On the photon energy moments and their `bias' corrections in B ->   X_s+\gamma
  Photon energy moments in B -> X_s+\gamma and the impact of experimental cuts are analyzed, including the biases exponential in the effective hardness missed in the conventional OPE. We incorporate the perturbative corrections fully implementing the Wilsonian momentum separation ab initio. This renders perturbative effects numerically suppressed while leaving heavy quark parameters and the corresponding light-cone distribution function well defined and preserving their physical properties. The moments of the distribution function are given by the heavy quark expectation values of which many have been extracted from the B -> X_c l\nu decays. The quantitative estimates for the biases in the heavy quark parameters determined from the photon moments show they cannot be neglected for E_cut \gsim 1.85GeV, and grow out of theory control for E_cut above 2.1GeV. Implications for the moments in the B -> X_c l\nu decays at high cuts are briefly addressed. 
D. Benson, I.I. Bigi and N. Uraltsev