# Limits on the charged Higgs parameters in the two Higgs doublet model using CMS \(\sqrt{s}=13\) TeV results

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## Abstract

The latest CMS results on the upper limits on \(\sigma _{H^\pm }\)BR(\(H^\pm \rightarrow \tau ^\pm \nu )\) and \(\sigma _{H^\pm }\)BR(\(H^+ \rightarrow t{\bar{b}}\)) for \(\sqrt{s}=13\) TeV at an integrated luminosity of 35.9 \(\hbox {fb}^{-1}\) are used to impose constraints on the charged Higgs \(H^\pm \) parameters within the Two Higgs Doublet Model (2HDM). The 2HDM is the simplest extension of the Standard Model (SM) under the same gauge symmetry to contain charged Higgs and is relatively little constrained compared to the Minimal Supersymmetric Standard Model (MSSM). The latest results lead to much more stringent constraints on the charged Higgs parameter space than for the earlier 8 TeV results. The CMS collaboration also studied the exotic bosonic decays \(H^\pm \rightarrow W^\pm A\) and \(A \rightarrow \mu ^+ \mu ^-\) for the first time and put upper limits on the BR(\(t\rightarrow H^+ b\)) for the light charged Higgs boson. These constraints lead to the exclusion of parameter space which is not excluded by the \(\tau \nu \) channel. For comparison the exclusion regions from flavor physics constraints are also discussed.

## 1 Introduction

The Standard Model (SM) of particle physics is the most successful model in explaining nearly all particle physics phenomenology. The discovery of a neutral scalar of mass 125 GeV with properties similar to the Higgs boson in SM [1, 2, 3, 4] makes SM the most acceptable model of particle physics. Despite being successful, the SM fails to explain the existence of dark matter, neutrino oscillations and the matter–antimatter asymmetry. SM also does not explain the mass hierarchy in elementary particles and gravity is not included. Apart from that, there is no fundamental reason to have only one Higgs doublet (i.e. minimal under the SM gauge symmetry) and the discovery of another scalar boson (neutral or charged) would require an extension of the SM. The simplest extension of SM under the same (SM) gauge symmetry is the Two Higgs Doublet Model (2HDM) [5, 6, 7, 8, 9, 10, 11]. So far there is no evidence for any other scalar up to a mass of a few TeV and hence the parameter space of 2HDM is getting significantly constrained by experimental observations [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]. The scalar sector of 2HDM consists of five scalars, two *CP* even scalars (*h* and *H*), one *CP* odd scalar (or pseudoscalar) *A* and two charged Higgs \(H^{\pm }\). The most general Yukawa sector (Type III) of 2HDM leads to flavor changing neutral currents (FCNCs) at tree level. To avoid the FCNC, Glashow and Weinberg implemented a discrete symmetry in the Yukawa sector which leads to four possible types of Yukawa interactions in 2HDM, i.e., Type I, Type II, Type X (lepton specific) and Type Y (flipped model). A brief review on 2HDM is given in Sect. 2.

The production of a charged Higgs particle, depending on its mass with respect to the top quark, can be divided into light (\(M_{H^\pm }\ll M_t\)), intermediate (\(M_{H^\pm }\sim M_t\)) and heavy (\(M_{H^\pm }\gg M_t\)) scenarios [31, 32, 33, 34]. Throughout the analysis the alignment limit is considered i.e. \(\sin (\beta -\alpha )\rightarrow 1\) (where the mixing angles \(\beta \) and \(\alpha \) are defined in Sect. 2), so that the neutral scalar *h* behaves like the SM Higgs boson. The precisely measured electroweak parameter *T* is highly sensitive on the mass splitting of \(H^\pm , H\) and *A*. The alignment limit and minimum mass splitting restricts the charged Higgs decay mostly into the fermionic sector and the experimental constraints put an exclusion bound on the charged Higgs (\(M_{H^\pm }\)–\(\tan \beta \)) parameter space. In this paper the 13 TeV CMS results [35, 36, 37] at an integrated luminosity of 35.9 \(\hbox {fb}^{-1}\) are used to restrict the charged Higgs parameter space as discussed in Sect. 4. Throughout the paper, the notation \(H^\pm \rightarrow \tau ^\pm \nu \) is used for both \(H^+\rightarrow \tau ^+ \nu \) and \(H^- \rightarrow \tau ^- {\bar{\nu }}\) (similarly for the tb channel). For the charged Higgs production cross section, \(\sigma _{H^\pm }\) denotes the sum of \(\sigma _{H^+}\) and \(\sigma _{H^-}\). A comparison of exclusion limits on charged Higgs parameter space from 13 TeV and 8 TeV CMS results is presented in Sect. 4 along with the indirect flavor physics constraint coming from \(B\rightarrow X_s \gamma \). As mentioned before, the bosonic decays of a charged Higgs boson into \(W^\pm h\), \(W^\pm H\) and \(W^\pm A\) are highly suppressed due to the alignment limit and the limited phase space. But once the bosonic decay channel is open, the bounds coming from the \(H^\pm \rightarrow \tau ^\pm \nu \) and \(H^+ \rightarrow t{\bar{b}}\) become weak [38, 39]. In this paper, the latest result from the CMS collaboration [37] is used in the Type I scenario in the mass range \(M_{H^\pm }\in [100,160]\) GeV, where the mass splitting \(M_{H^\pm }-M_A=85\) GeV and \(M_{H^\pm }\sim M_H\) is still allowed by the *T* parameter constraint.

