Leading logarithmic QCD corrections to the $B_s \to \gamma \gamma$ decays in the two Higgs doublet model

We calculate the leading logarithmic QCD corrections to the decay B s → γγ in the two-Higgs doublet model (2HDM) including O 7 -type long-distance effects and estimate the restrictions of the 2HDM parameters, tan β and m H , using the experimental data of B → X s γ decay provided by the CLEO Collaboration. A lower bound for the charged Higgs mass m H as a function of the renormalization scale μ is given for 2HDM model II. We further present the dependencies of the branching ratio Br( B s → γγ ) and the ratio | A + | 2 /| A − | 2 on m H and tan β logarithmic QCD corrections. The dependence on the renormalization scale is found to be strong for both ratios. An additional uncertainty arises from the variation of the parameters of the bound state model, ( m b , Λ s ). We see that to look for charged Higgs effects the measurement of the branching ratio Br( B s → γγ ) is promising