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 the mixing $B_{d,s}^0-{\bar{B}}_{d,s}^0$ 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 of $\Delta M_{B_s}$ which is the function of $m_{t^{\prime }}$. We find that one of our results can satisfy the present experimental low bound of $\Delta M_{B_s}$. We also get the constraints of the fourth generation CKM factor $V_{t^{{}^{\prime }}b}^{\ast }{V}_{t^{{}^{\prime }}d}$, which is the function of $t^{{}^{\prime }}$, from the experimental measurements of $\Delta M_{B_d}$. Thus, $\Delta M_{B_{d,s}}$ provide a possible test of the fourth generation and give a signal of the new physics.

Comments: 13 pages, 5 figures. accepted by Europ. Phys. Jour. C