Fourth generation effects in the $B_s \to \nu \bar{\nu} \gamma$ decay

If the fourth generation fermions exist, the new quarks could influence the branching ratio of the decay $B_s \to \nu \bar{\nu} \gamma$. We obtain two solutions of the fourth generation CKM factor $V^*_{t's} V_{t'b}$ from the decay of $B \to X_s \gamma$. With these two solutions we calculate the new contributions of the fourth generation quark to Wilson coefficients of the decay $B_s \to \nu \bar{\nu} \gamma$. The branching ratio of the decay $B_s \to \nu \bar{\nu} \gamma$ in the two cases are calculated. In one case, our results are quite different from that of SM, but almost same in another case. If a fourth generation should exist in nature and nature chooses the former case, this B meson decay could provide a possible test of the fourth generation existence.