Radiative corrections to the Yukawa coupling constants in two Higgs doublet models

A pattern of deviations in the Standard Model (SM) like Higgs boson (h) couplings from their SM predictions depends on the structure of the Higgs sector and the Yukawa interaction. In particular, in Two Higgs Doublet Models (THDMs) with a softly-broken Z2 symmetry, different characteristic patterns of deviation in Yukawa coupling constants (hff‾) can be allowed depending on four types of Yukawa interactions. We calculate hff‾ coupling constants at the one-loop level in all the types of THDMs. Even if there is no deviation in the hff‾ couplings at the tree level, they can deviate from the SM predictions by a few percent due to extra Higgs boson loop contributions. We find that if the deviations in the gauge couplings hVV(V=Z,W) are found with an enough large to be measured at the International Linear Collider (ILC), the scale factors for the hff‾ couplings do not overlap among the THDMs with four types of Yukawa interactions even taking into account the radiative corrections. Therefore, in such a case, we can indirectly determine the type of the THDMs at the ILC even without information from direct searches of the additional Higgs bosons.

We discuss a possibility that the parameter space of the two Higgs doublet model is significantly narrowed down by considering the synergy between direct searches for additional Higgs bosons at the LHC and its luminosity upgraded operation and precision measurements of the Higgs boson properties at future electron-positron colliders such as the International Linear Collider. We show that, in the case where the coupling constants of the discovered Higgs boson are slightly different from the predicted values in the standard model, most of the parameter space is explored by the direct searches of extra Higgs bosons, in particular for the decays of the extra Higgs bosons into the discovered Higgs boson, and also by the theoretical arguments such as perturbative unitarity and vacuum stability. This can be done because there appears an upper limit on the mass of the extra Higgs bosons as long as the deviation exists in the Higgs boson coupling. We also show that in the alignment limit where all the Higgs boson couplings take the standard model like values most of the parameter space cannot be excluded because most of the Higgs to Higgs decays are suppressed and also there is no upper limit on the masses from the theoretical arguments.

After the discovery of the standard model-like Higgs boson at the LHC, the structure of the Higgs sector remains unknown. We discuss how it can be determined by the combination of direct and indirect searches for additional Higgs bosons at future collider experiments. First of all, we evaluate expected excluded regions for the mass of additional neutral Higgs bosons from direct searches at the LHC with the 14 TeV collision energy in the two Higgs doublet models with a softly broken ${Z}_{2}$ symmetry. Second, precision measurements of the Higgs boson couplings at future experiments can be used for the indirect search of extended Higgs sectors if the measured coupling constant with the gauge boson slightly deviates from the standard model value. In particular, in the two Higgs doublet model with the softly broken discrete symmetry, there are four types of Yukawa interactions, so that they can be discriminated by measuring the pattern of deviations in Yukawa coupling constants. Furthermore, we can fingerprint various extended Higgs sectors with future precision data by detecting the pattern of deviations in the coupling constants of the standard model-like Higgs boson. We demonstrate how the pattern of deviations can be different among various Higgs sectors that predict the electroweak rho parameter to be unity, such as models with additional an isospin singlet, a doublet, triplets, or a septet. We conclude that, as long as the gauge coupling constant of the Higgs boson slightly differs from the standard model prediction but is enough to be detected at the LHC and its high-luminosity run or at the International Linear Collider, we can identify the nonminimal Higgs sector even without direct discovery of additional Higgs bosons at the LHC.

We discuss two Higgs doublet models with a softly-broken discrete S3 symmetry, where the mass matrix for charged-leptons is predicted as the diagonal form in the weak eigenbasis of lepton fields. Similarly to an introduction of Z2 symmetry, the tree level flavor changing neutral current can be forbidden by imposing the S3 symmetry to the model. Under the S3 symmetry, there are four types of Yukawa interactions depending on the S3 charge assignment to right-handed fermions. We find that extra Higgs bosons can be muon and electron specific in one of four types of the Yukawa interaction. This property does not appear in any other two Higgs doublet models with a softly-broken Z2 symmetry. We discuss the phenomenology of the muon and electron specific Higgs bosons at the Large Hadron Collider; namely we evaluate allowed parameter regions from the current Higgs boson search data and discovery potential of such a Higgs boson at the 14 TeV run.

