A segment-local Ward–Takahashi cancellation makes the fermion self-energy equal to its Feynman-gauge value off shell, yielding a gauge-invariant, on-shell-renormalized mass function m(q).
The Perturbative Pole Mass in QCD
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abstract
It is widely believed that the pole mass of a quark is infrared-finite and gauge-independent to all orders in perturbation theory. This seems not to have been proved in the literature. A proof is provided here.
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Gauge-Invariant Off-Shell Mass
A segment-local Ward–Takahashi cancellation makes the fermion self-energy equal to its Feynman-gauge value off shell, yielding a gauge-invariant, on-shell-renormalized mass function m(q).