The $b\to sγγ$ transition in softly broken supersymmetry

We study the effect of supersymmetric contributions to the effective quark transition $b\to s\gamma\gamma$, including leading order QCD effects. We apply the discussion to the decay $B_s\to\gamma\gamma$. Even though one-particle irreducible contributions could play a role, numerical cancelations make the amplitude for the two-photon emission strongly correlated to the $b\to s\gamma$ amplitude which is sharply constrained by experiment. A quite general statement follows: as long as non-standard physics effects appear only in the matching of the Wilson coefficients of the standard effective operator basis, the deviations from the standard model expectations of the decay rates induced by $b\to s\gamma\gamma$ are bound to follow closely the corresponding deviations on $b\to s\gamma$. Effects of new physics are therefore bound to be small.