Phenomenological discriminations of the Yukawa interactions in two-Higgs doublet models with $Z_2$ symmetry

There are four types of two-Higgs doublet models under a discrete $Z_2$ symmetry imposed to avoid tree-level flavour-changing neutral current, i.e. type-I, type-II, type-X and type-Y models. We investigate the possibility to discriminate the four models in the light of the flavour physics data, including $B_s-\bar B_s$ mixing, $B_{s,d} \to \mu^+ \mu^-$, $B\to \tau\nu$ and $\bar B \to X_s \gamma$ decays, the recent LHC Higgs data, the direct search for charged Higgs at LEP, and the constraints from perturbative unitarity and vacuum stability. After deriving the combined constraints on the Yukawa interaction parameters, we have shown that the correlation between the mass eigenstate rate asymmetry $A_{\Delta\Gamma}$ of $B_{s} \to \mu^+ \mu^-$ and the ratio $R={\cal B}(B_{s} \to \mu^+ \mu^-)_{exp}/ {\cal B}(B_{s} \to \mu^+ \mu^-)_{SM}$ could be sensitive probe to discriminate the four models with future precise measurements of the observables in the $B_{s} \to \mu^+ \mu^-$ decay at LHCb.