Predictions for $B \to K \gamma \gamma$ decays
  We present a phenomenological study of the rare double radiative decay $B\to K \gamma\gamma$ in the Standard Model (SM) and beyond. Using the operator product expansion (OPE) technique, we estimate the short-distance (SD) contribution to the decay amplitude in a region of the phase space which is around the point where all decay products have energy $\sim m_b/3$ in the rest frame of the $B$-meson. At lowest order in 1/Q, where $Q$ is of order $m_b$, the $B\to K \gamma\gamma$ matrix element is then expressed in terms of the usual $B\to K$ form factors known from semileptonic rare decays. The integrated SD branching ratio in the SM in the OPE region turns out to be $\Delta {\cal{B}}(B \to K \gamma \gamma)_{SM}^{OPE} \simeq 1 \times 10^{-9}$. We work out the di-photon invariant mass distribution with and without the resonant background through $B\to K \{\eta_c,\chi_{c0}\}\to K\gamma \gamma$. In the SM, the resonance contribution is dominant in the region of phase space where the OPE is valid. The present experimental upper limit on $B_s \to \tau^+ \tau^-$ decays, which constrains the scalar/pseudoscalar Four-Fermi operators with $\tau^+ \tau^-$, leaves considerable room for new physics in the one-particle-irreducible contribution to $B\to K \gamma \gamma$ decays. In this case, we find that the SD $B\to K \gamma \gamma$ branching ratio can be enhanced by one order of magnitude with respect to its SM value and the SD contribution can lie outside of the resonance peaks. 
Gudrun Hiller, A. Salim Safir