choice of parameters in the first type-I 2HDM benchmark scenario is In Figure 2 we show in colour the regions in the sin α -tan β plane that are allowed/favoured if the masses M H , M A , M H + and the quartic coupling λ 3 are fixed to the values given in (3.1) and the mixing angles α and β are varied. The red exclusion represents the ∆χ 2 = 5.99 contour (corresponding to a 95% confidence level (CL) for a Gaussian distribution) that follows from a χ 2 analysis of the combined LHC Run-I data on Higgs production and decay rates [1] excess [13]. From the location of the diamond it is evident that the benchmark scenario (3.1) accommodates the anomalies in both e + e − → ZH and pp → H → γγ, while simultaneously leading to an acceptable global Higgs fit.
The two panels in Figure 3 show the fractional contributions σ X H /σ H of each channel to H production (left panel) and the branching ratios of H (right panel) for the parameters specified in (3.1). Our calculation of σ X H and BR X H relies on the results presented in [27] and [28,29], respectively. From the left pie chart one infers that for the first benchmark scenario 74.9% of the total cross section σ H = 1.0 pb is due to the VBF, WH and ZH channels, while only 20.5% arise from ggH production. The pie chart on the right-hand side depicts the corresponding H branching ratios. We see that the five largest branching ratios are the ones to bottom quarks (67.8%), W bosons (10.1%), taus (6.9%), photons (5.6%) and gluons (5. It turns out that apart from [13] other existing LHC searches for neutral spin-0 resonances that probe the mass range to 100 GeV and below (see [30][31][32][33]) are not sensitive to a H with such properties. To be more specific the ATLAS di-photon search [30] sets an upper 95% CL limit on s Compared to the di-tau signal strength given in the last paragraph this bound is weaker by a factor of more than 500. Searches for light Higgses in pp → bbHX (H → bb) [32,33] are even less sensitive than the considered di-photon and ditau analyses. We add that the decay products in H → bb could in principle be reconstructed as a single, large radius high-p T jet and identified using jet substructure and dedicated b-tagging techniques. In fact, such a study has been recently performed by CMS [34], observing (bounding) Z → bb (h → bb) decays in the single-jet topology for the first time. However, the large Z → bb background and the poor mass resolution of the reconstructed jet mass suggest that detecting the small pp → H → bb signal expected in (3.1) is impossible at the LHC even at high luminosity. Beside a H with a mass of 95 GeV our first type-I 2HDM benchmark scenario (3.1) also contains a relatively light A and H + . The only existing LHC analyses that allow to constrain an A with a mass of 200 GeV are the A → τ + τ − searches [31,35]. The corresponding constraints are indicated in the upper left panel of Figure 4 by the blue and purple curve, respectively.The predictions for A production in gg → A have been obtained at next-to-next-to-leading order in QCD with HIGLU [36]. One sees that for M A = 200 GeV only values of tan β < 0.7 are excluded at 95% CL. The benchmark scenario (3.1) however employs tan β = 4.5 and is thus clearly allowed.
Direct limits on charged Higgs masses above the top threshold are due to the LHC searches for H + → tb (for the latest √ s = 13 TeV analysis see [40]) while indirect constraints on M H + are provided by B → X s γ [43][44][45], B-meson mixing [46][47][48][49] as well as B s → µ + µ − [41,42,50,51], but also follow from Z → bb [52][53][54] and the ρ parameter (the relevant formulas can be found in [29] for instance). The most stringent constraints on the M H + -tan β plane for the case of the type-I 2HDM are summarised in Figure 5. The results for the H + production cross sections are taken from [27]. The constraints that apply in the case of (3.1) are shown in the left panel of the figure. One observes that the measurements of B s → µ + µ − [41,42] provide at present the strongest limits on tan β for most charged Higgs masses. Numerically, we find for M H + = 250 GeV the bound tan β > 2.8, which does not rule out the choice of tan β made in (3.1). Improved LHC searches for B s → µ + µ − should however be able to exclude or find evidence for scenarios with tan β 4 and a charged Higgs with a mass not too far above the top threshold.
