Branching Ratios of the Charged Kaon Decays and Radiative Corrections for the Ke3 Decay Mode

Abstract

The CMD--2 experiment at the VEPP-2M accelerator at the Budker Institute of Nuclear Physics has collected $approx$ 1 million charged kaon decays, from which we extract a clean sample of $approx 74,000 K^+ $ decays, with $approx$ 50,000 $kmunu$, 18,000 $kpipi$, 4000 ($kmu3 + ke3$), and 2000 ($k3pc + 3pi0$) events. Based on these samples we present measurement of $ R_{2body} equiv Br(kpipi)/Br(kmunu) = 0.3292 pm 0.0048 mbox{stat} pm 0.011 mbox{sys}$, $R_{semilep} equiv (Br(kmu3) + Br(ke3))/Br(kpipi) = 0.477 pm 0.016 mbox{stat} pm 0.10 mbox{sys}$, and $R_{3pion} equiv (Br(k3pc)+Br(3pi0))/Br(kpipi) = 0.315 pm 0.014 mbox{stat} pm 0.054 mbox{sys}$. The ratio of the two semileptonic decays is extracted from the $K^-$ decays only and yields $R_{emu} equiv Br(K o pi^0 e u)/Br(K o pi^0 mu u) = 1.97 pm 0.09 mbox{stat} pm 0.81 mbox{sys}$. The strength of these measurements is the presence of all the major decay modes and systematics different from some other experiments. In this dissertation I also consider the radiative corrections for the $K_{e3}$ decay. This decay is of particular importance since it provides the best way to extract the value of the $V_{us}$ element of the CKM matrix. In turn, precise knowledge of $V_{us}$ is needed to resolve a long standing problem with a unitarity test of the CKM matrix.