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

Abstract

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 $V_{t^{\prime }s}^{\ast }{V}_{t^{\prime }b}$ 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.

10 pages, Latex

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