Since the charged Higgses couple to the CP-even spin-0 states, a lightish H + in general also modifies Γ (h → γγ) and Γ (H → γγ). The size of the modifications is however model dependent, because the form of the trilinear couplings λ hH + H − and λ HH + H − depends sensitively on the choice of the scalar potential. For our potential (2.1) it is always possible to arrange for the parameter we find that charged Higgs loops suppress Γ (h → γγ) by around 15% with respect to the case when only top and W-boson loops are considered. Since the effects of charged Higgs loops are non-negligible for the parameter choices (3.1), we have, unlike [15], included them in Figure 2 and in the right pie chart of Figure 3. We furthermore note that that for the adopted values of M H , M A , M H + and λ 3 , one can show (cf. [55]) that the resulting Higgs potential (2.1) is bounded from below and that the constraints arising from the ρ parameter are satisfied within 2σ, i.e. the value of ∆ρ = ρ − 1 falls into the range [−1.2, 2.4] · 10 −3 [56].

Star benchmark scenario
The second type-I 2HDM benchmark scenario that we study in detail is defined by The constraints on this benchmark scenario following from a global fit to the LHC Run-I Higgs data (red), the region favoured by the LEP anomaly in e + e − → ZH (blue) as well as the di-photon excess observed at CMS (green) are shown in Figure 6. The horizontal band (purple) corresponds to tan β values in the range of [4,6], which have been shown in [19] to be favoured by the leptonic excess in tth production as seen by ATLAS in the √ s = 13 TeV data [11]. The depicted constraints are obtained by fixing M H , M A , M H + and λ 3 to the values quoted above and varying α and β. The star indicates the choice of sin α and tan β made in (3.2). Since it is located in the overlap of all four shaded regions, it is not only consistent with the combined LHC Run-I Higgs data, but at the same time also fits the deviations seen in e + e − → ZH, pp → H → γγ and pp → tth.     Figure 1. In our numerical analysis, we employ the values 829 pb [57] and 288 pb [58] for the top-pair and single-top production cross section, respectively. These numbers correspond to pp collisions at √ s = 13 TeV. The dominance of cascade H production for the parameter choices (3.2) is easy to understand by analysing the M H + -dependence of BR X t and BR X H + . We show the relevant branching ratios in the left panel of Figure 8. Our calculation of the branching ratios is based on the formulas given in [19,29,59]. One observes that while BR H + b t decreases from around 1% to 0.1% between M H + = 110 GeV and M H + = 155 GeV, the branching ratio BR W + * H H + simultaneously increases from roughly 5% to 90%. As a result one obtains H production cross sections of σ At √ s = 8 TeV we find that the di-photon signal strength of H is a factor of around two below the sensitivity of the ATLAS search [30].
Since in the benchmark scenario (3.2) the 95 GeV Higgs H is produced dominantly in association with top quarks, a couple of comments concerning the Tevatron and LHC searches that target final states of this type seem to be in order. The existing tth searches fall broadly speaking into two classes. Firstly, more exclusive analyses (see [60][61][62][63] for the latest LHC searches of this type) that employ multivariate discriminants such as boosted decision decisions trees or neural networks, and are specifically tuned to the final state kinematics of the SM signal. Second, more inclusive searches based on cut-and-count approaches that impose only rather loose selection requirements to suppress backgrounds. Examples of the second type are the CDF searches for tth (h → bb) [9,10] and the ATLAS [11] and CMS [12] analyses that both look for associated production of a Higgs boson and tt in multi-lepton final states. The interesting observation is now that while most of the exclusive tth analyses show no significant deviations from the SM expectations or are inconclusive, the aforementioned inclusive results display small excesses. In fact, it has been pointed out in [19] that the existing excesses in tth searches can be explained by the contamination b followed by H → bb, τ + τ − , and that a model that naturally leads to such a contamination is the type-I 2HDM with low to moderate tan β and a light Higgs spectrum. The tan β range of [4, 6] that is favoured by the ATLAS multi-lepton excess in tth [19] is indicated in Figure 6 by a purple stripe. Concerning the latest combined h → γγ measurements by ATLAS [61] and CMS [62] it is important to mention that these analyses include the tth channel, but would have barely missed a H with 95 GeV, because they only considered di-photon invariant masses m γγ ∈ [105, 160] GeV and m γγ ∈ [100, 180] GeV, respectively. Future LHC searches for ttH (H → γγ) with an enlarged mass window should however find clear evidence of a signal, if the 95 GeV di-photon excess is a true sign of new physics and not just a fluke.
