A Z3 Froggatt-Nielsen model with one flavon reproduces quark and charged lepton hierarchies but yields neutrino mass-squared ratios too small by two orders of magnitude and random PMNS angles.
Lepton Masses and Mixing from Modular $S_4$ Symmetry
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abstract
We study models of lepton masses and mixing based on broken modular invariance. We consider invariance under the finite modular group $\Gamma_4 \simeq S_4$ and focus on the minimal scenario where the expectation value of the modulus is the only source of symmetry breaking, such that no flavons need to be introduced. After constructing a basis for the lowest weight modular forms, we build two minimal models, one of which successfully accommodates charged lepton masses and neutrino oscillation data, while predicting the values of the Dirac and Majorana CPV phases.
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A two-loop neutrino mass model with modular S4 and Z3 symmetries reproduces charged lepton masses and normal-ordering neutrino data while predicting observable LFV and viable DM candidates.
A two-Higgs-doublet model with SU(2)-based marginal operators produces unavoidable cyclic RG flows, pseudo-unitary behavior below pair-production threshold, and Russian Doll VEVs whose period is fixed by the Koide formula to yield three families.
Blow-up of magnetized T²/Z_N preserves total magnetic flux, total curvature, and effective flux on connecting lines, while the number of localized modes at each singularity increases by one per mass level increment.
citing papers explorer
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Why Quarks and Leptons Demand Different Symmetries: A Systematic $Z_3$ Froggatt-Nielsen Analysis
A Z3 Froggatt-Nielsen model with one flavon reproduces quark and charged lepton hierarchies but yields neutrino mass-squared ratios too small by two orders of magnitude and random PMNS angles.
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Two-loop neutrino mass model with modular $S_4$ symmetry
A two-loop neutrino mass model with modular S4 and Z3 symmetries reproduces charged lepton masses and normal-ordering neutrino data while predicting observable LFV and viable DM candidates.
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A rich structure of renormalization group flows for Higgs-like models in 4 dimensions
A two-Higgs-doublet model with SU(2)-based marginal operators produces unavoidable cyclic RG flows, pseudo-unitary behavior below pair-production threshold, and Russian Doll VEVs whose period is fixed by the Koide formula to yield three families.
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Massive modes on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$
Blow-up of magnetized T²/Z_N preserves total magnetic flux, total curvature, and effective flux on connecting lines, while the number of localized modes at each singularity increases by one per mass level increment.