Gauge Invariance and Finite Counterterms in Chiral Gauge Theories

Abstract

We derive the finite one-loop counterterm required to restore the Ward Identities broken by the regularization scheme in chiral gauge theories. Our result is an analytic expression applicable to a wide class of regularizations satisfying a few general properties. We adopt the background field method, which ensures background gauge invariance in the quantized theory, and focus on renormalizable chiral theories with arbitrary gauge group and fermions in general representations. Our approach can be extended to theories involving scalars, such as the Standard Model, or to non-renormalizable theories, such as the SMEFT. As a concrete application, we work out the finite counterterm at one loop in the Standard Model, within dimensional regularization and the Breitenlohner-Maison-'t Hooft-Veltman prescription for ${\gamma }_5$.

49 pages, 1 figure, 6 tables

References in corpus (7)

• Automated one-loop computations in the SMEFT
• Dimensional Regularization and Breitenlohner-Maison / 't Hooft-Veltman Scheme for ${\gamma }_5$ applied to Chiral YM Theories: Full One-Loop Counterterm and RGE Structure
• Two-loop application of the Breitenlohner-Maison/'t Hooft-Veltman scheme with non-anticommuting ${\gamma }_5$: Full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory
• A Note on Gauge Anomaly Cancellation in Effective Field Theories
• Comments on gauge anomalies at dimension-six in the Standard Model Effective Field Theory
• Veltman, renormalizability, calculability
• Renormalizable theories with symmetry breaking

Cited by in corpus (11)

• An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting ${\gamma }_5$
• Low-energy effective field theory below the electroweak scale: one-loop renormalization in the 't Hooft-Veltman scheme
• Computing Tools for Effective Field Theories
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• UV Completion of Neutral Triple Gauge Couplings
• Renormalisation Group Equations for BRST-Restored Chiral Theory in Dimensional Renormalisation: Application to Two-Loop Chiral-QED
• Anomalies From the Covariant Derivative Expansion
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Gauge-Invariant Quantum Fields
• Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting ${\gamma }_5$