Unstable Particles near Threshold

TL;DR

This paper investigates the behavior of unstable particles near their decay threshold, addressing the ill-defined wave function renormalization and proposing a spectral density-based approach to define branching ratios, revealing complex decay dynamics.

Contribution

It introduces a novel method to handle threshold singularities for unstable particles, enabling the use of narrow width approximation and redefining decay properties.

Findings

Resonance shapes vary across decay channels

No single decay width can describe near-threshold unstable particles

Non-exponential decay occurs at all time scales

Abstract

We explore physics of unstable particles when mother particle mass is around the sum of its daughter particle masses. In this case, the conventional wave function renormalization factor is ill-defined. We propose a simple resolution of the threshold singularity problem which still allows the use of narrow width approximation by defining branching ratio in terms of spectral density. The resonance peak and shape is different for different decay channels and no single decay width can be assigned to the unstable particles. Non-exponential decay happens in all time scales.