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

TL;DR

This paper investigates how the inclusion of a fourth quark generation affects meson mixing, CP violation, and rare decay processes, using experimental data to constrain and predict new physics effects within the hierarchical Wolfenstein parametrization.

Contribution

It provides a detailed analysis of the impact of a hypothetical fourth quark generation on meson mixing and rare decays, extending the Wolfenstein parametrization to explore new mixing hierarchies.

Findings

Constraints on fourth-generation mixing from experimental data

Predictions for $D^0-ar{D^0}$ mixing and $K_L o ext{pi}^0 uar{ u}$ branching ratios

Implications for CP asymmetry and unitarity triangle 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.