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 Nielsen Identities of the SM and the definition of mass
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abstract
In a generic gauge theory the gauge parameter dependence of individual Green functions is controlled by the Nielsen identities, which originate from an enlarged BRST symmetry. We give a practical introduction to the Nielsen identities of the Standard Model (SM) and to their renormalization and illustrate the power of this elegant formalism in the case of the problem of the definition of mass.We prove to all orders in perturbation theory the gauge-independence of the complex pole of the propagator for all physical fields of the SM, in the most general case with mixing and CP violation. At the amplitude level, the formalism provides an intuitive and general understanding of the gauge recombinations which makes it particularly useful at higher orders. We also include in an appendix the explicit expressions for the fermionic two-point functions in a generic R_\xi gauge.
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The paper presents first numerical one-loop hadronic W decay widths for an on-shell scheme with δV=0, where off-diagonal mass counterterms replace mixing-angle counterterms.
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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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Renormalization of mixing angles and computation of the hadronic $W$ decay widths
The paper presents first numerical one-loop hadronic W decay widths for an on-shell scheme with δV=0, where off-diagonal mass counterterms replace mixing-angle counterterms.