Two Higgs doublet models and $b\rightarrow s$ exclusive decays
Résumé
We computed the leading order Wilson coefficients relevant to all the exclusive $b\rightarrow s\ell ^+\ell ^-$ decays in the framework of the two Higgs doublet model (2HDM) with a softly broken $\mathbb {Z}_2$ symmetry by including the $\mathcal {O}(m_b)$ corrections. We elucidate the issue of appropriate matching between the full and the effective theory when dealing with the (pseudo-)scalar operators for which keeping the external momenta different from zero is necessary. We then make a phenomenological analysis by using the measured ${\mathcal {B}}(B_s\rightarrow \mu ^+\mu ^-)$ and ${\mathcal {B}}(B\rightarrow K \mu ^+\mu ^-)_{\mathrm {high}-q^2}$ , for which the hadronic uncertainties are well controlled, and we discuss their impact on various types of 2HDM. A brief discussion of the decays with $\tau $ -leptons in the final state is provided too.