## 2 Two Higgs doublet model (2HDM) review

*CP*invariance. The two Higgs doublets are parameterized as

*G*are the Nambu–Goldstone bosons that are eaten as the longitudinal components of the massive gauge bosons. The rotation matrix is given by

*l*) is either \(\Phi _1\) or \(\Phi _2\), depending on the Yukawa models of 2HDM. The four possible \({\mathcal {Z}}_2\) charge assignments of the quarks and charged leptons are summarized in Table 1.

Charge assignment under \({\mathcal {Z}}_2\) symmetry to avoid FCNC at tree level

Model | \(\Phi _1\) | \(\Phi _2\) | \(u_R\) | \(d_R\) | \(l_R\) | \(Q_L,L_L\) |
---|---|---|---|---|---|---|

Type I | \(+\) | − | − | − | − | \(+\) |

Type II | \(+\) | − | − | \(+\) | \(+\) | \(+\) |

Type X | \(+\) | − | − | − | \(+\) | \(+\) |

Type Y | \(+\) | − | − | \(+\) | − | \(+\) |

In Type I 2HDM, the second Higgs doublet \(\Phi _2\) couples to the fermions, so all the quarks and charged leptons get their masses from the VEV of \(\Phi _2\) (ie. \(v_2\)). In Type II 2HDM, up-type quarks couple to \(\Phi _2\) whereas down-type quarks and charged leptons couple to \(\Phi _1\). Hence in Type II up-type quarks get masses from \(v_2\) and down-type quarks and charged leptons get masses from \(v_1\). The Higgs sector of the Minimal Supersymmetric Standard Model (MSSM) is a special 2HDM whose Yukawa interaction is of Type II. For Type X (also called the Lepton Specific Model), the quark sector is similar to Type I but the charged leptons are coupled to \(\Phi _1\) and finally in the Type Y (also called the Flipped Model) the quark sector is similar to Type II but the leptons are coupled to \(\Phi _2\). Among them, Type II 2HDM has been most widely investigated because of its resemblance with MSSM.

*V*is the CKM matrix and \(P_{R,L}=\frac{1}{2}(1\pm \gamma _5)\) are the chirality projection operators (Table 2).

Choices of the couplings \(\xi _f\) for the four Yukawa models of 2HDM

Model | \(\xi _d\) | \(\xi _u\) | \(\xi _l\) |
---|---|---|---|

Type I | \(\cot \beta \) | \(\cot \beta \) | \(\cot \beta \) |

Type II | \(-\tan \beta \) | \(\cot \beta \) | \(-\tan \beta \) |

Type X | \(\cot \beta \) | \(\cot \beta \) | \(-\tan \beta \) |

Type Y | \(-\tan \beta \) | \(\cot \beta \) | \(\cot \beta \) |

## 3 \(H^{\pm }\) production and decay channels

^{1}The intermediate charged Higgs scenario is considered for \(M_{H^\pm }\) close to top quark i.e. \(150\lesssim M_{H^\pm }\lesssim 200\) GeV. In this region, the non-resonant top quark production mode also contributes along with the single-resonant and double-resonant modes. Cross sections at NLO QCD accuracy in the 4FS scheme as given in Ref. [31] are considered. Figure 1 shows the leading order (LO) diagrams of charged Higgs production in the three scenarios.

^{2}Since the \(H^\pm \) interaction to the quark sector of Type I and Type X and similarly that for Type II and Type Y are the same, the production cross sections in different models are related by \(\sigma ^{H^\pm }_{\text {Type I}}=\sigma ^{H^\pm }_{\text {Type X}}\) and \(\sigma ^{H^\pm }_{\text {Type II}}=\sigma ^{H^\pm }_{\text {Type Y}}\).

For the case of charged Higgs fermionic decays, in Type I all the fermionic couplings are proportional to \(\cot \beta \) and hence the branching fractions are independent of \(\tan \beta \). The \(\tau \nu \) channel is the dominant decay channel for light charged Higgs in Type I. However, for heavy charged Higgs scenario in Type I, the Br(\(H^\pm \rightarrow \tau \nu \)) is suppressed by \(M_{\tau }^2/M_{t}^2\) over Br(\(H^+ \rightarrow t{\bar{b}}\)), leading to nearly \(100\%\) branching fraction in the \(t{\bar{b}}\) channel. In Type II and Type X the lepton sector coupling to \(H^\pm \) being proportional to \(\tan \beta \), the decay into \(\tau \nu \) is dominant for light \(H^\pm \) and quite sizable for heavy \(H^\pm \) for \(\tan \beta > rsim 1\). As seen in Fig. 2 for heavy \(H^\pm \) scenario in Type X, the \(H^\pm \) branching fraction to \(\tau \nu \) starts to dominate over the \(t{\bar{b}}\) channel for large \(\tan \beta \). In Type Y, because of the \(\cot \beta \) dependence in the lepton sector the \(\tau \nu \) channel gets suppressed compared to the hadronic decay modes (dominantly into \(t{\bar{b}}\) for heavy \(H^\pm \)). The branching fractions computed using the public code Hdecay [42, 43] are shown in Fig. 2 for \(M_{H^\pm }=250\) GeV, for all Yukawa types of 2HDM. The code Hdecay also includes the three-body decay of the charged Higgs particle, i.e., \(H^+ \rightarrow t^* {\bar{b}} \rightarrow W^+ b {\bar{b}}\) below the two-body decay threshold of \(H^+ \rightarrow t {\bar{b}}\) mode [44]. Note that the branching fraction of \(H^\pm \) into the fermionic sector is given for situations where there are no \(H^\pm \) decays into the neutral scalars.

