How to define physical properties of unstable particles

TL;DR

This paper investigates how to properly define physical properties of unstable particles using effective quantum field theory, emphasizing the importance of residues at complex poles of the S-matrix for accurate characterization.

Contribution

It demonstrates that physical properties of unstable particles should be derived from residues at complex poles, ensuring invariance under field redefinitions, through a one-loop calculation.

Findings

Physical properties are best extracted from residues at complex poles.

Invariance under field redefinitions is confirmed for these properties.

One-loop calculations support the proposed definition.

Abstract

In the framework of effective quantum field theory we address the definition of physical quantities characterizing unstable particles. With the aid of a one-loop calculation, we study this issue in terms of the charge and the magnetic moment of a spin-1/2 resonance. By appealing to the invariance of physical observables under field redefinitions we demonstrate that physical properties of unstable particles should be extracted from the residues at complex (double) poles of the corresponding S-matrix.