Constraints on the mass and mixing of the fourth generation quark from directCPviolationε′/εand rareKdecays

Abstract

We investigate the ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ for $\stackrel{\ensuremath{\rightarrow}}{K}\ensuremath{\pi}\ensuremath{\pi}$ in a sequential fourth generation model. By giving the basic formulas for ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ in this model, we analyze the numerical results which are dependent on ${m}_{{t}^{\ensuremath{'}}}$ and the imaginary part of the fourth CKM factor, $\mathrm{Im}{V}_{{t}^{\ensuremath{'}}s}^{*}{V}_{{t}^{\ensuremath{'}}d}$ (or ${V}_{{t}^{\ensuremath{'}}s}^{*}{V}_{{t}^{\ensuremath{'}}d}$ and the fourth generation CKM matrix phase $\ensuremath{\theta}).$ We find that, unlike the SM, when taking the central values of all parameters for ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon},$ the values of ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ 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 ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ 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 ${m}_{{t}^{\ensuremath{'}}}$ is excluded.