Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.15455 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We present a systematic analysis of a minimal supersymmetric $Z_3$ discrete flavor symmetry as a solution to the fermion mass hierarchy problem. With generation-dependent $Z_3$ charges on the right-handed chiral superfields and a single flavon chiral superfield, holomorphy of the superpotential restricts the Yukawa operators so that a single expansion parameter $ε\simeq 0.015$ structurally accounts for the hierarchical pattern of quark and charged lepton mass ratios with $\mathcal{O}(1)$ Yukawa couplings. A Monte Carlo scan over $10^5$ random $\mathcal{O}(1)$ coefficient sets confirms that adjacent-generation mass ratios generically fall within the experimental ranges. The CKM mixing angles are reproducible with specific coefficient choices ($χ^2/\text{dof} \simeq 1.6$) but are not structurally predicted. Extended to neutrinos within a type-I seesaw, the framework fails decisively on two fronts. First, the mass spectrum is far too hierarchical: $Δm_{21}^2/Δm_{31}^2 \lesssim 10^{-4}$, two orders of magnitude below the observed $0.030$. Second, the PMNS mixing angles are generically $\mathcal{O}(1)$ random -- consistent with Haar-distributed unitaries -- providing no mechanism to predict the observed pattern. When $M_R$ carries the $Z_3$ charge structure dictated by the Majorana charge algebra, an unsuppressed off-diagonal entry combines with the hierarchical column texture of the Dirac mass: the seesaw congruence transformation over-suppresses both light masses $m_1, m_2$ to $\mathcal{O}(ε^3)$, deepening the ratio $Δm_{21}^2/Δm_{31}^2$ to $\mathcal{O}(ε^6) \sim 10^{-11}$. These results motivate a sectorial view of flavor where different fermion sectors arise from distinct symmetry mechanisms.