Effects of the fourth generation on $\Delta M_{B_{d,s}}$ in $B^0$–$\bar B^0$ mixing

Abstract.

We investigate the mass differences $\Delta M_{B_{d,s}}$ in $B^0_{d,s}$–$\bar B^0_{d,s}$ mixing with a new up-like quark $t^{\prime}$ in the sequential fourth generation model. We give the basic formulae for $\Delta M_{B_{d,s}}$ in this model and obtain two kinds of numerical results for $\Delta M_{B_{s}}$ as a function of $m_{t^{\prime}}$. We find that one of our results can satisfy the present experimental lower bound of $\Delta M_{B_s}$. We also get the constraints of the fourth generation CKM factor $V^*_{t'b}V_{t'd}$, as a function of $t'$, from the experimental measurements of $\Delta M_{B_d}$. Thus, $\Delta M_{B_{d,s}}$ provides a possible test of the fourth generation and may give a signal of new physics.