Spurion Analysis of $\mathbb{Z}_M/\mathbb{Z}_2$ Non-Invertible Selection Rules: Low-Order versus All-Order Zeros
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| Format: | Preprint |
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2025
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| _version_ | 1866909863161888768 |
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| author | Suzuki, Motoo Xu, Ling-Xiao |
| author_facet | Suzuki, Motoo Xu, Ling-Xiao |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_18972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spurion Analysis of $\mathbb{Z}_M/\mathbb{Z}_2$ Non-Invertible Selection Rules: Low-Order versus All-Order Zeros Suzuki, Motoo Xu, Ling-Xiao High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Spurion Analysis of $\mathbb{Z}_M/\mathbb{Z}_2$ Non-Invertible Selection Rules: Low-Order versus All-Order Zeros |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.18972 |