Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models
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| Format: | Preprint |
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2025
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| author | Varzielas, Ivo de Medeiros Liu, Ming-Shau Sengupta, Amartya Talbert, Jim |
| author_facet | Varzielas, Ivo de Medeiros Liu, Ming-Shau Sengupta, Amartya Talbert, Jim |
| contents | We demonstrate that, upon minimizing a renormalizable, single-scalar potential invariant under a non-Abelian symmetry, special orientations in the associated vacuum alignment of the scalar multiplet correspond to the preservation of a discrete residual flavour symmetry in the broken phase of the theory. Conversely, we show that these special scalar alignments are perturbed when additional Lagrangian operators (e.g. renormalizable, multi-flavon operators and/or effective, higher-dimensional operators) are present that break said residual symmetry, leading to a vacuum reorientation and phenomenological consequences. We therefore construct a one-to-one correspondence principle between broken residual symmetries and vacuum alignment corrections, providing a mechanism to identify (and correct) a subtle but persistent form of phenomenologically relevant fine-tuning embedded in -- but often ignored by -- most successful non-Abelian flavour models. We first establish this correspondence in a set of toy models based on the S4 permutation symmetry, and then apply the lessons learned to the more realistic A4 Altarelli-Feruglio and $Δ(27)$ Universal Texture Zero models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_19789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models Varzielas, Ivo de Medeiros Liu, Ming-Shau Sengupta, Amartya Talbert, Jim High Energy Physics - Phenomenology We demonstrate that, upon minimizing a renormalizable, single-scalar potential invariant under a non-Abelian symmetry, special orientations in the associated vacuum alignment of the scalar multiplet correspond to the preservation of a discrete residual flavour symmetry in the broken phase of the theory. Conversely, we show that these special scalar alignments are perturbed when additional Lagrangian operators (e.g. renormalizable, multi-flavon operators and/or effective, higher-dimensional operators) are present that break said residual symmetry, leading to a vacuum reorientation and phenomenological consequences. We therefore construct a one-to-one correspondence principle between broken residual symmetries and vacuum alignment corrections, providing a mechanism to identify (and correct) a subtle but persistent form of phenomenologically relevant fine-tuning embedded in -- but often ignored by -- most successful non-Abelian flavour models. We first establish this correspondence in a set of toy models based on the S4 permutation symmetry, and then apply the lessons learned to the more realistic A4 Altarelli-Feruglio and $Δ(27)$ Universal Texture Zero models. |
| title | Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.19789 |