Spurion Analysis of ${\mathbb{Z}}_M/{\mathbb{Z}}_2$ Non-Invertible Selection Rules: Low-Order versus All-Order Zeros

Abstract

Motivated by recent progress in the spurion analysis of non-invertible selection rules (NISRs) arising from near-group fusion algebras, we further generalize the framework to a class of NISRs obtained from ${\mathbb{Z}}_2$ orbifolding of a ${\mathbb{Z}}_M$ symmetry, denoted as ${\mathbb{Z}}_M/{\mathbb{Z}}_2$. Many structural features are carried over: for instance, our labeling scheme enables systematic tracking of all couplings when constructing composite amplitudes from simpler building blocks at arbitrary loop orders in perturbation theory. Our analysis provides a transparent understanding of both low-order and all-order zeros of couplings under radiative corrections. Furthermore, we examine the fate of low-order zeros when the fusion algebra is not faithfully realized -- a situation not captured by the vanilla argument of ``loop-induced groupification'' -- and formulate a conjecture on the related aspects of particle decoupling and effective theory. Finally, we discuss the low-order versus all-order zeros in Yukawa textures from the perspective of spurion analysis.

Comments: 26 pages, 3 figures, comments welcome