Multichannel Decay: Alternative Derivation of the i-th Channel Decay Probability

F. Giacosaa, b aInstitute of Physics, Jan Kochanowski University, Uniwersytecka 7, 25-406, Kielce, Poland bInstitute for Theoretical Physics, J.W. Goethe University, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany

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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 a 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, 137200 (2022). 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 not one either. 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.

DOI:10.12693/APhysPolA.142.436 topics: decay law, unstable particles, multichannel decay