Flavor and CP Violation with Fourth Generations Revisited

The Standard Model predicts a very small CP violation phase $\sin2\Phi^{\rm SM}{B_s} \simeq -0.04$$ in $B_s$–${\bar{B}}_s$ mixing. %, i.e. of order ${\lambda }^2\eta$. Any finite value of ${\mathrm{\Phi }}_{B_s}$ measured at the Tevatron would imply New Physics. With recent hints for finite $\sin 2{\mathrm{\Phi }}_{B_s}$, % have appeared from CDF and D\O, experiments at the Tevatron, we reconsider the possibility of a 4th generation. As recent direct search bounds have become considerably heavier than 300 GeV, we take the $t^{\mathrm{\prime }}$ mass to be near the unitarity bound of 500 GeV. Combining the measured values of $\mathrm{\Delta }{m}_{B_s}$ with $\mathcal{B}(B\to X_s{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-})$, together with typical $f_{B_s}$ values, we find a sizable $\sin2\Phi^{\rm SM4}{B_s} \sim -0.33$\mathrm{.}Using$m_{b’} = 480$ GeV, we extract the range % a range of values, $0.06<\mathrm{\mid }{V}_{t^{\mathrm{\prime }}b}\mathrm{\mid }<0.13$ from the constraints of $\mathrm{\Gamma }(Z\to b\bar{b})$, $\mathrm{\Delta }{m}_D$ and ${\cal B}(K^+\to\pi^+\nu\bar\nu)$\mathrm{.}Afuturemeasurementof${\cal B}(K_L\to\pi^0\nu\bar\nu)$willdetermine$V_{t’d}$.