Analysis of $W^\pm+4\gamma$ in the 2HDM Type-I at the LHC

We analyse a light charged Higgs boson in the 2-Higgs Doublet Model (2HDM) Type-I, when its mass satisfies the condition $M_{H^{\pm}}<M_{t}+M_{b}$ and the parameter space is consistent with theoretical requirements of self-consistency as well as the latest experimental constraints from Large Hadron Collider (LHC) and other data. Over such a parameter space, wherein the Standard Model (SM)-like state discovered at the LHC in 2012 is the heaviest CP-even state of the 2HDM, it is found that the decay modes of the charged Higgs boson are dominated by $H^{\pm} \rightarrow W^{\pm *} h$. Furthermore, the light neutral Higgs boson $h$ dominantly decays into two photons. Under these conditions, we find that the production and decay process $ p p \to H^\pm h \to {W^\pm}^{(*)} h h \to l \nu_{l} + 4 \gamma$ ($l=e,\mu$) is essentially background free. However, since the $W^{\pm(*)}$ could be largely off-shell and the $h$ state is very light, so that both the lepton coming from the former and the photons coming from the latter could be rather soft, we perform here a full Monte Carlo (MC) analysis at the detector level demonstrating that such a $W^{\pm} + 4\gamma$ signal is very promising, as it would be yielding significant excesses at the LHC with an integrated luminosity of $L=$ 300 $fb^{-1}$ at both $\sqrt{s}= 13$ and $14 ~\text{TeV}$.


I. INTRODUCTION
in [1], it was found that the associated production process pp → H ± h could lead to a potentially detectable W ± +4γ final state. According to the parton level analysis in [1], it was observed that this signature is almost background free and could have a large significance.
Therefore, it is worth to examine whether this statement is robust enough after taking into account parton shower, hadronisation, heavy flavour decays and detector effects.
In this paper, like in [1], we assume that the heaviest CP-even Higgs boson H is the observed SM-like Higgs boson, which properties are consistent with measurements at the LHC. Furthermore, due to the constraints from EW precision tests, it is noted that the lighter Higgs boson h can be lighter than 125 GeV. In such a parameter space, a light charged Higgs boson H ± is thus accompanied by a light Higgs boson h. We focus our collider phenomenology study on the signal process pp → H ± h → W ± ( * ) hh → ν + 4γ ( = e, µ) and examine its feasibility at the LHC. It will eventually be found that, after taking into account theoretical and experimental constraints, there are points in the 2HDM Type-I parameter space which can be either discovered or ruled out already with the current integrated luminosity at the LHC and that, with the full Run 3 data set, or a tenth of the High-Luminosity LHC (HL-LHC) one [2,3], a definite statement on this BSM scenario can be made.
The paper is organised as follows. In Sect. II, we briefly describe the 2HDM and its Yukawa scenarios, then introduce a few Benchmark Points (BPs) for our MC analysis which pass all present constraints, both theoretical and experimental. In Sect. III, we perform a detailed collider analysis of these BPs and examine the potential to discover the aforementioned signature of this 2HDM Type-I scenario. In Sect. IV, we present some conclusions.

II. THE 2HDM
The scalar sector of the 2HDM contains two complex SU (2) doublets with hypercharge where v 1 and v 2 are the Vacuum Expectation Values (VEVs) of the neutral Higgs field components that break spontaneously the EW gauge symmetry to the Electro-Magnetic potential involving two Higgs doublets can be written as: The hermiticity of the potential requires all parameters to be real except m 2 12 , λ 5 , λ 6 and λ 7 . For simplicity, we will work with a CP-conserving scalar potential by choosing m 2 12 and λ 5,6,7 to be real. Note that, in Z 2 symmetric models, terms that are proportional to λ 6 and λ 7 in the scalar potential are absent, to ensure the suppression of FCNCs at tree level (as already remarked upon).
The Yukawa Lagrangian, which describes the interactions between the (pseudo)scalar fields and the fermion sector, is given as follows: where Q L and L L are the weak isospin quark and lepton doublets, u R and d R denote the right-handed quark singlets and Y u 1,2 , Y d 1,2 and Y l 1,2 are coupling matrices in flavour space. The implementation of the aforementioned discrete symmetry, depending on the Z 2 assignments, leads to four Types of 2HDM: commonly denoted as Type-I, -II, -X and -Y. In the mass eigenstate basis, their treatment can be unified in the following form: where P L,R = (1 ± γ 5 )/2 and V denotes the Cabibbo-Kobayashi-Maskawa (CKM) matrix.
In our study, like in [1], we choose to focus on Type-I, where only one doublet Φ 2 couples to all fermions and thus the Higgs-fermion couplings are flavour diagonal in the fermion mass basis and depend only on two angles, α (parameterising the mixing between h and H) and β (which tangent is given by the ratio of the two VEVs), as shown in Tab I.