We investigate single- and double-$h$, the discovered Standard Model (SM)-like Higgs boson, production at future $e^+e^-$ colliders in Composite 2-Higgs Doublet Models (C2HDMs) and Elementary 2-Higgs Doublet Models (E2HDMs) with a softly-broken $Z_2$ symmetry. We first survey their parameter spaces allowed by theoretical bounds from perturbative unitarity and vacuum stability as well as by future data at the Large Hadron Collider (LHC) with an integrated luminosity up to 3000 fb$^{-1}$ under the assumption that no new Higgs boson is detected. We then discuss how different the cross sections can be between the two scenarios when $\kappa_V^{}$, the $hVV$ ($V=W^\pm,Z$) coupling normalised to the SM value, is taken to be the same value in the both scenario We find that if $\kappa_V^2$ is found to be, e.g., $0.98$, then the cross sections in C2HDMs with $f$ (the compositeness scale) in the TeV region can be maximally changed to be about $-15\%$, $-18\%$, $-50\%$ and $-35\%$ for the $e^+e^-\to t \bar t h$, $e^+e^-\to Zhh$, $e^+e^-\to e^+e^-hh$ and $e^+e^-\to t\bar{t}hh$ processes, respectively, with respect to those in E2HDMs. Thus, a future electron-positron collider has the potential to discriminate between E2HDMs and C2HDMs, even when only $h$ event rates are measured.

We discuss scenarios with wrong-sign (WS) Yukawa couplings for the discovered Higgs boson in the Yukawa-aligned two Higgs doublet model. In the WS scenario, Yukawa couplings for down-type quarks and/or charged leptons have an opposite sign as compared to those of the Higgs boson in the standard model, which can be consistent with current flavor data and the Higgs signal strengths. The phenomenology of additional Higgs bosons in such a scenario can be significantly different from that with right-sign Yukawa couplings, mainly due to a larger Higgs boson mixing to be required in the wrong-sign case. We show the parameter space which is excluded or explored by direct searches for the additional Higgs bosons at the current and high-luminosity LHC under the constraints from perturbative unitarity and vacuum stability. In particular, we find that most of the parameter space is explored in the WS scenario with the Type-X (lepton specific) Yukawa interaction which is a special case of the Yukawa alignment realized by imposing a softly-broken ℤ2 symmetry. We propose that multi-Higgs events from pair productions of the additional Higgs bosons can be the smoking gun signature to probe the WS scenario, and give the expected number of events at the high-luminosity LHC.

A detailed simulation study is performed for multi-$\ensuremath{\tau}$ signatures at the Large Hadron Collider, which can be used to probe additional Higgs bosons with lepton-specific Yukawa interactions. We here consider the two Higgs doublet model with the Type-X Yukawa interaction, where nonstandard Higgs bosons predominantly decay into tau leptons. These extra Higgs bosons can be pair produced at hadron colliders. Consequently, multi-$\ensuremath{\tau}$ originated signals appear in the final state as a promising signature of such a model. We find that the main background can be considerably reduced by requiring the high multiplicity of leptons and tau-jets with appropriate kinematical cuts in the final state. Thus, assuming the integrated luminosity of a hundred of inverse fb, the excess can be seen in various three- and four-lepton channels. With the integrated luminosity of thousands of inverse fb, the determination of the mass as well as ratios of leptonic decay branching ratios of these Higgs bosons would also be possible.

We investigate the impact of electroweak (EW), scalar and QCD corrections to the full set of decay branching ratios of an additional CP-even Higgs boson (H) in the two Higgs doublet model with a softly broken Z2 symmetry. We employ the improved gauge independent on-shell scheme in the renormalized vertices. We particularly focus on the scenario near the alignment limit in which couplings of the discovered 125 GeV Higgs boson (h) coincide with those of the standard model while the Hhh coupling vanishes at tree level. The renormalized decay rate for H→hh can significantly be changed from the prediction at tree level due to non-decoupling loop effects of additional Higgs bosons, even in the near alignment case. We find that the radiative corrections to the branching ratio of H→hh can be a few ten percent level in the case with the masses of additional Higgs bosons being degenerate under the constraints of perturbative unitarity, vacuum stability and the EW precision data. Further sizable corrections can be obtained for the case with a mass difference among the additional Higgs bosons.

We study the Higgs boson mass spectrum of a classical scale invariant realization of the two Higgs doublet model (SI-2HDM). The classical scale symmetry of the theory is explicitly broken by quantum loop effects due to gauge interactions, Higgs self-couplings and top quark Yukawa couplings. We determine the allowed parameter space compatible with perturbative unitarity and electroweak precision data. Taking into account the LEP and the recent LHC exclusion limits on a standard-model-like Higgs boson HSM, we obtain rather strict constraints on the mass spectrum of the heavy Higgs sector of the SI-2HDM. In particular, if MHSM 125 GeV, the SI-2HDM strongly favors scenarios in which at least one of the nonstandard neutral Higgs bosons has a mass close to 400 GeV and is generically degenerate with the charged Higgs boson, whilst the third neutral Higgs scalar is lighter than 500 GeV.

