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 wi(t) that the decay occurs between (0, t) in the i-th channel is a relevant object. The general form of the function wi(t) was recently presented in PLB 831 (2022), 137200. Here, we provide a novel and detailed 'joint' derivation of both p(t) and wi(t). As it is well known, p(t) is not an exponential function; similarly, wi(t) is also not such. In particular, the ratio wi/wj (for i = j) is not a simple constant, as it would be in the exponential limit. The functions wi(t) and their mutual ratios may therefore represent a novel tool to study the non-exponential nature of the decay law.