Non-exponential decay in quantum field theory and in quantum mechanics: the case of two (or more) decay channels

TL;DR

This paper investigates non-exponential decay behaviors in quantum field theory and quantum mechanics for particles with multiple decay channels, revealing oscillations around expected decay ratios and highlighting deviations from classical exponential decay models.

Contribution

It provides a comparative analysis of decay probabilities in QFT and QM, demonstrating oscillatory deviations from the Breit-Wigner limit in multi-channel decay scenarios.

Findings

Decay ratio oscillates around the mean value in full treatments.

Deviations from exponential decay can be significant.

Decay properties are analyzed using scalar particle models and Lee Hamiltonians.

Abstract

We study the deviations from the exponential decay law, both in quantum field theory (QFT) and quantum mechanics (QM), for an unstable particle which can decay in (at least) two decay channels. After a review of general properties of non-exponential decay in QFT and QM, we evaluate in both cases the decay probability that the unstable particle decays in a given channel in the time interval between $t$ and $t+dt.$ An important quantity is the ratio of the probability of decay into the first and the second channel: this ratio is constant in the Breit-Wigner limit (in which the decay law is exponential) and equals the quantity $\Gamma_{1}/\Gamma_{2}$, where $\Gamma_{1}$ and $\Gamma_{2}$ are the respective tree-level decay widths. However, in the full treatment (both for QFT and QM) it is an oscillating function around the mean value $\Gamma_{1}/\Gamma_{2}$ and the deviations from this mean value can be sizable. Technically, we study the decay properties in QFT in the context of a superrenormalizable Lagrangian with scalar particles and in QM in the context of Lee Hamiltonians, which deliver formally analogous expressions to the QFT case.