QCD corrections to b->s gamma gamma induced decays: B->X-s gamma gamma and B-s->gamma gamma

We present a complete calculation of the leading-order QCD corrections to the quark level decay amplitude for b-->s gamma gamma and study their relevance for both the inclusive branching ratio B(B-->X-s gamma gamma) and for the exclusive decay channel B-s-->gamma gamma. In addition to the uncertainties in the short distance calculation, due to the choice of the renormalization scale, an appreciable uncertainty in both B-s-->gamma gamma and B-->X-s gamma gamma is introduced by the matrix element calculation. We also briefly discuss some long distance effects, especially those due to the eta(c) resonance for the inclusive rate. Finally, a brief analysis of the IR singularities of the two photon spectrum in the inclusive case is given.