Effects of the $K^+\to\pi^+\nu\bar{\nu}$ and of other processes on the mixing hierarchies in the four-generation model

Abstract

We analyze in the four-generation model the first measurement of the branching ratio of rare kaon decay $K^+\to\pi^+\nu\bar{nu}$, along with the other processes of $K_L-K_S$ mass difference $\Delta m_K$, CP-violating parameter $\epsilon_K, B_d-\bar{B_d}$ mixing, $B_s-\bar{B_s}$ mixing, $B(K_L\to\mu\bar{\mu})$, and the upper bound values of $D^0-\bar{D^0}$ mixing and $B(K_L\to\pi^0\nu\bar{\nu})$, and try to search for mixing of the fourth generation in the hierarchical mixing scheme of the Wolfenstein parametrization. Using the results for the mixing of the fourth generation, we discuss predictions of the $D^0-\bar{D^0}$ mixing ($\Delta m_D$) and the branching ratio of directly CP-violating decay process $K_L\to\pi^0\nu\bar{\nu}$, and the effects on the CP asymmetry in neutral B meson decays and the unitarity triangle.