No classical limit of quantum decay for broad states

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 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 σ 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.