*h*,

*H*or

*A*. The couplings to \(W^\pm \) and neutral scalars are (all fields are incoming)

*h*is suppressed. The decays into the

*H*and

*A*channels depend on the mass splitting allowed by the

*T*parameter. In the generic 2HDM, there are no mass relations between \(H^\pm , H\) and

*A*unlike MSSM and for some parameter choice, the bosonic decays can be more dominant over the fermionic decays once the channels are open.

## 4 Experimental constraints

The theoretical constraints of 2HDM consist of vacuum stability [45, 46], perturbative unitarity [47, 48] and tree level unitarity [49, 50, 51]. The Electro-Weak Precision Observables (EWPOs) \(S (0.05\pm 0.11), T (0.09\pm 0.13) \) and \(U (0.01\pm 0.11)\) [52, 53], specially the *T* parameter [54], restrict the mass splitting of \(H^\pm \), *H* and *A*. In this paper, \(M_{H^\pm }=M_H=M_A\) is considered to impose the exclusion limits from the \(H^\pm \rightarrow \tau ^\pm \nu \) and \(H^+ \rightarrow t {\bar{b}}\) channels over the mass range \(M_{H^\pm } \in [80,2000]\) GeV. Perturbative unitarity for a wide region of \(\tan \beta \) can be satisfied by a proper choice of the soft \({\mathcal {Z}}_2\) breaking parameter, \(m_{12}^2=M_A^2 \sin \beta \cos \beta \). The theoretical constraints are checked using the package 2Hdmc-1.7.0 [55]. The alignment limit \(\sin (\beta -\alpha )\rightarrow 1\) is the condition most favored by the experimentalists. In this limit the couplings of the neutral scalar *h* in 2HDM is similar to the SM Higgs boson and can be identified with the observed 125 GeV Higgs boson. In the alignment limit the other *CP* even scalar, *H*, behaves as gauge-phobic i.e. its coupling to the gauge bosons \(W^\pm /Z\) is very suppressed. In the context of a charged Higgs analysis for the \(H^\pm \rightarrow \tau ^\pm \nu \) and \(H^+ \rightarrow t{\bar{b}}\) channels, the alignment limit is useful as it completely suppresses the \(H^\pm \rightarrow W^\pm h\) decay. LEP experiments [56] have given limits on the mass of the charged Higgs boson in 2HDM from the charged Higgs searches in Drell–Yan events, \(e^+ e^- \rightarrow Z/\gamma \rightarrow H^+ H^-\), excluding \(M_{H^\pm } \lesssim 80\) GeV (Type II) and \(M_{H^\pm } \lesssim 72.5\) GeV (Type I) at \(95\%\) confidence level. Among the constraints from *B* meson decays (flavor physics constraints), the \(B\rightarrow X_s\gamma \) decay [57] puts a very strong constraint on Type II and Type Y 2HDM, excluding \(M_{H^\pm } \lesssim 580\) GeV and almost independently of \(\tan \beta \). For Type I and Type X, the \(B\rightarrow X_s\gamma \) constraint is sensitive only for low \(\tan \beta .\) So for \(M_H^{\pm } \lesssim 580\) GeV, Type II and Type Y are not considered further.

^{3}The exclusion regions are shown with green colors in Fig. 3 using the 8 TeV CMS results at an integrated luminosity of 19.7 \(\hbox {fb}^{-1}\) for Type I and Type X. In Type X the leptonic coupling being proportional to \(\tan \beta \) excludes a slightly larger region of \(\tan \beta \). Using the upper bounds on the \(\sigma _{H^\pm }\)BR\((H^\pm \rightarrow \tau ^\pm \nu )\) from the latest CMS results [35] for \(\sqrt{s}=13\) TeV at an integrated luminosity of 35.9 \(\hbox {fb}^{-1}\), a much larger region of \(\tan \beta \) is excluded as shown in red colors in Fig. 3 for both Type I and Type X. Just above \(M_{H^\pm }=160\) GeV \(\tan \beta \lesssim 1\) is allowed by this channel in the Type X model. This is because the exclusion in Type X at low \(\tan \beta \) is less severe than Type I.

