Constraints on the Mass and Mixing of the 4th Generation Quark From Direct CP Violation$ε^{\prime}/ε$ and Rare K Decays

Abstract

We investigate the $ε^{\prime} /ε$ for $K\to ππ$ in a sequential fourth generation model. By giving the basic formulae for $ε^{\prime}/ε$ in this model, we analyze the numerical results which are dependent of $m_{t^{\prime}}$ and imaginary part of the fourth CKM factor, ${Im}V^{*}_{t^{'}s}V_{t^{'}d}$ (or $V^{*}_{t^{'}s}V_{t^{'}d}$ and the fourth generation CKM matrix phase $θ$). We find that, unlike the SM, when taking the central values of all parameters for $ε^{\prime}/ε$, the values of $ε^{\prime}/ ε$ can easily fit to the current experimental data for all values of hadronic matrix elements estimated from various approaches. Also, we show that the experimental values of $ε^{\prime}/ε$ and rare K decays can provide a strong constraint on both mass and mixing of the fourth generation quark. When taking the values of hadronic matrix elements from the lattice or 1/N expansion calculations, a large region of the up-type quark mass $m_{t^{\prime}}$ is excluded.