A General Prescription for Spurion Analysis of Non-Invertible Selection Rules

TL;DR

This paper develops a unified method for spurion analysis in particle physics models with non-invertible fusion algebra-based selection rules, enabling systematic tracking of couplings in complex scattering processes.

Contribution

It introduces a general prescription for spurion analysis applicable to non-invertible fusion algebras, extending previous frameworks and supporting broader auxiliary descriptions.

Findings

Unified framework for spurion analysis in non-invertible fusion algebras

Systematic tracking of coupling constants in particle scattering

Streamlined analysis of near-group and $ ext{Z}_M/ ext{Z}_2$ fusion algebras

Abstract

We formulate a general prescription for spurion analysis in particle-physics models whose selection rules are described by commutative non-invertible fusion algebras. The construction applies to fusion algebras containing non-invertible basis elements that need not be self-conjugate, thereby allowing us to systematically track coupling constants in arbitrary particle scattering processes at tree and loop orders, but without assuming faithful realization of the fusion algebra, or no other quantum numbers for dynamical particles. This unifies and streamlines the previous analysis of near-group fusion algebras and of the $\mathbb{Z}_M/\mathbb{Z}_2$ fusion algebras, and supports the broader viewpoint that the non-invertible selection rules often admit auxiliary descriptions using lifted Abelian groups with a structured set of explicit breaking terms.