$b\to s\ell^+\ell^-$ Transitions in Two-Higgs-Doublet Models

In this article we study $b\to s\mu^+\mu^-$ transitions and possible correlations with the anomalous magnetic moment of the muon ($a_\mu$) within two-Higgs-doublet models with generic Yukawa couplings, including the possibility of right-handed neutrinos. We perform the matching on the relevant effective Hamiltonian and calculate the leading one-loop effects for $b\to s\ell\ell^{(\prime)}$, $b\to s\gamma$, $\Delta B=\Delta S=2$, $b\to s\nu\bar\nu$ and $\ell\to\ell^\prime\gamma$ transitions in a general $R_\xi$ gauge. Concerning the phenomenology, we find that an explanation of the hints for new physics in $b\to s\mu^+\mu^-$ data is possible once right-handed neutrinos are included. If lepton flavour violating couplings are allowed, one can account for the discrepancy in $a_\mu$ as well. However, only a small portion of parameter space gives a good fit to $b\to s\mu^+\mu^-$ data and the current bound on $h\to\tau\mu$ requires the mixing between the neutral Higgses to be very small if one aims at an explanation of $a_\mu$.