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The photon energy spectrum in B-> X_s + γin perturbative QCD through O(α_s^2)

We derive the dominant part of the O(α_s^2) correction to the photon energy spectrum in the inclusive decay B-> X_s+gamma. The detailed knowledge of the spectrum is important for relating the theoretical calculations of the B-> X_s + γdecay rate and the experimental measurements where a cut on the photon energy is applied. In addition, moments of the photon energy spectrum are used for the determination of the b-quark mass and other fundamental parameters of heavy quark physics. Our calculation reduces the theoretical uncertainty associated with uncalculated higher orders effects and shows that, for B-> X_s+γ, QCD radiative corrections to the photon energy spectrum are under theoretical control.