Multichannel decay: alternative derivation of the $i$-th channel decay probability

Abstract

In the study of decays, it is quite common that an unstable quantum state/particle has multiple distinct decay channels. In this case, besides the survival probability $p(t)$, also the probability $w_i(t)$ that the decay occurs between $(0,t)$ in the $i$-th channel is a relevant object. The general form of the function $w_i(t)$ was recently presented in PLB \textbf{831} (2022), 137200. Here, we provide a novel and detailed `joint' derivation of both $p(t)$ and $w_i(t)$. As it is well known, $p(t)$ is not an exponential function; similarly, $w_i(t)$ is also not such. In particular, the ratio $w_i/w_j$ (for $i\ne j)$ is not a simple constant, as it would be in the exponential limit. The functions $w_i(t)$ and their mutual ratios may therefore represent a novel tool to study the non-exponential nature of the decay law.

Comments: 8 pages. Prepared as a proceedings contribution for the 4th Jagiellonian Symposium on Advances in Particle Physics and Medicine, Jagiellonian University, 10-15/7/2022, Kraków, Poland