BEYOND THE WEISSKOPF–WIGNER APPROXIMATION IN THE $K^0-\bar K^0$ SYSTEM

Abstract

We reanalyze the time evolution of the [Formula: see text] system in the language of certain spectral function whose Fourier transforms give the time-dependent survival and transition amplitudes. Approximating the spectral function by a one-pole ansatz we obtain insight into the limitation of the validity of the one-pole approximation. It will be shown that the same validity restrictions apply to the known formulae of the Weisskopf–Wigner approximation as well. The present analysis can also be applied to the effect of so-called vacuum regeneration of KL and KS. As a result of this possibility new contributions to the well-known oscillatory terms will enter the time-dependent transition probabilities. It will be shown that the order of magnitude of this new effect is very small and, in principle, its exact determination lies outside the scope of the one-pole ansatz.