Unstable particles near threshold

Abstract

We explore the physics of unstable particles when the mother particle’s mass is approximately the sum of the masses of its daughter particles. In this case, the conventional wave function renormalization factor used for the narrow width approximation is ill-defined. We propose a simple resolution of the problem that allows the use of the narrow width approximation by defining the wave function renormalization factor and the branching ratio in terms of the spectral density. We test new definitions by calculating the cross section in the Higgs portal model and a significant improvement is obtained. Meanwhile, no single decay width can be assigned to the unstable particles and non-exponential decay occurs at all time scales.