A. Constraints on the 2HDM
There are certain theoretical restrictions and experimental constraints on the scalar potential that have to be imposed in order to obtain a viable realisation of the 2HDM. We note that both theoretical consistency and experimental data have already limited the parameter space of the 2HDM.
In our study, we consider the following theoretical constraints.
(4) Limits from the EW oblique parameters S, T and U [6], for which we check their consistency at 95% Confidence Level (CL) with the following measurements [7]:  (Note that we have used SuperIso v4.1 [12] to compute the exclusions from flavour physics observables and 2HDMC [13] to check the theoretical constraints as well as the parameters S, T and U .)

B. Parameter space scans
In this work, we concentrate on the scenario in which the h state is fermiophobic, which occurs near the alignment limit sin(β − α) ∼ 0. In such a limit, all fermionic decays of the lightest CP-even Higgs boson are suppressed, so that h → γγ can become significant.
In the SM, the γγ decay of the Higgs boson is generated by the dominant W ± loop and the subdominant top quark one, which have opposite signs and thus cancel one another somewhat. In the 2HDM, the additional H ± loop also contributes. In the Type-I case, one has the following coupling dependencies for the lightest CP-even state: hW + W − ∼ sin(β − α), hqq ∼ cos α/ sin β while the hH + H − vertex is given by the parameters of the scalar potential. Since, for fermionic loops, the coupling is proportional to cos α and when sin(β − α) is negative and cos(β − α) is positive, cos α will be cancelled for a particular tan β, which is when h becomes fermiophobic and h → γγ is enhanced because the aforementioned cancellation no longer occurs.
A numerical scan of the 2HDM Type-I parameters was performed in Ref. [1], which satisfied all theoretical and experimental constraints mentioned above. Based on the same scan, in this work, we propose the following 14 BPs given in Tab. III. There are three comments to make on these 14 BPs.
• The mass of the charged Higgs boson can vary from 91.49 GeV to 168.69 GeV. The CP-even Higgs boson h is always lighter than 125 GeV and lighter than the H ± state.
The W ± boson from the charged Higgs boson decaying via H ± → W ± ( * ) h could be either on-shell or off-shell. If it is off-shell, the charged lepton emerging from it might be soft (as already remarked upon), like in BP5-BP10.
• For these BPs, the main production process of a charged Higgs boson is pp → H ± h, which cross section can be up to one order of magnitude larger than those of pp → H ± A and pp → H ± H ∓ , which are alternative discovery modes in this region of 2HDM Type-I parameter space [14][15][16]. Therefore, in the present analysis, we will focus on the W ± + 4γ signature stemming from the pp → H ± h production process only.

III. COLLIDER PHENOMENOLOGY
In this section, we present a detailed MC analysis at a detector level, including both signal and background events.

A. Event generation
Here we briefly describe MC event generation.
• We use MadGraph5 aMC@NLO v2.8.2 [17] (MG) to compute the cross sections and generate both signal and background events at parton level. We have adopted the following kinematic cuts (in pseudorapidity, transverse momentum and Missing E T (MET), where E T is the transverse energy (or momentum)) in order to improve the efficiency of the MC event generation |η(l, j, γ)| < 2.5, p T (j, γ, l) > 10 GeV, ∆R(l, j, γ) > 0.5, MET > 5 GeV, (9) where j refers here to parton. The signal events are generated at LO, the cross sections for each BPs at the LHC with √ s = 13 (14) TeV are listed in the last two column of Tab. III. The backgrounds are treated at LO, but this apparent inconsistency will become irrelevant once selection cuts are implemented, as the signal will be proven to be essentially backgound free for all BPs.
• After generating both signal and background events at the parton level, we pass them to Pythia v8 [18] to simulate initial and final state radiation (i.e., the QED and QCD emission), parton shower, hadronisation and heavy flavour decays.
• We use Delphes v3.4.2 [19] to simulate the detector effects. For each event, we cluster final particles into jets and we adopt the anti-k t jet algorithm [20] with jet parameter ∆R = 0.5 in the FastJet package [21] 1 . Following the ATLAS analysis of [25], we will take the fake rate as 0.001, which describes the probability to mistag a jet as a photon.
Notice that, in the following, we will present event rates corresponding to an LHC energy of √ s = 13 TeV and 14 TeV and integrated luminosity of L = 300 fb −1 .

