= Pole mass
{title2=$m_{\rm pole}$}
{wiki}
= Physical mass
{synonym}
For a stable <particle> represented by an isolated <propagator> pole, the <pole mass> $M$ is defined by the pole at invariant <momentum> squared $p^2=M^2$. It is a property of the complete <propagator> pole, distinct from an arbitrary running <mass> parameter defined in a <renormalization scheme>.
An unstable <resonance> generally has a complex pole, often parametrized as $s_p=(M-i\Gamma/2)^2$; its real <mass> and width conventions must then be specified. A peak position in a measured distribution need not coincide exactly with that pole parameter because of backgrounds, thresholds and resolution. Confined fields or infrared-singular charged states require further qualifications before the simple isolated stable-particle picture applies. The pole location and the chosen field's pole residue are different quantities.
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