A Note on Gauge Anomaly Cancellation in Effective Field Theories

Abstract

The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.

arXiv commentCorrected a numerical error in expression of the coefficients ${\xi }_{\phi A}$ and ${\xi }_{\phi \phi }$, conclusion unchanged

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• The Standard Model effective field theory at work
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• Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for ${\gamma }_{\ast }$
• Searching for pseudo Nambu-Goldstone boson dark matter production in association with top quarks
• Comments on gauge anomalies at dimension-six in the Standard Model Effective Field Theory
• UV Completion of Neutral Triple Gauge Couplings
• Anomalies From the Covariant Derivative Expansion