Mass and width of an unstable particle

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.

Comments: 11 pages, 7 figures. Minor improvements, references added. Discussion and appendices added