2HDMs predictions for $\bar {B} \rightarrow X_{S \gamma}$ in NLO QCD

The decay $B \to X_s \gamma$ is studied at the Next to Leading Order in QCD in a class of models containing at least two Higgs doublets and with only one charged Higgs boson non-decoupled at low-energy. The two-loop matching condition is calculated and it is found to agree with existing results. The complete dependence of the Wilson coefficients on the matching scale is given. The size of the Next to Leading Order corrections is extensively discussed. Results for branching ratios, possible CP asymmetries and lower bounds on the charged Higgs mass are presented when the convergence of the perturbative series appears fast enough to yield reliable predictions. Regions in the parameter space of these models where the Next to Leading Order calculation is still not a good approximation of the final result for these observables are singled out