Observability of parameter space for charged Higgs boson in its bosonic decays in two Higgs doublet model Type-1

This study explores the possibility of discovering through its bosonic decays, i.e., (where ϕ = h or A), within the Type-I two Higgs doublet model (2HDM). The main objective is to demonstrate the available parameter space after applying recent experimental and theoretical exclusion limits. We suggest that = 150 GeV is the most probable mass for the decay channel in collisions at = 8, 13, and 14 TeV. We also report on the application of a modern machine learning approach to a multivariate technique for heavy charged Higgs production in association with a single top quark through weak interaction to demonstrate its observability in comparison with the most relevant Standard Model backgrounds using the neural networks of boosted decision Tree (BDT), likelihood (LH), and multilayer perceptron (MLP).


I. INTRODUCTION
In 2HDM, H ± is allowed to decay freely in fermions and gauge bosons.In Type-I, H ± −→ AW ± (decay to a neutral Higgs "A" and "W-boson") is a dominant channel.The decay mode into τ + ν τ reaches branching ratios of more than 90% below the t b threshold and the muonic one ranges at a few 10 −4 [1].All other leptonic decay channels of the charged Higgs bosons are not important to be considered.As we know that there is a fermiophobic charged Higgs decay for large tanβ values, and it decays like H ± → W ± φ (φ = h, H, A) if kinematically allowed and it would be dominant decay even for virtual W ± .Thus, it is the most encouraging mode of decay, for larger tanβ values.
In Type-I 2HDM, the bosonic decays of light H ± were recently studied at the LHC [3].For decay processes H ± → W ± A and H ± → W ± h, Branching Ratios are calculated in [3].The H ± → W ± h reaches a BR of 10% below the top-bottom threshold, at tanβ values from 2-3 and m H ± = 160 GeV.
For the production process, pp → tbH ± , which is generally the most dominant mode for H + , SM inclusive processes with top-quark pairs are inevitably an important background regardless of how φ decays [4].Hence for more conventional 2HDM scenarios, the signal process from φ → τ τ and φ → bb provides promising avenue near the alignment limit [5,6].Moreover in 2HDM, BR(φ → τ τ ) and BR(φ → bb) with the relative size predicted under additional model assumptions, the search results from the two signatures may be combined to improve the sensitivity coverage of the 2HDM parameter space.The 2HDMC-1.7.0 [7] is used to put theoretical constraints and experimental bounds are applied.For that purpose, HiggsBounds [8] and HiggsSignals [9] libraries are interfaced with 2HDMC, and also ScannerS [10] is used to put the most recent experimental bound on the selected parameters and compare whether it is allowed or not experimentally.

II. REVIEW OF 2HDM
The scalar potential of 2HDM [11] has 14 parameters, including the charge violation, and CP violation.The general term for scalar potential is as follows, where (λ i , i = 1, 2, 3, ...., 7) are dimensionless coupling parameters, m 2 11 , m 2 22 and m 2 12 are squares of masses.To treat the 2HDM potential as charge and parity conserving potential, all the parameters should be real.The vacuum expectation value VEV is acquired by each scalar-doublet when electroweak symmetry breaks.The two doublets are, These two doublets lead to eight fields among which three correspond to massive W ± and Z 0 vector bosons, and the remaining five fields lead to five physical Higgs bosons.
where i=1,2 with The experimentally obtained value of V SM is 246.22 GeV.The obtained fields are given as, and Mass-matrix of charged Higgs states are diagonalized by rotational angle and it is defined as Similarly mass-matrix of scalar Higgs states are diagonalized by the rotational angle α and satisfies following relation, where, λ 345 = λ 3 + λ 4 + λ 5

