No classical limit of quantum decay for broad states

TL;DR

This paper demonstrates that broad quantum states, such as the sigma meson, do not follow an exponential decay law at any time, highlighting the limitations of classical decay models for such states.

Contribution

It introduces a method to recover quantum decay evolution from experimental data and applies it to broad states, revealing non-exponential decay at all times.

Findings

Broad states like the sigma meson do not exhibit exponential decay.

The proposed method effectively reconstructs decay dynamics from data.

Classical exponential decay models are invalid for broad resonances.

Abstract

Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow states. The non exponential nature at large times is however hard to establish from experiments. A method to recover the time evolution of unstable states from a parametrization of the amplitude fitted to data is presented. We apply the method to a realistic example of a very broad state, the sigma meson and reveal that an exponential decay is not a valid approximation at any time for this state. This example derived from experiment, shows the unique nature of broad resonances.