Revisiting $B_s \to \mu^+\mu^-$ in the two-Higgs doublet models with $Z_2$ symmetry

TL;DR

This paper analyzes the rare decay $B_s o \mu^+\mu^-$ within four types of two-Higgs doublet models with $Z_2$ symmetry, deriving full one-loop Wilson coefficients and updating parameter bounds, finding similar contributions across models.

Contribution

It derives comprehensive one-loop Wilson coefficients for all four 2HDMs considering recent aligned 2HDM calculations, including a new term enhanced by $ an^2eta$ in type-II models.

Findings

All four 2HDMs contribute similarly to the decay rate within constrained parameters.

The soft $Z_2$ breaking parameter $M$ can significantly affect type-II models.

Discrimination between models based on $B_s o \mu^+\mu^-$ observables is unfeasible.

Abstract

We revisit the rare leptonic decay $B_s \to \mu^+ \mu^-$ in the two-Higgs doublet models with a softly broken $Z_2$ symmetry, namely type-I, type-II, type-X and type-Y 2HDMs. We have derived the relevant full one-loop Wilson coefficients of the four 2HDMs from the recent calculation in the aligned two-Higgs doublet model by Li, Lu and Pich, which could be mapped to all the four 2HDMs for both large and small $\tan\beta$. It is found that, a new term associated with the soft $Z_2$ symmetry breaking parameter $M$ can be enhanced by $\tan^2\beta$ in the type-II 2HDM, which has not been considered in the literature. Imposing both theoretical and experimental constraints, we have renewed the bounds on the parameter spaces of the four 2HDMs. Different from our previous paper, however, we find that all the four 2HDMs give sizable and similar contributions to $\overline{\mathcal B}(B_s \to \mu^+ \mu^-)$ within the stringently restricted parameter spaces, but very tiny as regards the mass-eigenstate rate asymmetry $\mathcal A_{\Delta\Gamma}$; this makes it unfeasible to discriminate the four types of 2HDM with the correlations between the observables in $B_s \to \mu^+ \mu^-$ decay.