A. Theoretical and Experimental Bounds
The general potential of 2HDM is too complex as compared to the one in the standard model SM.The 2HDM imposes theoretical constraints on the potential to guarantee the stability of potential.
The Higgs potential should be positive throughout the field space.This ensures that a stable vacuum configuration for asymptotically large field values is maintained.The quartic terms are the leading terms at large field space values.The following substitutions are helpful, where, After making these substitutions, and omitting the common factor r 4 , the quartic terms of the potential can be expressed as, From above equation we can see that the potential will be positive if, If λ 6 = 0 = λ 7 , a case for natural conservation of flavor, then an extra condition must be satisfied, If either λ 6 = 0 or λ 7 = 0 then the above condition changes to, Scattering matrices are unitary in order to conserve probability.In the theory of weak couplings, the contribution of higher order terms decreases gradually.While in the theory of strong couplings, individual contributions increase arbitrarily.The eigenvalues (L i ) of S-matrices must satisfy the condition L i ≤ 16π in order to achieve the tree-level unitarity that means the saturation of Smatrices up to tree-level unitarity.
Perturbation constraints requires that the quartic Higgs couplings must satisfy the condition | One can imagine that some interaction channels are non-perturbative while others are perturbative.| λ i |= 4πξ , is another way to explain this constraint, where ξ = 0.8 1 .
This gives | λ i |≤ 10 for λ i , as the upper bound. 1 The value is arbitrarily chosen as an upper bound Alongside theoretical constraints, there are also experimental constraints coming from B-Physics and various experiments on different colliders from recent Higgs searches.Here we discuss some important constraints.Also, using SuperIso V.3.2 [12], we list the SM prediction values provided in this category.The Standard Model BR for (B µ → τ ν) SM reported in [12] is: The standard model estimation may, in fact, be contrasted to the most recent heavy flavour averaging (HFAG) result.[13].
so the ratio will become, This causes the exclusion of two sectors of (tanβ)/m H ± ratio in 2HDM [14].This implies that for tanβ ≥ 1, the mass of charged Higgs must be greater than 800 GeV for Type-II 2HDM [15].As we know that the ( B µ → τ ν τ ) decay depends on | V ub | so the ( B µ → Dlν ) (semi-leptonic) decay also depends on | V ub | , i.e. more precisely known as compared to | V ub | and the branching ratio of ( B µ → τ ν τ ) is fifty times greater than the branching ratio of (B µ → τ ν) in standard model but it is still difficult to detect because two neutrinos exist in its final state.The 2HDM deals only with the numerator of the ratio.
and allow us to reduce to some extent the theoretical uncertainties.The experimental outcomes by BaBar collaborations and SM predictions [14] are as follows.
For (B → X s γ), this special transition is mediated by H ± and it includes Flavor-changing neutral current (FCNC) and W ± contributions.As to the respective BR, the contribution of charged Higgs is always positive so to probe Type-II 2HDM, this can be used efficiently.For this transition, the NNLO-SM predicted (3.34 ± 0.22) × 10 −4 for BR(B → X s γ) SM [16].So, for BR(B → X s γ) exp recently experimentally calculated value is (3.32 ± 0.15) × 10 −4 , For Type-II Yukawa interactions, this constraint excludes the light-charged Higgs.Higher order analysis [17] estimated lower limit of M H ± is 380 GeV at 95% C.L.However, it is important to mention that the bound in [17] does not include novel experimental and theoretical predictions and hence the numerical results maybe outdated.

III. DISCUSSION
The branching ratios are calculated using HDECAY [23] through the anyHdecay interface of ref [10], and predictions for gluon-fusion and bb-associated Higgs production at hadron colliders are obtained using tabulated results from SUSHI [24].The V H-associated (sub)channel cross section predictions are made using the HiggsBounds parametrizations, and the charged Higgs production in association with a top-quark is tested using the HiggsBounds and HiggsSignals.These above constraints and calculations are implemented in ScannerS.Figure 1In Type-I 2HDM, tanβ vs BR(H + → W + h) is scanned in the face of theoretical (left) and experimental (right) restrictions with respect to tan β values for different masses of m H + .One can see that for m H + = 800 and 1000 GeV, the BR(H + → W + h) remains between 70% → 80%.For m H + = 600 GeV, the maximum BR reaches more than 80% for large tan β values.For tan β > 3, the maximum BR is achieved for m + H = 400 GeV.For m H + = 200 GeV, the BR remains less than 20% across the tan β range.
. At a 95% confidence-level (CL), yellow colour zones are omitted from LHC Higgs data, and black/grey zones are omitted from theoretical restrictions (constraints).
Figure 3In Type-I 2HDM, tanβ vs BR(H is scanned in the presence of theoretical constraints as well as experimental constraints with

