Two Higgs doublet models and &ITb&IT → &ITs&IT exclusive decays

We computed the leading order Wilson coefficients relevant to all the exclusive b -> sl(+)l decays in the framework of the two Higgs doublet model (2HDM) with a softly broken Z(2) symmetry by including the 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 B(B-S -> mu(+)mu) and B(B -> K mu(+)mu)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.