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

Understand

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.