*tb*channel, unlike the \(\tau \nu \) channel, is not clean enough and suffers from various QCD backgrounds, but sophisticated analysis is used to study the

*tb*channel in both 8 TeV and 13 TeV by the CMS collaboration. The CMS 8 TeV upper limit on \(\sigma (pp \rightarrow t(b)H^+)\) assuming BR(\(H^+ \rightarrow t {\bar{b}}) = 100\%\) [59] restricts the parameter space for \(200<M_{H^\pm }<600\) GeV. The exclusion region using the 8 TeV results are shown in green colors in Fig. 4 for Type I. A recent paper from the CMS collaboration [36] for \(\sqrt{s}=13\) TeV and 35.9 \(\hbox {fb}^{-1}\) puts an upper limit at \(95\%\) CL on \(\sigma _{H^\pm }\text {BR}(H^+ \rightarrow t{\bar{b}})\) with the single-lepton and dilepton final states combined. The resulting exclusion regions in the \(M_{H^\pm }\)–\(\tan \beta \) plane for heavy charged Higgs \(M_{H^\pm }\in [200,2000]\) GeV in Type I and \(M_{H^\pm }\in [600,2000]\) in Type II are shown in Fig. 4 with red colors. Since the charged Higgs leptonic decay mode in TypeY is much suppressed compared to the \(H^+ \rightarrow t{\bar{b}}\) mode and for the Type X scenario, the \(H^+ \rightarrow t {\bar{b}}\) mode is dominant for low \(\tan \beta \) as shown in Fig. 2 (bottom two plots). The exclusion regions of Type X and Type Y are equivalent to the exclusion regions of Type I and Type II, respectively.

*A*. But once the bosonic decays are kinematically allowed, the charged Higgs boson can significantly decay into these channels. Figure 5 shows the exclusion regions coming from the \(H^\pm \rightarrow \tau ^\pm \nu \) channel where the mass difference \(M_{H^\pm }-M_A=85\) GeV is considered for \(M_{H^\pm }\in [100,160]\) GeV and \(M_{H^\pm }\sim M_H\). The red regions are excluded by using the upper limits on \(\sigma _{H^\pm }BR(H^\pm \rightarrow \tau ^\pm \nu )\) CMS 13 TeV observations and the green regions are excluded by using the upper limits on BR\((t \rightarrow H^+ b )\)BR(\(H^\pm \rightarrow \tau ^\pm \nu \)) CMS 8 TeV observations. For this choice of the mass difference, the exclusion regions are less than for Fig. 3 because of the significant decay of \(H^\pm \) into \(W^\pm A\). As mentioned above, in Type X the leptonic coupling being proportional to \(\tan \beta \) excludes a larger region than for Type I.

*A*is \(\sim 85\) GeV for \(M_{H^\pm }\in [100,160]\) GeV. The charged Higgs produced in

*pp*collision in LHC at an integrated luminosity of 35.9 \(\hbox {fb}^{-1}\) decays dominantly into \(W^\pm \) and

*A*with final states \(e\mu \mu \) or \(\mu \mu \mu \). In this analysis, the CMS assumed BR(\(H^\pm \rightarrow W^\pm A) = 1\) and BR(\(A\rightarrow \mu ^+ \mu ^-) = 3\times 10^{-4}\). Also this is the first experimental result in the channel \(H^\pm \rightarrow W^\pm A\), \(A\rightarrow \mu ^+ \mu ^-\) at LHC to put upper limits on BR\((t \rightarrow H^+ b)\). Such a low branching fraction of \(A\rightarrow \mu ^+ \mu ^-\) can be realized in Type I 2HDM where BR\((A\rightarrow \mu ^+ \mu ^-) \sim 2.4\times 10^{-4}\) for \(A\in [15,75]\) GeV and it goes very well with the CMS assumption. The other assumption, BR(\(H^\pm \rightarrow W^\pm A)=1\), is satisfied in Type I scenario when \(\tan \beta \ge 1\) as seen in Fig. 6. In Type I scenario the charged Higgs coupling to the fermionic sector being proportional to \(\cot \beta \), the assumption BR(\(H^\pm \rightarrow W^\pm A)=1\) starts to fail for \(\tan \beta < 1\). The theoretical constraints can be satisfied with a proper choice of \(m^2_{12}\) and the oblique parameter

*T*can be satisfied by considering \(M_{H^\pm }\cong M_H\). The observed upper limits at 95\(\%\) CL on BR\((t \rightarrow H^+ b)\) for \(M_H^{\pm }\in [100,160]\) GeV and \(M_{H^\pm }-M_A=85\) GeV with the above assumptions are used to find the exclusion region. In Fig. 6 the red region (above \(\tan \beta \ge 1\)) shows the exclusion region where we have smoothly fitted the observed CMS upper limit on BR\((t \rightarrow H^+ b)\) in the range of 0.63 to 2.9\(\%\). Other 2HDMs like Type II and Type Y are not considered, as for this mass range of charged Higgs Type II and Type Y are ruled out by the \(B\rightarrow X_s \gamma \) constraint. Unlike Type I where all the fermionic couplings of

*A*are proportional to \(\cot \beta \), in Type X the pseudoscalar coupling to the lepton sector is proportional to \(\tan \beta \) whereas its coupling to the quark sector is proportional to \(\cot \beta \). Thus the BR\((A\rightarrow \mu ^+\mu ^-)\) increases with \(\tan \beta \). The CMS assumption is satisfied in Type X scenario only when \(\tan \beta \) is close to 1 and for this situation the theoretically estimated BR\((t\rightarrow H^+ b)\) is the same as in Type I (because of the same coupling) and above the upper limit of the CMS observation. Comparing Figs. 5 and 6, the exclusion regions coming from the \(\tau \nu \) channel are weak once the \(H^\pm \rightarrow W^\pm A\) channel is open. Figure 6 (bottom plot) excludes the regions of parameter space which are not excluded in Fig. 5 (top plot).

