Spurion analysis of ℤM/ℤ2 non-invertible selection rules: low-order versus all-order zeros

A bstract 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 ℤ 2 orbifolding of a ℤ M symmetry, denoted as ℤ M / 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.