Beyond leading-order corrections to bar{B} -> X_s gamma at large tan beta: the charged-Higgs-boson contribution

Abstract

Among the O(alpha_s tan beta) contributions to the Wilson coefficients C_7 and C_8, relevant for the decay bar{B} -> X_s gamma, those induced by two-loop diagrams with charged-Higgs-boson exchange and squark-gluino corrections are calculated in supersymmetric models at large tan beta. The calculation of the corresponding Feynman integrals is exact, unlike in previous studies that are valid when the typical supersymmetric scale M_SUSY is sufficiently larger than the electroweak scale m_weak (\sim m_W, m_t) and the mass of the charged Higgs boson m_{H^\pm}. Therefore, the results presented here can be used for any value of the various supersymmetric masses. These results are compared with those of an approximate calculation, already existing in the literature, that is at the zeroth order in the expansion parameter (m_weak^2,m_H^2)/M_SUSY^2, and with the results of two new approximate calculations in which the first and second order in the same expansion parameter are retained, respectively. This comparison allows us to assess whether the results of these three approximate calculations can be extended beyond the range of validity for which they were derived, i.e., whether they can be used for m_H^2 \gtap M_SUSY^2 and/or M_SUSY^2 \sim m_weak^2. It is found that the zeroth-order approximation works well even for m_H \gtap M_SUSY, provided M_SUSY^2 >> m_weak^2. The inclusion of the higher-order terms improves the zeroth-order approximation for m_H^2 << M_SUSY^2, but it worsens it for m_H \gtap M_SUSY$.