FIG. 4 :
FIG. 4: In Type-I 2HDM, m H + against tanβ BR(H + → W + h) (left) and BR(H + → t b) (right) isscanned in the presence of theoretical constraints as well as experimental constraints with

Figure
Figure 4InType-I 2HDM, m H + against tanβ BR(H + → W + h) (left) and BR(H + → t b) (right) is scanned in the presence of theoretical constraints as well as experimental constraintswith m h =125 GeV, m H =300 GeV, m H + =m A , sin(β − α)=0.85,we set m 2 12 = [m 2 H + ][tanβ] [1+tanβ 2 ] .At a 95% confidence-level (CL),yellow colour zones are omitted from LHC Higgs data, and black/grey zones are omitted from theoretical restrictions (constraints)figure.4 shows that for tanβ ∈ [2, 3] and m H + ∈ [150, 210], the BR(H + → W + h) shows up in the region from [0.06,0.07]as shown in the vertical palette.It is also observed that for tanβ ∈ [2, 3] and m H + ∈ [150, 210], the BR(H + → tb) shows up in the region from [0.65,0.7]as shown in the vertical palette.Under a same range of m H + and tanβ, BR(H + → tb) becomes boosted towards the point that it overrides all the other decay modes.When going over light-charged Higgs to heavy-charged Higgs, we see there are most observable states that exist in the defined region.

FigureFIG. 8 :
Figure 7In Type-I 2HDM, m H + vs m A BR(H + → W A) (left) and BR(H + → tb) (right) is scanned in face of theoretical as well as experimental restrictions (constraints) with m h =125 GeV,

FigureFIG. 9 :
Figure 8In THDM Type-I, BR(H + → W + h)+BR(H + → W + A) is mapped over sin(β − α) vs tanβ with m 2 12 =5000 GeV −2 on the left while m 2 12 vs tanβ with sin(β − α)=0.65 is shown on the right.Other parameters are m h =m A =125 GeV, m H =300 GeV and m H + =170 GeV.At a 95% confidence-level (CL), yellow colour zones are omitted from LHC Higgs data, and black/grey zones are omitted from theoretical restrictions (constraints)figure.8 shows a scan over arbitrarily chosen and fixed m H + between 160 GeV and 180 GeV i.e. 170 GeV.It shows the size of BR(H ± → W ± * h + W ± * A) over the sin(β − α) vs tanβ (left) and m 2 12 vs tanβ (right).The right panel shows the effect of the soft Z 2 breaking term m 12 .It is clear that for some special choices of tanβ and m 2 12, the BR(H ± → W ± * h + W ± * A) could reach above 50% for sin(β − α) between 0.6 and 0.7.The right figure is drawn by fixing sin(β − α) at 0.65, and variation is shown as a function of m 2 12 .The favorable green zones are located in regions with m 2 12 > 12, 000 GeV. Figure9InType-I 2HDM, the rates for σ(pp → t t) × BR(t → H + b) × BR(H + → W φ) with
85, we set m 2 12 = ] figure.2that for smaller tanβ values, the H + → tb decay mode is most dominant while for higher values, the H + → W h becomes most probable.However, for m H + = 200 GeV, the scenario is different, as BR(H + → tb) is dominant while BR(H + → W h) FIG. 3: In Type-I 2HDM, tanβ vs BR(H+ → W + h) (left) tanβ vs BR(H + → t b) (right) isscanned in the presence of theoretical constraints as well as experimental constraints with m h