K^+\to\pi^+\nu\bar{\nu} with four generations and its effects on unitarity triangle

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}, using the constraints from \Delta m_K, \epsilon_K, B_d-\bar{B_d} mixing, \Gamma (b\to s\gamma), B_s-\bar{B_s} mixing, D^0-\bar{D^0} mixing, B(K_L\to\pi^0\nu\bar{\nu}) and B(K_L\to\mu\bar{\mu}), and study its effects on the unitarity triangle. With the results of searching for the maximum mixing of the fourth generation, we predict that D^0-\bar{D^0} mixing \Delta m_D and the branching ratio of "direct" CP-violating decay process K_L\to\pi^0\nu\bar{\nu} could attain the values 1-2 orders of magnitude larger than the predictions of the Standard Model.