Flavor and CP Violation with Fourth Generations Revisited

The Standard Model predicts a very small CP violation phase $\sin2Φ^{\rm SM}_{B_s} \simeq -0.04$%= \arg M_{12} \simeq \arg\,(V^*_{ts}V_{tb})^2$in$B_s$--$\bar B_s$mixing.$λ^2η$. Any finite value of$Φ_{B_s}$measured at the Tevatron would imply New Physics. With recent hints for finite$\sin2Φ_{B_s}$,$t'$mass to be near the unitarity bound of 500 GeV. Combining the measured values of$Δm_{B_s}$with${\cal B}(B \to X_s\ell^+\ell^-)$, together with typical$f_{B_s}$values, we find a sizable$\sin2Φ^{\rm SM4}_{B_s} \sim -0.33$. Using$m_{b'} = 480$GeV, we extract the range$0.06 < |V_{t'b}| < 0.13$from the constraints of$Γ(Z\to b\bar b)$,$Δm_{D}$and${\cal B}(K^+\toπ^+ν\barν)$. A future measurement of${\cal B}(K_L\toπ^0ν\barν)$will determine$V_{t'd}$.

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