For completeness, the indirect constraints from the flavor physics is also considered in the paper as the *B* meson decay depends strongly on the parameters \(M_{H^\pm }\) and \(\tan \beta \). The public code SuperIso-3.7 [61] is used for flavor physics computation. As mentioned above, for Type II and Type Y, a charged Higgs boson lighter than \(\sim 580\) GeV is completely ruled out for a large region of \(\tan \beta \) by the BR(\(B\rightarrow X_s \gamma \)) constraint [62], which is measured to be \((3.32\pm 0.15)\times 10^{-4}\) [63]. For Type I (and similarly for Type X) the BR(\(B\rightarrow X_s \gamma \)) constraint excludes \(\tan \beta \lesssim 2 \). In Figs. 3, 4, 5 and 6 the regions below the black dashed lines are excluded by the BR(\(B\rightarrow X_s \gamma \)) observation. In Type II (and similarly in Type Y) for \(M_{H^\pm }\) above 600 GeV, the rare decay of \(B_s \rightarrow \mu ^+ \mu ^-\) (the branching fraction of which is measured to be (\(3.0\pm 0.6\pm 0.25)\times 10^{-9}\)) as reported by LHCb collaboration excludes a greater region of parameter space than the \(B\rightarrow X_s\gamma \) constraint. For the Type II scenario in Fig. 4 the region below the black continuous line is excluded by BR(\(B_s \rightarrow \mu ^+ \mu ^-\)) constraint.

## 5 Summary and conclusions

The 2HDM is the simplest extension of SM containing charged Higgs. The two most dominant channels, \(H^\pm \rightarrow \tau ^\pm \nu \) and \(H^+ \rightarrow t {\bar{b}}\), for the search of \(H^\pm \) are studied using the latest CMS results for \(\sqrt{s}=13\) TeV at an integrated luminosity of 35.9 fb \(^{-1}\). The \(\tau \nu \) channel excludes a large region of \(\tan \beta < {\mathcal {O}}(15)\) for a charged Higgs mass less than 160 GeV both in Type I and Type X. For a heavy charged Higgs boson, the \(\tau \nu \) channel does not lead to any significant constraint on the parameter space. However, in this case, the *tb* channel excludes a significant range of values of \(\tan \beta \) in Type I and II and this behavior is carried over to Type X and Type Y. The exclusion regions obtained from the 13 TeV CMS results are compared with the exclusion regions from 8 TeV CMS results. Exclusion bounds from *B* meson decays are also discussed for all Yukawa types of 2HDM. The fermionic channels are studied for situations where the exotic decays of a charged Higgs boson into a gauge boson and neutral scalars (\(H^\pm \rightarrow W^\pm /h/H/A\)) are suppressed either by the alignment limit or due to limited phase space. But once the bosonic decay channels are open, they can be the dominant charged Higgs decay channels and the constraints from \(H^\pm \rightarrow \tau ^\pm \nu \) and \(H^+ \rightarrow t{\bar{b}}\) will be less restrictive. The CMS collaboration for the first time studied the exotic bosonic decay channel \(H^\pm \rightarrow W^\pm A\) and \(A \rightarrow \mu ^+ \mu ^-\) to put upper limits on BR(\(t \rightarrow H^+ b\)) for \(M_{H^\pm } \in [100,160]\) GeV with a mass splitting of \(M_{H^\pm }-M_A=85\) GeV. These results are used to exclude a significant parameter space of the charged Higgs boson in Type I 2HDM which is not excluded by the \(\tau \nu \) channel. It is expected that a significant parameter space of the charged Higgs boson will be excluded in all Yukawa types of 2HDM (as well as in MSSM) if these exotic bosonic decay channels of charged Higgs are analyzed by CMS or ATLAS collaborations for various charged Higgs mass ranges.

## Footnotes

- 1.
Since the charged Higgs production cross sections scales with the glue–glue luminosity, in the mass range of 200–600 GeV, the production cross section increases by a factor of 4–6 from 8 to 13 TeV.

- 2.
The cross sections are provided in https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWGMSSMCharged .

- 3.
The constraints of charged Higgs bosons decaying in the fermionic sector are useful only when the charged Higgs bosonic decays are suppressed.

## Notes

### Acknowledgements

The author would like to thank Ravindra K. Verma and Aravind H. Vijay for some useful discussions. The author also acknowledges Pankaj Jain for discussions and useful comments on the paper.