The Higgs spectrum of (3.2) also contains a lightish A with a mass of 205 GeV. In order to understand how to search for such a pseudoscalar in the most efficient way, we show in the two panels of Figure 9 the branching ratios of A (left) and the corresponding gg → A → X signal strengths at √ s = 13 TeV (right). One observes that for M A 160 GeV (M A 135 GeV) the A → ZH branching ratio exceeds the one to bottom (tau) pairs. In consequence, LHC searches for ZH production with Z → + − and H → bb, τ + τ − [38,64] provide good opportunities to test and to constrain type-I 2HDM realisation with a neutral Higgs spectrum à la (3. is parametrically suppressed by a factor of cot 2 (β − α) compared to A → ZH, another interesting probe of such fermiophobic scenarios is the A → Zh channel (see e.g. [65]). In fact, as can be seen from Figure 4, for M A > 205 GeV the existing searches for A → Zh/H provide the most stringent bounds on tan β in the case of all benchmark scenarios. For M A = 205 GeV, we find that the parameter space with tan β < 1.8 is excluded at 95% CL by the CMS search for A → ZH [38]. The benchmark scenario (3.2) is thus clearly viable. Notice that the limit on tan β that we have derived from the A → ZH search ends slightly above 200 GeV, because the CMS collaboration studies only signal benchmarks with M A > M H + M Z . Since off-shell decays of A to ZH are important in our case (see left panel in Figure 9) dropping this restriction would allow to extend the shown bound down to M A < M H + M Z . Given this limitation and the fact that [38] is based on only 19.8 fb −1 of √ s = 8 TeV data, one can expect future LHC searches for A → ZH to be able to notably improve the constraints on fermiophobic type-I 2HDM scenarios. We finally add that the parameter choices (3.2) give rise to a signal strength of around 66 fb (7 fb) for pp TeV. The most relevant constraints on the M H + -tan β plane for the case of the type-I 2HDM are shown in Figure 5. For M H + = 125 GeV one observes from the left panel that values of tan β < 3.7 are disfavoured at 95% CL by the latest CMS search for H + → τ + ν τ [39]. The choice of tan β = 5.5 made in (3.2) represents therefore a viable option. We also emphasise that the contributions of charged Higgs loops to Γ (h → γγ) and Γ (H → γγ) have been taken into account in Figure 6 and in the pie chart shown on the right-hand side in Figure 7. Numerically, we find that κ h γ = 0.80 and observe that charged Higgs effects in the benchmark scenario lead to a Higgs potential (2.1) that is bounded from below and to a ρ parameter that is compatible with the existing 2σ limits.

Triangle benchmark scenario
In our third type-I 2HDM benchmark scenario we adopt the following choice of parameters The constraints on this benchmark scenario are summarised in Figure 10 Figure 11. The left pie chart shows that 41.4% of σ H = 3.6 pb are due to A production in gluon-fusion (ggA) with A → W ∓ H ± → W ∓ W ± H. An example of a Feynman diagram that gives rise to this exotic H production mode is displayed in the middle of Figure 1. The combination of the VBF, WH and ZH channels (the ggH channel itself) is instead subleading and amounts to 32.7% (22.3%).
In Figure 12 Figure 11. As Figure 2 but for the third type-I 2HDM benchmark scenario (3.3 Type-I 2HDM, ▲ It remains to be verified that the H, A and H + featured in our third type-I 2HDM parameter scenario are phenomenologically viable. In this context, we first note that the sensitivity of the ATLAS di-photon search at √ s = 8 TeV [30] is by a factor of approximately 1.8 too low to probe the parameter choices (3.3). Likewise, di-tau searches such as [31] provide no relevant constraints. In the case of the A, one observes from the lower left panel in Figure 4 that for M A = 350 GeV the ATLAS search for A → Zh [37] requires tan β > 3.3. The 95% CL bound on tan β that follows from the B s → µ + µ − measurements of CMS and LHCb [41,42] reads tan β > 3.3 for M H + = 170 GeV -see the left panel in Figure 5. At present the M A , M H + and tan β values chosen in (3.3) are thus allowed. Future LHC searches for A → Zh/H and/or B s → µ + µ − should however be able to probe model realisations that feature parameters not much different from (3.3).
The predictions shown in Figure 10 and in the right pie chart of Figure 11 again include the contributions of charged Higgs loops to Γ (h → γγ) and Γ (H → γγ). We find that charged Higgs effects suppress the di-photon h and H decay rates by 10% and 20% compared to the case with only top-quark and W-boson contributions. Numerically, we obtain κ h γ = 0.78. To conclude the discussion of the third benchmark scenario, we mention that for the choice of parameters employed in (3.3) the Higgs potential is bounded from below and the constraint ∆ρ ∈ [−1.2, 2.4] · 10 −3 that follows from the electroweak precision measurements is satisfied. The allowed parameter regions corresponding to (3.4) are displayed in Figure 13. The red, blue and green contours enclose the parameters that a preferred by the LHC Run-I Higgs data, the LEP excess in e + e − → ZH and the CMS di-photon anomaly, respectively. As before the parameters M H , M A , M H + and λ 3 have been kept fixed when calculating the constraints. The values of sin α and tan β as chosen in (3.4) are indicated by a square, and one observes that these parameters lead to a consistent overall picture.

