Beyond leading-order corrections to B̄ → X_s γ at large tan β: The charged-Higgs-boson contribution

Among the O(α_s tan β) contributions to the Wilson coefficients C₇ and C₈, relevant for the decay B̄ →X_sγ, those induced by two-loop diagrams with charged-Higgs-boson exchange and squark-gluino corrections are calculated in supersymmetric models at large tan β. 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 (∼m_W,m_t) and the mass of the charged Higgs boson m_H±. 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_weak²,m_H²)/M _SUSY², 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≳M_SUSY and/or M_SUSY∼m _weak. It is found that the zeroth-order approximation works well even for m_H≳M_SUSY, provided M_sUSY ²≫m_weak². The inclusion of the higher-order terms improves the zeroth-order approximation for m_H² ≪M_sUSY², but it worsens it for m_H≳ M_SUSY.