$B_{s,d}\to \gamma \gamma$ Decay with the Fourth Generation

We calculate the branching ratios of $B_{s,d}\to \gamma \gamma$ decay in the sequential fourth generation model. We find that the theoretical values of the branching ratios, $\mathrm{B}\mathrm{R}(B_s\to \gamma \gamma )$, including the contributions of $t^{\mathrm{\prime }}$, are much different from the minimal standard model (SM) predictions. The new physics contribution can provide one to two orders enhancement to the standard model prediction of $\mathrm{B}\mathrm{R}(B_s\to \gamma \gamma )$. But due to the tiny values of 4th generation CKM matrix element $V_{t^{\mathrm{\prime }}d}^{\ast }{V}_{t^{\mathrm{\prime }}b}$, the new physics effect on $\mathrm{B}\mathrm{R}(B_d\to \gamma \gamma )$ is very small and can not be distinct from the SM prediction. It is shown that the decay $B_s\to \gamma\gamma$ can give the test of new physics signals from the 4th generation model.