## References

- 1.ATLAS collaboration, G. Aad et al., Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett.
**B716**, 1–29 (2012). arXiv:1207.7214 - 2.ATLAS collaboration, G. Aad et al., Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC, Phys. Lett.
**B726**, 88–119 (2013). arXiv:1307.1427 - 3.CMS collaboration, S. Chatrchyan et al., Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett.
**B716**, 30–61 (2012). arXiv:1207.7235 - 4.CMS collaboration, S. Chatrchyan et al., Observation of a New Boson with Mass Near 125 GeV in \(pp\) Collisions at \(\sqrt{s}\) = 7 and 8 TeV, JHEP
**06**, 081 (2013). arXiv:1303.4571 - 5.J.F. Gunion, H.E. Haber, The CP conserving two Higgs doublet model: the approach to the decoupling limit. Phys. Rev. D
**67**, 075019 (2003). arXiv:hep-ph/0207010 ADSCrossRefGoogle Scholar - 6.J.F. Gunion, H.E. Haber, G.L. Kane, S. Dawson, The Higgs Hunter’s Guide. Front. Phys.
**80**, 1–404 (2000)Google Scholar - 7.G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher, J.P. Silva, Theory and phenomenology of two-Higgs-doublet models. Phys. Rept.
**516**, 1–102 (2012). arXiv:1106.0034 ADSCrossRefGoogle Scholar - 8.S. Davidson, H.E. Haber, Basis-independent methods for the two-Higgs-doublet model. Phys. Rev. D
**72**, 035004 (2005). arXiv:hep-ph/0504050 ADSCrossRefGoogle Scholar - 9.A. Pich, P. Tuzon, Yukawa alignment in the two-Higgs-doublet model. Phys. Rev. D
**80**, 091702 (2009). arXiv:0908.1554 ADSCrossRefGoogle Scholar - 10.J. Bernon, J.F. Gunion, H.E. Haber, Y. Jiang, S. Kraml, Scrutinizing the alignment limit in two-Higgs-doublet models: m\(_h\)=125 GeV. Phys. Rev. D
**92**, 075004 (2015). arXiv:1507.00933 ADSCrossRefGoogle Scholar - 11.J. Bernon, J.F. Gunion, H.E. Haber, Y. Jiang, S. Kraml, Scrutinizing the alignment limit in two-Higgs-doublet models. II. m\(_H\)=125 GeV. Phys. Rev
**D93**, 035027 (2016). arXiv:1511.03682 ADSGoogle Scholar - 12.M. Aoki, S. Kanemura, K. Tsumura, K. Yagyu, Models of Yukawa interaction in the two Higgs doublet model, and their collider phenomenology. Phys. Rev. D
**80**, 015017 (2009). arXiv:0902.4665 ADSCrossRefGoogle Scholar - 13.F. Mahmoudi, O. Stal, Flavor constraints on the two-Higgs-doublet model with general Yukawa couplings. Phys. Rev. D
**81**, 035016 (2010). arXiv:0907.1791 ADSCrossRefGoogle Scholar - 14.M. Maniatis, O. Nachtmann, On the phenomenology of a two-Higgs-doublet model with maximal CP symmetry at the LHC. II. Radiative effects. JHEP
**04**, 027 (2010). arXiv:0912.2727 ADSzbMATHCrossRefGoogle Scholar - 15.M. Jung, A. Pich, P. Tuzon, Charged-Higgs phenomenology in the Aligned two-Higgs-doublet model. JHEP
**11**, 003 (2010). arXiv:1006.0470 ADSzbMATHCrossRefGoogle Scholar - 16.C.-Y. Chen, S. Dawson, Exploring two Higgs doublet models through Higgs production. Phys. Rev. D
**87**, 055016 (2013). arXiv:1301.0309 ADSCrossRefGoogle Scholar - 17.C.-W. Chiang, K. Yagyu, Implications of Higgs boson search data on the two-Higgs doublet models with a softly broken \(Z_2\) symmetry. JHEP
**07**, 160 (2013). arXiv:1303.0168 ADSCrossRefGoogle Scholar - 18.B. Coleppa, F. Kling, S. Su, Constraining type II 2HDM in light of LHC Higgs searches. JHEP
**01**, 161 (2014). arXiv:1305.0002 ADSGoogle Scholar - 19.C.-Y. Chen, S. Dawson, M. Sher, Heavy Higgs searches and constraints on two Higgs doublet models. Phys. Rev. D
**88**, 015018 (2013). arXiv:1305.1624 ADSCrossRefGoogle Scholar - 20.P. Bechtle, S. Heinemeyer, O. Stal, T. Stefaniak, G. Weiglein, Applying exclusion likelihoods from LHC searches to extended Higgs sectors. Eur. Phys. J. C
**75**, 421 (2015). arXiv:1507.06706 ADSCrossRefGoogle Scholar - 21.V. Keus, S.F. King, S. Moretti, K. Yagyu, CP violating two-Higgs-doublet model: constraints and LHC predictions. JHEP
**04**, 048 (2016). arXiv:1510.04028 ADSGoogle Scholar - 22.A.G. Akeroyd et al., Prospects for charged Higgs searches at the LHC. Eur. Phys. J. C
**77**, 276 (2017). arXiv:1607.01320 ADSCrossRefGoogle Scholar - 23.G. Cacciapaglia, A. Deandrea, S. Gascon-Shotkin, S. Le Corre, M. Lethuillier, J. Tao, Search for a lighter Higgs boson in Two Higgs Doublet Models. JHEP
**12**, 068 (2016). arXiv:1607.08653 ADSCrossRefGoogle Scholar - 24.M. Krawczyk, S. Moretti, P. Osland, G. Pruna, R. Santos, Prospects for 2HDM charged Higgs searches. J. Phys. Conf. Ser.
