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The inclusive radiative decay of the B meson is known to provide strongconstraints on many popular extensions of the Standard Model. Such constraintscrucially depend on precision of the Standard Model predictions. One of themain contributions to the theoretical uncertainty is due to certainNext-to-Next-to-Leading Order QCD corrections whose values at the physicalcharm quark mass m_c have been estimated using interpolation between the m_c=0and m_c >> m_b limits. A direct determination of such corrections at thephysical value of m_c requires calculating hundreds of two-scale four-looppropagator diagrams with unitarity cuts. Applying the integration-by-partsmethod, we express the corrections in terms of master integrals. Asymptoticexpansions of these integrals at m_c >> m_b serve as boundary conditions fordifferential equations in z=m_c^2/m_b^2 that are being numerically solved.Here, we present our final results for the diagrams involving massless andmassive fermion loops on the gluon lines. For the two-body cuts, we confirm theanalytical expressions and/or numerical fits that are already present in theliterature. In the four-body case, we make the correction complete by includingseveral diagrams that have previously been only estimated using interpolationin m_c. We also report the status of the ongoing calculation of the remainingdiagrams where no closed fermion loops on the gluon lines are present.

On charm-mass dependent NNLO corrections to B -> Xs gamma