A study on the radiative dileptonic decays $B^0(B_s)\to\gamma\ell^+\ell^-$

We study the rare radiative dileptonic decays $B^0(B_s)\to \gamma\ell^+\ell^-$ ($\ell=e,\mu$) in the standard model. By using the $B$ meson wave function constrained by non-leptonic decays, the branching ratios turn out to be of the order of $10^{-9}$ for $B_s\to\gamma\mu^+\mu^-$, $\gamma e^+ e^-$ and $10^{-10}$ for $B^0\to\gamma\mu^+\mu^-$, $\gamma e^+ e^-$. Based on the study, these decays are accessible at the near future LHC-b experiment, which are useful to determine the $B(B_s)$ wave function.