Mass and width of an unstable particle

We show that the mass and width of an unstable particle are precisely defined by the pole in the complex energy plane, $\mu =m-(i\mathrm{/}2)\mathrm{\Gamma }$, by identifying the width, $\mathrm{\Gamma }$, 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.