Facts of life with gamma(5)

TL;DR

The paper addresses the difficulty of handling $\\gamma_5$ in dimensional regularization for chiral fermions in the electroweak Standard Model, where naive anticommutation can produce spurious gauge-violating anomalies. It develops gauge-invariant chiral Feynman rules incorporating an $AC(\\mu)$ term and shows that a fully chirally invariant DR is incompatible with the trace condition, leaving two practical routes: (i) a chirally improved HV scheme with $AC(\\mu)$ treated as a perturbation, or (ii) $AC(\\mu)=0$ with an anticommuting $\\gamma_5$ (NDR), with hard anomalies handled in 4D. The author advocates the NDR approach as the practical, efficient path used in decades of SM radiative-correction calculations, avoiding the need for exhaustive WT/ST identity restoration. The analysis clarifies long-standing gamma5 regularization debates and provides actionable guidance for reliable higher-order electroweak computations.

Abstract

The increasing precision of many experiments in elementary particle physics leads to continuing interest in perturbative higher order calculations in the electroweak Standard Model or extensions of it. Such calculations are of increasing complexity because more loops and/or more legs are considered. Correspondingly efficient computational methods are mandatory for many calculations. One problem which affects the feasibility of higher order calculations is the problem with gamma(5) in dimensional regularization. Since the subject thirty years after its invention is still controversial I advocate here some ideas which seem not to be common knowledge but might shed some new light on the problem. I present arguments in favor of utilizing an anticommuting gamma(5) and a simple 4-dimensional treatment of the hard anomalies.

Figures (1)

• Figure 1: The VVA triangle diagrams.