Square benchmark scenario
In Figure 14 we present the breakdown of the different H production channels and the values of the branching ratios of H for the fourth parameter scenario (3.4). An inspection of the left pie chart reveals that 32.4% of σ H = 1.5 pb stem from associated H ± H production. A graph that contributes to this production mode is shown on the right-hand side in Figure 1. We calculate the relevant cross section with MadGraph5_aMCNLO [66] at next-to-leading order in QCD using an UFO implementation [67] of the 2HDM model discussed in [68]. It follows that for the parameter choices (3.4), H production through pp → W ± * → H ± H is almost as important as the combination of the VBF, WH and ZH channels which gives rise to 53.9% of the total cross section. As before H production via ggH is only of very limited importance.
The dominance of H ± H production is readily understood by noticing that the ratio between the W ± H ∓ H and W ± W ∓ H or ZZH coupling is simply given by tan 2 (β − α). For a sufficiently fermiophobic H and very light H and H + states, the H production rate in pp → W ± * → H ± H can thus be comparable to or even larger than the VBF, WH and ZH modes taken together [20,21]. Our results for the H branching ratios corresponding to (3.4) are displayed on the right-hand side in   Figure 4 by the red curve. One sees that for M A = 80 GeV only values of tan β < 0.4 are excluded at 95% CL. The benchmark scenario (3.4) however employs tan β = 4.2 and is thus clearly allowed. We also mention that Γ (h → Z * A) is far too small to be subject to the existing indirect LHC constraints on the total Higgs decay width Γ h (the relevant √ s = 13 TeV results can be found in [69,70]). One finally needs to check that a H + with a mass of 87 GeV is consistent with all direct and indirect constraints in the type-I 2HDM. Strong lower bounds on M H + arise from LEP searches for pair-produced charged Higgs bosons [71]. We find that in our type-I 2HDM benchmark scenario (3.4) charged Higgs masses below 86.9 GeV are excluded at 95% CL. At low mass direct limits also arise from LHC searches for H + → τ + ν τ with the latest results given in [39,72]. As can be seen from the panels in Figure 5, in the range M H + ∈ [85, 105] GeV the H + → τ + ν τ search [39] in fact provides presently the strongest constraint on tan β. Numerically, we find for M H + = 87 GeV the bound tan β > 4.1, which does not rule out the choice of tan β made in (3.4). Improved LHC searches for H + → τ + ν τ should however be able to exclude or find evidence for scenarios with tan β 5 and a charged Higgs of mass close to M Z . 26 Figure 14. As Figure 2 but for the fourth type-I 2HDM benchmark scenario (3.4). The label "H ± H" in the left panel refers to associated H production via pp → W ± * → H ± H. Only values of BR X H that are larger than 2% are explicitly given.
One motivation for a H + with a mass close to M W is that such a state can partly explain the 2.3σ excess [56] observed in the lepton-flavour universality ratio R τ/ = 2BR τ + ν τ W+ / =e,µ BR + ν W+ . Using the results of [73], we in fact find that the deviation in R τ/ is reduced to 1.9σ in the benchmark scenario (3.1) as a result of the contamination of the W + → τ + ν τ signal by H + → τ + ν τ decays. We furthermore note that while most LEP searches focus on the H + → τ + ν τ and H + → cs channels also H + → W + A (A → bb) has been considered to cover the possibility of pseudoscalars with M A < 70 GeV. For such scenarios the M H + -limits weaken and we observe that in the type-I 2HDM only charged Higgs masses below 81.4 GeV are excluded at 95% CL if M A is taken to be 50 GeV. In such a case the deviation in R τ/ would be reduced to 1.4σ. Although a A with 50 GeV can be shown to pass the direct constraints from h → AA → µ + µ − bb [74] as well as the indirect bounds from the LHC searches for off-shell h production (see [69,70] for example), we do not consider the case M A = 50 GeV here. The reason is that such a choice does not allow to simultaneously explain the LEP anomaly in e + e − → ZH and the CMS excess in H → γγ, as a result of the large partial H → Z * A decay width that suppresses BR γγ H . We finally add that a precision measurement of R τ/ is challenging for ATLAS and CMS due to triggering and the uncertain tau identification efficiency, but may be possible at LHCb by performing a dedicated analysis [75,76].