**873**, 012048 (2017). arXiv:1703.05925 CrossRefGoogle Scholar - 25.A. Arbey, F. Mahmoudi, O. Stal, T. Stefaniak, Status of the charged Higgs Boson in two Higgs doublet models. Eur. Phys. J. C
**78**, 182 (2018). arXiv:1706.07414 ADSCrossRefGoogle Scholar - 26.A. Arhrib, R. Benbrik, H. Harouiz, S. Moretti, A. Rouchad, A guidebook to hunting charged Higgs Bosons at the LHC. arXiv:1810.09106
- 27.D. Bhatia, U. Maitra, S. Niyogi, Discovery prospects of a light Higgs boson at the LHC in type-I 2HDM. Phys. Rev. D
**97**, 055027 (2018). arXiv:1704.07850 ADSCrossRefGoogle Scholar - 28.S. Gori, H.E. Haber, E. Santos, High scale flavor alignment in two-Higgs doublet models and its phenomenology. JHEP
**06**, 110 (2017). arXiv:1703.05873 ADSzbMATHCrossRefGoogle Scholar - 29.A. Arhrib, R. Benbrik, R. Enberg, W. Klemm, S. Moretti, S. Munir, Identifying a light charged Higgs boson at the LHC Run II. Phys. Lett. B
**774**, 591–598 (2017). arXiv:1706.01964 ADSCrossRefGoogle Scholar - 30.L. Barak, Search for charged higgs bosons with the atlas detector. Nucl. Particle Phys. Proc.
**273–275**, 896–900 (2016)ADSCrossRefGoogle Scholar - 31.C. Degrande, R. Frederix, V. Hirschi, M. Ubiali, M. Wiesemann, M. Zaro, Accurate predictions for charged Higgs production: closing the \(m_{H^{\pm }}\sim m_t\) window. Phys. Lett. B
**772**, 87–92 (2017). arXiv:1607.05291 ADSCrossRefGoogle Scholar - 32.M. Flechl, R. Klees, M. Kramer, M. Spira, M. Ubiali, Improved cross-section predictions for heavy charged Higgs boson production at the LHC. Phys. Rev. D
**91**, 075015 (2015). arXiv:1409.5615 ADSCrossRefGoogle Scholar - 33.C. Degrande, M. Ubiali, M. Wiesemann, M. Zaro, Heavy charged Higgs boson production at the LHC. JHEP
**10**, 145 (2015). arXiv:1507.02549 ADSCrossRefGoogle Scholar - 34.LHC Higgs Cross Section Working Group collaboration, D. de Florian et al., Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector. arXiv:1610.07922
- 35.CMS collaboration, A.M. Sirunyan et al., Search for charged Higgs bosons in the H\(^{\pm } \rightarrow \tau ^{\pm }\nu _\tau \) decay channel in proton-proton collisions at \(\sqrt{s}=\) 13 TeV, arXiv:1903.04560
- 36.CMS collaboration, C. Collaboration, Search for a charged Higgs boson decaying into top and bottom quarks in proton-proton collisions at 13 TeV in events with electrons or muonsGoogle Scholar
- 37.CMS collaboration, A.M. Sirunyan et al., Search for a light charged Higgs boson decaying to a W boson and a CP-odd Higgs boson in final states with e\(\mu \mu \) or \(\mu \mu \mu \) in proton-proton collisions at \(\sqrt{s}=\) 13 TeV, arXiv:1905.07453
- 38.F. Kling, A. Pyarelal, S. Su, Light charged higgs bosons to AW/HW via top decay. JHEP
**11**, 051 (2015). arXiv:1504.06624 ADSCrossRefGoogle Scholar - 39.B. Coleppa, F. Kling, S. Su, Charged Higgs search via \(AW^\pm /HW^\pm \) channel. JHEP
**12**, 148 (2014). arXiv:1408.4119 ADSCrossRefGoogle Scholar - 40.M. Czakon, A. Mitov, Top++: a program for the calculation of the top-pair cross-section at hadron colliders. Comput. Phys. Commun.
**185**, 2930 (2014). arXiv:1112.5675 ADSCrossRefGoogle Scholar - 41.R. Harlander, M. Kramer, M. Schumacher, Bottom-quark associated Higgs-boson production: reconciling the four- and five-flavour scheme approach. arXiv:1112.3478
- 42.A. Djouadi, J. Kalinowski, M. Spira, HDECAY: A Program for Higgs boson decays in the standard model and its supersymmetric extension. Comput. Phys. Commun.
