Predictions for $B\to K\gamma \gamma$ decays

Abstract

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 $\Delta \mathcal{B}(B\to K\gamma \gamma {)}_{SM}^{OPE}\simeq 1\times 10^{-9}$. 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.

17 pages, 4 figures; Note added on Schouten identity and 2 references added; v4: typos in Eqs (8), (44) and erroneous statement on mixing before Eq (44) fixed. All results and conclusions unchanged

References in corpus (1)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)

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