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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. %, i.e. of order $λ^2η$. Any finite value of $Φ_{B_s}$ measured at the Tevatron would imply New Physics. With recent hints for finite $\sin2Φ_{B_s}$, % have appeared from CDF and DØ\, 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 $t'$ 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 %a typical value of $m_{b'} = 480$ GeV, we extract the range % a range of values, $0.06 < |V_{t'b}| < 0.13$ 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 $V_{t'd}$.