Spurious gauge-invariance and γ 5 in dimensional regularization

Abstract

Abstract Dimensional regularization is arguably the most popular and efficient scheme for multi-loop calculations. Yet, when applied to chiral (gauge) theories like the Standard Model and its extensions, one is forced to deal with the infamous “γ 5 problem”. The only formulation that has been demonstrated to be consistent at all orders in perturbation theory, known as Breiteinlohner-Maison-’t Hooft-Veltman scheme, is rather cumbersome because of the lack of manifest chiral gauge-invariance. In this paper we point out that this drawback can be alleviated by the introduction of auxiliary fields that restore a spurious version of gauge-invariance. If combined with the background field method, all 1PI amplitudes and the associated counterterms are formally covariant and thus severely constrained by the symmetries. As an illustration we evaluate the symmetry-restoring counterterms at 1-loop in the most general renormalizable gauge theory with Dirac fermions and scalar fields, the Standard Model representing a particular example.

Keywords

• Anomalies in Field and String Theories
• Gauge Symmetry
• Renormalization and Regularization
• Electroweak Precision Physics