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

Abstract

We calculate the leading logarithmic QCD corrections to the decay B_s --> \gamma \gamma in the two Higgs doublet model (2HDM) including O_7 type long distance effects and estimate the restrictions of the 2HDM parameters, tan\beta and m_H, using the experimental data of B --> X_s \gamma decay provided by the CLEO collaboration. A lower bound for the charged Higgs mass m_H as a function of the renormalization scale \mu is given for 2HDM model II. We further present the dependencies of the branching ratio Br(B_s --> \gamma \gamma) and the ratio |A^{+}|^2/|A^{-}|^2 on m_H and tan\beta including leading 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, \bar{\Lambda}_s). We see, that to look for charged Higgs effects the measurement of the branching ratio Br(B_s --> \gamma \gamma) is promising.