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).
Stability of the Scalar Mass against Loop Corrections
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abstract
We show that the renormalized loop corrections to the scalar mass are suppressed if the field in the loop is heavy. Here, treating the renormalized mass is important, as it is the only observable. This means that the physics of a low-energy scalar field is insensitive to that of ultraviolet.
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Renormalization defines a gauge-invariant mass function at every virtuality in gauge theories.
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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).
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The Gauge-Invariant Mass Function
Renormalization defines a gauge-invariant mass function at every virtuality in gauge theories.