One-parameter modular models predict exact high-scale mass relations m_s^5 = 2√2 m_d^3 m_b^2, m_μ^3 = √2 m_e m_τ^2 and m_s^2 m_τ = √2 m_e m_b^2 that become compatible with observed fermion masses after RG evolution and SUSY thresholds.
Fermion mass hierarchies, large lepton mixing and residual modular symmetries
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A benchmark model using genus-2 modular invariance generates quark mass hierarchies and CP violation via moduli VEVs near invariant points, with mass ratios vanishing in the symmetric limit and mixing angles reproduced.
A finite modular symmetric model generates inflation via a Coleman-Weinberg potential from vector-like quarks, with Im(τ) as inflaton and Re(τ) as heavy axion, matching cosmological observations and predicting possible isocurvature perturbations.
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 dark matter fermion is shown to simultaneously explain the relic density, satisfy direct detection and collider bounds, and produce observable rates for muon-to-electron transitions in a viable parameter region.
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Fermion mass relations in one-parameter modular models
One-parameter modular models predict exact high-scale mass relations m_s^5 = 2√2 m_d^3 m_b^2, m_μ^3 = √2 m_e m_τ^2 and m_s^2 m_τ = √2 m_e m_b^2 that become compatible with observed fermion masses after RG evolution and SUSY thresholds.
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Quark hierarchies and CP violation from the Siegel modular group
A benchmark model using genus-2 modular invariance generates quark mass hierarchies and CP violation via moduli VEVs near invariant points, with mass ratios vanishing in the symmetric limit and mixing angles reproduced.
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Finite modular Coleman-Weinberg inflation
A finite modular symmetric model generates inflation via a Coleman-Weinberg potential from vector-like quarks, with Im(τ) as inflaton and Re(τ) as heavy axion, matching cosmological observations and predicting possible isocurvature perturbations.
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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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Dark Matter as a Source for Lepton Flavor Violation
A dark matter fermion is shown to simultaneously explain the relic density, satisfy direct detection and collider bounds, and produce observable rates for muon-to-electron transitions in a viable parameter region.