**108**, 56–74 (1998). arXiv:hep-ph/9704448 ADSzbMATHCrossRefGoogle Scholar - 43.A. Djouadi, J. Kalinowski, M. Muehlleitner, M. Spira, HDECAY: Twenty\(_{++}\) years after. Comput. Phys. Commun.
**238**, 214–231 (2019). arXiv:1801.09506 ADSCrossRefGoogle Scholar - 44.A. Djouadi, J. Kalinowski, P.M. Zerwas, Two and three-body decay modes of SUSY Higgs particles. Z. Phys. C
**70**, 435–448 (1996). arXiv:hep-ph/9511342 CrossRefGoogle Scholar - 45.N.G. Deshpande, E. Ma, Pattern of symmetry breaking with two higgs doublets. Phys. Rev. D
**18**, 2574–2576 (1978)ADSCrossRefGoogle Scholar - 46.S. Nie, M. Sher, Vacuum stability bounds in the two Higgs doublet model. Phys. Lett. B
**449**, 89–92 (1999). arXiv:hep-ph/9811234 ADSCrossRefGoogle Scholar - 47.B.W. Lee, C. Quigg, H.B. Thacker, Weak interactions at very high energies: the role of the higgs-boson mass. Phys. Rev. D
**16**, 1519–1531 (1977)ADSCrossRefGoogle Scholar - 48.B. Grinstein, C.W. Murphy, P. Uttayarat, One-loop corrections to the perturbative unitarity bounds in the CP-conserving two-Higgs doublet model with a softly broken \( {\mathbb{Z}} _{2} \) symmetry. JHEP
**06**, 070 (2016). arXiv:1512.04567 ADSCrossRefGoogle Scholar - 49.S. Kanemura, T. Kubota, E. Takasugi, Lee-Quigg-Thacker bounds for Higgs boson masses in a two doublet model. Phys. Lett. B
**313**, 155–160 (1993). arXiv:hep-ph/9303263 ADSCrossRefGoogle Scholar - 50.A.G. Akeroyd, A. Arhrib, E.-M. Naimi, Note on tree level unitarity in the general two Higgs doublet model. Phys. Lett. B
**490**, 119–124 (2000). arXiv:hep-ph/0006035 ADSCrossRefGoogle Scholar - 51.A. Arhrib, Unitarity constraints on scalar parameters of the standard and two Higgs doublets model, in Workshop on Noncommutative Geometry, Superstrings and Particle Physics Rabat, Morocco, June 16-17, 2000, (2000). arXiv:hep-ph/0012353
- 52.W. Grimus, L. Lavoura, O.M. Ogreid, P. Osland, A Precision constraint on multi-Higgs-doublet models. J. Phys.
**G35**, 075001 (2008). arXiv:0711.4022 ADSzbMATHCrossRefGoogle Scholar - 53.W. Grimus, L. Lavoura, O.M. Ogreid, P. Osland, The Oblique parameters in multi-Higgs-doublet models. Nucl. Phys. B
**801**, 81–96 (2008). arXiv:0802.4353 ADSzbMATHCrossRefGoogle Scholar - 54.Particle Data Group collaboration, M. Tanabashi, K. Hagiwara, K. Hikasa, K. Nakamura, Y. Sumino, F. Takahashi et al., Review of particle physics, Phys. Rev. D
**98**, 030001 (2018)Google Scholar - 55.D. Eriksson, J. Rathsman, O. Stal, 2HDMC: Two-Higgs-doublet model calculator physics and manual. Comput. Phys. Commun.
**181**, 189–205 (2010). arXiv:0902.0851 ADSzbMATHCrossRefGoogle Scholar - 56.ALEPH, DELPHI, L3, OPAL, LEP collaboration, G. Abbiendi et al., Search for Charged Higgs bosons: Combined Results Using LEP Data, Eur. Phys. J.
**C73**, 2463 (2013). arXiv:1301.6065 - 57.Heavy Flavor Averaging Group (HFAG) collaboration, Y. Amhis et al., Averages of \(b\)-hadron, \(c\)-hadron, and \(\tau \)-lepton properties as of summer (2014). arXiv:1412.7515
- 58.ATLAS collaboration, G. Aad et al., Search for charged Higgs bosons decaying via \(H^{\pm } \rightarrow \tau ^{\pm }\nu \) in fully hadronic final states using \(pp\) collision data at \(\sqrt{s} = 8\) TeV with the ATLAS detector, JHEP
**03**, 088 (2015). arXiv:1412.6663 - 59.CMS collaboration, V. Khachatryan et al., Search for a charged Higgs boson in pp collisions at \( \sqrt{s}=8 \) TeV, JHEP
**11**, 018 (2015). arXiv:1508.07774 - 60.ATLAS collaboration, G. Aad et al., Search for charged Higgs bosons in the \(H^{\pm } \rightarrow tb\) decay channel in \(pp\) collisions at \(\sqrt{s}=8 \) TeV using the ATLAS detector, JHEP
**03**, 127 (2016). arXiv:1512.03704 - 61.F. Mahmoudi, SuperIso v2.3: A Program for calculating flavor physics observables in Supersymmetry. Comput. Phys. Commun.
**180**, 1579–1613 (2009)ADSCrossRefGoogle Scholar - 62.M. Misiak, M. Steinhauser, Weak radiative decays of the B meson and bounds on \(M_{H^\pm }\) in the two-higgs-doublet model. Eur. Phys. J. C
**77**, 201 (2017). arXiv:1702.04571 ADSCrossRefGoogle Scholar - 63.HFLAV collaboration, Y. Amhis et al., Averages of \(b\)-hadron, \(c\)-hadron, and \(\tau \)-lepton properties as of summer 2016, Eur. Phys. J.
**C77**, 895 (2017). arXiv:1612.07233

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