As in all other 2HDM benchmark scenarios the results displayed in Figure 13 and in the right pie chart of Figure 14 take into account charged Higgs contributions to Γ (h → γγ) and Γ (H → γγ). These corrections lead to a suppression of around 10% (30%) for a h (H) relative to the case with only top-quark and W-boson contributions, resulting in κ h γ = 0.80. We have also verified that for the parameters employed in (3.4) the Higgs potential is bounded from below and that the constraints that arise from the ρ parameter are fulfilled at 2σ.

Conclusions
In 2016 the ATLAS and CMS collaborations each have collected around 40 fb −1 of LHC data at √ s = 13 TeV. While most of the measurements they have performed are in full agreement with the corresponding SM predictions some glitches have been observed. For instance there are excesses in the multi-lepton channel of tth production at about 2σ [11,12] and an unexpected bump at around 95 GeV in the di-photon mass spectrum [13, 14] with a global (local) significance of 2.8σ (1.3σ). Although none of these deviations is on its own statistically significant, it seems like an interesting and useful exercise to try to understand if these anomalies can arise in a coherent way from physics beyond the SM.
In our article, we have shown that the type-I 2HDM can provide a very economic explanation of both the multi-lepton and di-photon excess observed at LHC, while simultaneously addressing two historic 2σ Higgs anomalies that linger around since the times of LEP [8] and the Tevatron [9,10]. The key ingredient to describe the observed Higgs excesses is a moderately-tostrongly fermiophobic CP-even Higgs H with a mass of 95 GeV. Due to its fermiophobic nature such a H has an enhanced di-photon branching ratio making it possible to obtain a signal strength of the order of 0.1 pb by the combination of VBF, WH and ZH production alone. A sizeable H production rate can however also arise from either top-quark pair and single-top production followed by (−) t → H ± b or from ggA production with A → W ∓ H ± → W ∓ W ± H. In cases where the H is strongly fermiophobic and the charged Higgs is very light the process pp → W ± * → H ± H can finally provide an efficient way to produce the non-SM CP-even Higgs.
By means of a detailed numerical analysis we have then demonstrated that all the considered Higgs excesses can be simultaneously reproduced if H production is dominated by tt production followed by the cascade (−) t → H ± b . This option can be realised in the type-I 2HDM in parameter regions with M H + 130 GeV and tan β ∈ [4, 6]. If the inclusive H cross section instead receives the largest contribution from VBF production, ggA production with A → W ∓ H ± → W ∓ W ± H or associated H ± H production only the CMS excess in H → γγ and the LEP anomaly in e + e − → ZH can be explained, while the deviations seen in the tth channel remain unaccounted for. We find that in order for pp → W ± * → H ± H to be the leading production mechanism one has to have M H + 100 GeV, whereas cascade H production initiated by gg → A is the dominant production channel for M H + M A /2 170 GeV. The sum of the VBF, WH and ZH channels can finally give a sizeable inclusive H cross section even for moderately heavy charged Higgses. We stress that one firm conclusion that can be drawn from our analysis is that in the considered new-physics model any di-photon excess should be associated with additional detector activity such as forward or bottom-quark jets. This feature should provide useful handles in future LHC analyses to improve the separation of new-physics signal and SM backgrounds.
All type-I 2HDM realisations that we have explored in our work include other light Higgses besides H. The current constraints from direct and indirect searches for spin-0 resonances can however be shown to be satisfied for the four benchmark scenarios that we have discussed in detail. Future LHC searches for charged Higgses in the H + → τ + ν τ channel or improved measurements of flavour observables such as B s → µ + µ − should nevertheless be able to exclude parts of the parameter space that leads to a simultaneous explanation of the discussed anomalies. This state-ment is particularly true for model realisations that lead to sizeable H ± H production rates or exotic Higgs signatures involving the decay chains (−) t → H ± since in all these cases the charged Higgs has to be necessarily light. The best search strategy for the A depends strongly on its mass. For pseudoscalars with M A 160 GeV, we find that the channels A → γγ and A → τ + τ − offer only limited sensitivity to tan β values significantly above 1. Better prospects to probe the fermiophobic type-I 2HDM scenarios discussed in our article seem to be provided by A → Zh/H searches, which already now furnish the leading restrictions on tan β for larger pseudoscalar masses.