B. Event reconstruction
The mass M h can be reconstructed on an event-by event basis by pairing the four photons into two pairs by minimising the following χ 2 : Obviously, there are 3 combinatorics for each event. When the combination which minimises the χ 2 is found, we label the larger invariant mass of the pair of two photons as M 1 γγ and the other one is then labelled as M 2 γγ . The distributions of these two reconstructed masses of h for, e.g., BP5 are displayed in Fig. 1  The distribution of the reconstructed mass of the charged Higgs boson is shown in Fig. 2.
Since there is missing energy, we use the standard method as the W ± boson reconstruction.
There are then two possible candidates for the light Higgs state, one is produced in the charged Higgs boson decay and the other is produced in association with it. Thus, we obtained two possible H ± masses. As shown in Fig. 2, the correct one is rather sharp, while the wrong one is more dispersed. hadron decays, though this should not be necessary, as we shall demonstrate next.

C. Significances
We now estimate the tagging efficiency for leptons and photons at detector level by using Delphes. We generate 10k events for each BP and count the percentage of events where a lepton in the final state can be successfully reconstructed and recognised, while for the photon case we count four photons total efficiencies, then convert to single photon efficiency.
The efficiencies for our BPs are s shown in Thus, we can derive the acceptance efficiency at detector level, det , which can be expressed as a function of the mistagging rate of jets, lepton reconstruction and photon detection efficiencies as where n j denotes the jet number and 4 − n j denotes the photon number. By using this acceptance efficiency at detector level, we can estimate the detection efficiency for the whole parameter space of our 2HDM Type-I scenario.
Since the W ± bosons in the final state could be either on-shell or off-shell, depending on the BP, in this work, we adopt two sets of cuts (see Ref. [1]) to examine how the efficiencies can change. The first set of cuts is To determine the fiducial efficiencies of each point in the parameter space, we use the relation = σ(cuts) × det /σ(no cuts).
The results for the fiducial efficiencies are shown in Fig. 5   cuts, we can see that the first one has a better acceptance efficiency than the second one in covering a wider region of parameter space.
Before moving on to compute the significances of our signal for the BPs introduced, we present Tab. IV for the purpose of confirming the statement made in Ref. [1], that none of the backgrounds is really observable for any realistic LHC and HL-LHC luminosity. (Results are shown here for 13 TeV, but the conclusion is the same for 14 TeV.) We also present the predicted cross sections for the signals emerging from the BPs after taking into account the cuts and the detector acceptance efficiency in Tabs. V and VI, where we have considered √ s = 13 and 14 TeV, respectively. Due to the fact that the quark fluxes cannot be greatly enhanced when the collision energy increases from 13 to 14 TeV, we notice that the cross sections of the signal processes can only increase by 5% to 10% between the lower and higher center-of-mass energies.
To compute the significances, due to the tiny number of background events, we can neglect the latter safely. Therefore, the predicted significances can be computed by using the relation The corresponding results are shown in Tab. VII. We find that the predicted significances are larger than 5 for all 14 BPs in our 2HDM Type-I scenario when the luminosity is assumed to be 300 fb −1 , both at √ s = 13 and 14 TeV. The predicted significances for both energies and the given luminosity over the (M h , M H ± ) plane are shown in Fig. 6, which are obtained from the described convolution of production cross sections with cut and acceptance efficiencies at detector level. To obtain the results given here, for each point on the (M h , M H ± ) plane, we allow tan β and sin(β − α) to vary and take the maximal significance. In such a figure, it should be pointed out that, when m h < 62.5 clear that some amount of fine-tuning in sin(β − α) and/or tan β is necessary to obtain large significances. However, for any tan β > 5, there is always a choice of sin(β − α) that allows one to make a definite statement at both the LHC stages considered on the portion of parameter space of the 2HDM Type-I that we have sampled.
We conclude our numerical analysis by noting that, altogether, as we can observe from  Figs. 6-7, it is the first set of cuts given in Eq. (12) that yields better significances than the one in Eq. (13).

IV. CONCLUSIONS
In this paper, we have examined the feasibility of the signature W ± + 4γ, where the W ± decays leptonically in electrons and muons, from the associated production of the charged Higgs boson and lightest neutral Higgs state of the 2HDM Type-I (i.e., via pp → H ± h → W ±( * ) hh → ν + 4γ) at the LHC with a collision energy of √ s = 13 and 14 TeV and an integrated luminosity of L = 300 fb −1 . Our analysis has been a detector level study exploiting full MC event generation including parton shower, hadronisation and heavy flavour decays.
By doing so, we have confirmed a previous study done solely at the parton level, as we have proven that, even in presence of background generated by both real and fake photons (from   jets), the signal is essentially background free, so that significances only depend upon the signal cross sections and the collider integrated luminosities. We have also provided some reliable estimates for the detector efficiency and associated heat maps which can expedite an estimate of the signal significance over the relevant 2HDM Type-I parameter space, which we deem useful for current LHC working groups. Finally, for more thorough experimental analyses, we have also published 14 BPs, where the W ± boson can be either on-shell or off-shell, depending on the mass difference M H ± − M h .