B_(s,d) to γγ 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, ${\rm BR}(B_{s}\to\gamma\gamma)$, including the contributions of $t'$, 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 ${\rm BR}(B_{s}\to\gamma\gamma)$. But due to the tiny values of 4th generation CKM matrix element $V_{t'd}^* V_{t'b}$, the new physics effect on ${\rm BR}(B_{d}\to\gamma\gamma)$ 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.