Mass and width of an unstable particle

TL;DR

This paper clarifies the precise definitions of mass and width for unstable particles using complex energy poles, and applies this to the Z and W bosons, revealing small deviations from their quoted masses.

Contribution

It provides a rigorous definition of mass and width for unstable particles via complex poles and clarifies the Breit-Wigner resonance formulas.

Findings

Z boson mass is 26 MeV below the quoted value

W boson mass is 20 MeV below the quoted value

Clarifies the physical interpretation of resonance parameters

Abstract

We show that the mass and width of an unstable particle are precisely defined by the pole in the complex energy plane, $\mu = m - (i/2)\Gamma$, by identifying the width, $\Gamma$, with the particle's decay rate and the mass, $m$, with the oscillatory frequency. We find that the physical $Z$ boson mass lies 26 MeV below its quoted value, while the physical $W$ boson mass lies 20 MeV below. We also clarify the various Breit-Wigner formulae that are used to describe a resonance.