B -> X_s gamma gamma and B_s -> gamma gamma in supersymmetry with broken   R-parity
  We examine the effects of R-parity violating (RPV) supersymmetry on the two-photon B decays B -> X_s gamma gamma and B_s -> gamma gamma. We find that, although there are many one-loop RPV diagrams that can contribute to these two-photon B decays, the RPV effect is dominated by a single diagram. This diagram, named here lambda-irreducible, has a distinct topology which is irrelevant for the b -> s gamma amplitude at one-loop and has thus a negligible effect on the one-photon decay B -> X_s gamma. We show that the lambda-irreducible RPV diagram can give BR(B_s -> gamma gamma) ~ 5*10^(-6) and BR(B -> X_s gamma gamma) ~ 6*10^(-7), which is about 16 and 5 times larger than the SM values, respectively. Although the enhancement to the decay width of B -> X_s gamma gamma is not that dramatic, we find that the energy distribution of the two photons is appreciably different from the SM, due to new threshold effects caused by the distinct topology of the RPV lambda-irreducible diagram. Moreover, this diagram significantly changes the forward-backward asymmetry with respect to the softer photon in B -> X_s gamma gamma. Thus, the RPV effect in B -> X_s gamma gamma can be discerned using these observables. 
Alexander Gemintern, Shaouly Bar-Shalom and Gad Eilam