We study lepton flavor violation (LFV) associated with tau leptons in the framework of the two Higgs doublet model, in which LFV couplings are introduced as a deviation from Model II Yukawa interaction. Parameters of the model are constrained from experimental results and also from requirements of theoretical consistencies such as vacuum stability and perturbative unitarity. Current data for rare tau decays provide substantial upper limits on the LFV Yukawa couplings in the large $\mathrm{tan}\ensuremath{\beta}$ region ($\mathrm{tan}\ensuremath{\beta}\ensuremath{\gtrsim}30$), which are comparable with predictions in fundamental theories. Here $\mathrm{tan}\ensuremath{\beta}$ is the ratio of vacuum expectation values of the two Higgs doublets. We show that a search for the LFV decays ${\ensuremath{\phi}}^{0}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ensuremath{\mp}}$ $({\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{e}^{\ensuremath{\mp}})$ of neutral Higgs bosons (${\ensuremath{\phi}}^{0}=h,H$ and $A$) at future collider experiments can be useful to further constrain the LFV couplings especially in the relatively small $\mathrm{tan}\ensuremath{\beta}$ region ($\mathrm{tan}\ensuremath{\beta}\ensuremath{\lesssim}30$), where rare tau decay data cannot give any strong limit.

H-COUP Version 3: A program for one-loop corrected decays of any Higgs bosons in non-minimal Higgs models

We evaluate the baryon number abundance based on the charge transport scenario of top quarks in the CP-violating two Higgs doublet model, in which Yukawa interactions are aligned to avoid dangerous flavor changing neutral currents, and coupling constants of the lightest Higgs boson with the mass 125 GeV coincide with those in the standard model at tree level to satisfy the current LHC data. In this model, the severe constraint from the electric dipole moment of electrons, which are normally difficult to be satisfied, can be avoided by destructive interferences between CP-violating phases in Yukawa interactions and scalar couplings in the Higgs potential. Viable benchmark scenarios are proposed under the current available data and basic theoretical bounds. We find that the observed baryon number can be reproduced in this model, where masses of additional Higgs bosons are typically 300–400 GeV. Furthermore, it is found that the triple Higgs boson coupling is predicted to be 35–55 % larger than the standard model value.

We consider two Higgs doublet models with a softly broken U(1) symmetry, for various limiting values of the scalar mixing angles $\alpha$ and $\beta$. These correspond to the Standard Model Higgs particle being the lighter CP-even scalar (alignment) or the heavier CP-even scalar (reverse alignment), and also the limit in which some of the Yukawa couplings of this particle are of the opposite sign from the vector boson couplings (wrong sign). In these limits we impose a criterion for naturalness by demanding that quadratic divergences cancel at one loop. We plot the allowed masses of the remaining physical scalars based on naturalness, stability, perturbative unitarity and constraints coming from the $\rho$ parameter. We also calculate the $h\to \gamma\gamma$ decay rate in the wrong sign limit.

We calculate radiative corrections to decay rates of CP-odd Higgs boson A for various decay modes in the four types of two Higgs doublet models with the softly broken discrete Z2 symmetry. The decay branching ratios are evaluated at the next-to-leading order for electroweak corrections and the next-to-next-to-leading order for QCD corrections. We comprehensively study the impact of the electroweak corrections on the decay rates and the branching ratios. We find that the radiative corrections can sizably modify the branching ratios, especially for the A→Zh decay mode in the nearly alignment scenario, where coupling constants of the SM-like Higgs boson h are close to those in the standard model. We also show correlations between the branching ratios of A and the scaling factor of the SM-like Higgs boson coupling including higher-order corrections. In addition, we show characteristic predictions on the decay pattern depending on the types of Yukawa interaction, by which we can discriminate the types of Yukawa interaction in future collider experiments.

The objective of this study is to correlate the scaling factor of the Standard Model (SM) like Higgs boson and the cross section ratio of the process $e^+ e^- \rightarrow hhf\overline{f}$ where $f\neq t$, normalized to SM predictions in the type I of the Two Higgs Doublet Model. All calculations have been performed at $\sqrt{s}=500$ GeV and $1 \leq \tan{\beta} \leq 30$ for masses $m_H = m_A = m_{H^\pm} = 300GeV$ and $m_H=300$ GeV, $m_A=m_{H^\pm}=500$ GeV. The working scenario is by taking without alignment limit, that is $s_{\beta-\alpha}= 0.98$ and $s_{\beta-\alpha}= 0.99,$ $0.995$, which gives the enhancement in the cross section, particularly a few times greater than the predictions of the SM due to resonant-impacts of the additional heavy neutral Higgs bosons. This shows that enhancement in cross section occurs on leaving the alignment i.e., $s_{\beta-\alpha}=1$, at which all the higgs that couple to vector bosons and fermions have the same values as in SM at tree level. A large value of enhancement factor is obtained at $s_{\beta-\alpha}= 0.98$ compared to $s_{\beta-\alpha}= 0.99,$ $0 .995$. Furthermore, the decrease in the enhancement factor is observed for the case when $m_H=300$ GeV, $m_A=m_{H^\pm}=500$ GeV. The behavior of the scaling factor with $\tan{\beta}$ is also studied, which shows that for large values of $\tan\beta$, the scaling factor becomes equal to $s_{\beta-\alpha}$. Finally a convincing correlation is achieved by taking into account, the experimental and theoretical constraints e.g, perturbative unitarity, vacuum stability and electroweak oblique parameters.