Magnetic dipole operator contributions to the photon energy spectrum in B¯→Xsγ at O(αs2)

We compute the O(αs2) contributions to the photon energy spectrum of the inclusive decay B¯→Xsγ associated with the magnetic penguin operator O7O7. They are an essential part of the ongoing NNLO calculation of this important decay. We use two different methods to evaluate the master integrals, one based on the differential equation approach and the other on sector decomposition, leading to identical results which in turn agree with those of a recent independent calculation by Melnikov and Mitov. We study the numerical relevance of this set of NNLO contributions in the photon energy spectrum and discuss the change of bottom quark mass scheme.