Role of electromagnetic dipole operator in the electroweak penguin dominated vector meson decays of $B$ meson

The pure annihilation type decays $B^0_d\to\phi\gamma$ and $B_s\to\rho\gamma$ receive only color suppressed penguin contributions with a very small branching ratio in the standard model. When we include the previously neglected electromagnetic dipole operator, the branching ratios can be enhanced one order magnitude larger than previous study using QCD factorization approach. That is ${\cal BR}(\bar B^0_d\to\phi\gamma)\simeq 1 \times 10^{-11}$ and ${\cal BR}(B_s\to\rho\gamma) \sim (6-16)\times 10^{-10}$. The new effect can also give a large contribution, of order $10^{-9}$, to transverse polarization of $B\to\phi\rho$ and $B\to \omega\phi$ which is comparable to the longitudinal part. These effects can be detected in the LHCb experiment and the Super-B factories.