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.
Modular S 4 models of lepton masses and mixing
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abstract
We investigate models of charged lepton and neutrino masses and lepton mixing based on broken modular symmetry. The matter fields in these models are assumed to transform in irreducible representations of the finite modular group $\Gamma_4 \simeq S_4$. We analyse the minimal scenario in which the only source of symmetry breaking is the vacuum expectation value of the modulus field. In this scenario there is no need to introduce flavon fields. Using the basis for the lowest weight modular forms found earlier, we build minimal phenomenologically viable models in which the neutrino masses are generated via the type I seesaw mechanism. While successfully accommodating charged lepton masses, neutrino mixing angles and mass-squared differences, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation (CPV) phases, as well as specific correlations between the values of the atmospheric neutrino mixing parameter $\sin^2\theta_{23}$ and i) the Dirac CPV phase $\delta$, ii) the sum of the neutrino masses, and iii) the effective Majorana mass in neutrinoless double beta decay. We consider also the case of residual symmetries $\mathbb{Z}^{ST}_3$ and $\mathbb{Z}^S_2$ respectively in the charged lepton and neutrino sectors, corresponding to specific vacuum expectation values of the modulus.
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An exhaustive scan of Δ(96) Modular Littlest Seesaw models yields 35 viable residual-symmetry patterns with new fixed PMNS columns and sharp, testable predictions beyond TM1.
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.
Incomplete zero-mode multiplets under Scherk-Schwarz phases in magnetized compactifications violate modular symmetry as a group but retain control over couplings via full modular forms.
Upcoming neutrino experiments are projected to substantially reduce the number of viable leptonic flavor models in five popular classes by measuring mass ordering, theta_23 octant, delta_CP, and absolute mass scale.
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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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An exhaustive scan of Δ(96) Modular Littlest Seesaw models yields 35 viable residual-symmetry patterns with new fixed PMNS columns and sharp, testable predictions beyond TM1.
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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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More about modular symmetries and non-invertible properties in magnetized compactifications
Incomplete zero-mode multiplets under Scherk-Schwarz phases in magnetized compactifications violate modular symmetry as a group but retain control over couplings via full modular forms.
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The Future of Lepton Flavor
Upcoming neutrino experiments are projected to substantially reduce the number of viable leptonic flavor models in five popular classes by measuring mass ordering, theta_23 octant, delta_CP, and absolute mass scale.