QCD Corrections to $b\to s\gamma\gamma$ and Exclusive $B_s\to \gamma\gamma$ Decay

Abstract

The short distance QCD corrections to $b\to s\gamma \gamma$ are calculated in the leading logarithmic approximation. The equivalence of operator basis reduction for S-matrix elements by using the equations of motion or by proving a low energy theorem is discussed. We apply the above results to the exclusive $B_s\to \gamma\gamma$ decay. The branching ratio of this decay is found to be $5\times 10^{-7}$ in the Standard Model. We also found that QCD corrections modify considerably the ratio between CP-even and CP-odd two-photon amplitudes.