The pole mass is the value of the invariant momentum at a pole of the full propagator. It is independent of the renormalization scheme, whereas a running mass parameter generally depends on the renormalization scale.
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The term "pole mass" is commonly used in the context of particle physics and refers to the mass of a particle as it would be measured in a specific way. More precisely, the pole mass is defined as the mass of a particle that corresponds to the position of the pole of the particle's propagator in a quantum field theory. The propagator describes how the particle behaves in terms of its interactions with other particles.