2025/12/22 by Ivo de Medeiros Varzielas, Varzielas, Ivo de Medeiros, Ming-Shau Liu +5 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Noncommutative and Quantum Gravity Theories
paper · doi:10.48550/arxiv.2512.19789
openalex publication_date 2025/12/22 · openalex created_date 2025/12/25 · openalex updated_date 2026/07/28
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.