Simple Modular S3 Models for Lepton Masses and Mixing
Abstract
We perform a systematic study of an economical class of modular S3 lepton-flavor models without enlarging the continuous gauge symmetry or introducing right-handed neutrinos or additional flavon fields. We provide a complete classification of all inequivalent realizations allowed by the S3 singlet--doublet representation structure and the admissible modular-weight assignments. Their phenomenological viability is investigated for both normal ordering (NO) and inverted ordering (IO) using Bayesian model comparison and parameter-correlation analysis based on current neutrino-oscillation data. We identify 18 viable models for NO and 19 for IO, with 14 satisfying the experimental constraints in both orderings. The viable models successfully accommodate current neutrino-oscillation data while yielding nontrivial predictions for leptonic CP violation, Majorana phases, and observables probing the absolute neutrino-mass scale. Among these predictions, the absolute-mass observables provide the clearest separation between the two orderings. At the best-fit points, the predicted ranges of the effective electron-neutrino mass (mβ) are completely disjoint between NO and IO, whereas those of the sum of neutrino masses (∑i mi) and the effective Majorana mass (mββ) show only partial separation. The IO models generally predict a higher absolute neutrino-mass scale and are consequently more strongly constrained by cosmological observations and more accessible to neutrinoless double-beta-decay searches. Our results show that, despite its economical field content, the modular S3 framework accommodates a diverse set of phenomenologically viable lepton-flavor realizations with experimentally testable predictions.
Related
- Level-Four Modular Symmetry Selected by the Harmonic Pattern of Quark and Lepton Masses
- The conformal origin of the lepton flavor mixing matrix
- Cosmological constraints on extra radiation and early dark energy with lepton asymmetry and varying quark masses
- Flavorful Lepton-Number-Violating SMEFT: Loop Mixing, 0νββ and Rare Meson Decays
- Neutrino masses and mixing angles in the Plan B Model
BibTeX
@misc{vien2026simple,
title = {{Simple Modular $S_3$ Models for Lepton Masses and Mixing}},
author = {V. V. Vien and Mayengbam Kishan Singh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12323},
eprint = {2609.12323},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12323},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Simple Modular S_3 Models for Lepton Masses and Mixing
AU - V. V. Vien
AU - Mayengbam Kishan Singh
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12323
UR - https://arxiv.org/abs/2609.12323
AB - We perform a systematic study of an economical class of modular S_3 lepton-flavor models without enlarging the continuous gauge symmetry or introducing right-handed neutrinos or additional flavon fields. We provide a complete classification of all inequivalent realizations allowed by the S_3 singlet--doublet representation structure and the admissible modular-weight assignments. Their phenomenological viability is investigated for both normal ordering (NO) and inverted ordering (IO) using Bayesian model comparison and parameter-correlation analysis based on current neutrino-oscillation data. We identify 18 viable models for NO and 19 for IO, with 14 satisfying the experimental constraints in both orderings. The viable models successfully accommodate current neutrino-oscillation data while yielding nontrivial predictions for leptonic CP violation, Majorana phases, and observables probing the absolute neutrino-mass scale. Among these predictions, the absolute-mass observables provide the clearest separation between the two orderings. At the best-fit points, the predicted ranges of the effective electron-neutrino mass (m_β) are completely disjoint between NO and IO, whereas those of the sum of neutrino masses (∑_i m_i) and the effective Majorana mass (m_ββ) show only partial separation. The IO models generally predict a higher absolute neutrino-mass scale and are consequently more strongly constrained by cosmological observations and more accessible to neutrinoless double-beta-decay searches. Our results show that, despite its economical field content, the modular S_3 framework accommodates a diverse set of phenomenologically viable lepton-flavor realizations with experimentally testable predictions.
ER -