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 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.

References in corpus (6)

• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• Finding the sigma pole by analytic extrapolation of $\pi \pi$ scattering data
• Quantum reflection and dwell times of metastable states
• Model independent determination of the sigma pole
• Long Tail of Quantum Decay from Scattering Data
• Review of Scalar Mesons

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