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

Abstract

We present the first study of the rare annihilation decay ${\bar{B}}_d^0\to \varphi \gamma$ in the Standard Model. Using QCD factorization formalism, we find $\mathcal{B}({\bar{B}}_d^0\to \varphi \gamma )=3.6\times 10^{-12}$. 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 $|{\lambda }_{i23}^{{}^{\prime \prime }}{\lambda }_{i12}^{{}^{\prime \prime }}|$ and $|{\lambda }_{i32}^{{}^{\prime }}{\lambda }_{i12}^{{}^{\prime }\ast }|$, $\mathcal{B}({\bar{B}}_d^0\to \varphi \gamma )$ 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.

Comments: References added. RPV Lambda' contributions are included