Quantifying non-invertible chiral symmetry breaking

TL;DR

This paper investigates the breaking of non-invertible chiral symmetries in the Standard Model, quantifying the symmetry breaking scales and effective charges through explicit calculations, with a focus on massless QED with Yukawa couplings.

Contribution

It provides a quantitative analysis of non-invertible symmetry breaking scales and effective charges, extending the understanding of symmetry breaking beyond invertible symmetries.

Findings

Calculated symmetry breaking scales and effective charges for non-invertible symmetries.

Explicitly demonstrated symmetry breaking in massless QED with Yukawa couplings.

Discussed potential methods to quantify breaking of general non-invertible symmetries.

Abstract

It has recently been suggested that the chiral symmetry of the Standard Model is not explicitly broken by its ABJ anomaly, but is instead made non-invertible. In this work, I quantify the breaking of non-invertible symmetries of this type by calculating the symmetry breaking scales and effective charges $q(r)$ originally studied for continuous invertible higher-form symmetries. As an example I consider the explicit breaking of the chiral symmetry of massless QED by introducing Yukawa couplings between the electron and a massive real scalar in the UV. I briefly comment on how one might quantify the breaking of general non-invertible symmetries.