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<p>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 <i>ℤ</i><sub>2</sub> orbifolding of a <i>ℤ</i><sub><i>M</i></sub> symmetry, denoted as <i>ℤ</i><sub><i>M</i></sub>/<i>ℤ</i><sub>2</sub>. 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月23日

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  • Motoo Suzuki,
  • Ling-Xiao Xu

摘要

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 ℤ2 orbifolding of a ℤM symmetry, denoted as ℤM/ℤ2. 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.