The $B\to X_s{l}^{+}{l}^{-}$ and $B\to X_s\gamma$ decays with the fourth generation

Abstract

If the fourth generation fermions exist, the new quarks could influence the branching ratios of the decays of $B\to X_s\gamma$ and $B\to X_s{l}^{+}{l}^{-}$. We obtain two solutions of the fourth generation CKM factor $V_{t^{{}^{\prime }}s}^{\ast }{V}_{t^{{}^{\prime }}b}$ from the decay of $B\to X_s\gamma$. We use these two solutions to calculate the new contributions of the fourth generation quark to Wilson coefficients of the decay of $B\to X_s{l}^{+}{l}^{-}$. The branching ratio and the forward-backward asymmetry of the decay of $B\to X_s{l}^{+}{l}^{-}$ in the two cases are calculated. Our results are quite different from that of SM in one case, almost same in another case. If Nature chooses the formmer, the $B$ meson decays could provide a possible test of the forth generation existence.

Comments: 10 pages, 5 figures