The rare ${\bar{B}}_d^0\to \varphi \gamma$ decays in Standard Model and as a probe of R-parity violation

We present the first study of the rare annihilation decay $\bar{B}^0_d \to \phi\gamma$intheStandardModel\mathrm{.}UsingQCDfactorizationformalism,wefind${\cal B}(\bar{B}^0_d \to\phi\gamma)=3.6\times 10^{-12}$. The smallness of the decay rate in the Standard Model make the decay a sensitive probe of new physics contributions. As an example, we calculate the effects of R-parity violating couplings. Within the available upper bounds for $\mathrm{\mid }{\lambda }_{i23}^{{}^{\mathrm{\prime }\mathrm{\prime }}}{\lambda }_{i12}^{{}^{\mathrm{\prime }\mathrm{\prime }}}\mathrm{\mid }$ and $\mathrm{\mid }{\lambda }_{i32}^{{}^{\mathrm{\prime }}}{\lambda }_{i12}^{{}^{\mathrm{\prime }}\ast }\mathrm{\mid }$, $\mathcal{B}({\bar{B}}_d^0\to \varphi \gamma )$ could be enhanced to order of ${10}^{-9}\sim {10}^{-8}$, which might be accessible at LHCB, B-TeV and the planning super high luminosity B factories at KEK and SLAC.