Two Higgs doublet models and [Formula omitted] exclusive decays

We computed the leading order Wilson coefficients relevant to all the exclusive [Formula omitted] decays in the framework of the two Higgs doublet model (2HDM) with a softly broken [Formula omitted] symmetry by including the [Formula omitted] 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 [Formula omitted] and [Formula omitted], 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 [Formula omitted]-leptons in the final state is provided too.