NNLO fermionic corrections to the charm quark mass dependent matrix elements in B -> X_s gamma

Abstract

We compute the virtual O(alpha_s^2) fermionic contributions to the charm quark mass dependent matrix elements of the B -> X_s gamma decay. In the case of a massless quark loop insertion into the gluon propagator, our result obtained as an expansion in z=m_c^2/m_b^2 and an exact expression in terms of multi-fold MB integrals, confirms the findings of Bieri, Greub and Steinhauser [19]. We observe, however, large deviations in the case of a b-quark loop insertion.The charm quark loop shows smaller, but still noticeable differences.