Constraining Fourth Generation with $B\to X_s \gamma$

Abstract

Using the theoretical and experimental results on $B \to X_s \gamma$, a four-generation SM is analyzed to constrain the combination of the $4\times 4$ Cabibbo-Kobayashi-Maskawa factor $V_{t^\prime s}^* V_{t^\prime b}$ as a function of the $t^\prime$--quark mass. It is observed that the results for the above--mentioned physical quantities are essentially different from the previous predictions for certain solutions of the CKM factor. Influences of the new model is used to predict CP violation in $B \to X_s \gamma$ decay at the order of $A_{CP}=5%$, stemming from the appearance of complex phases of $V_{t^\prime s}^* V_{t^\prime b}$ and of Wilson coefficients $C_7$, $C_8$, in the related process. The above mentioned physical quantities can serve as efficient tools in search of the fourth generation.