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Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries
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abstract
In modular-invariant models of flavour, hierarchical fermion mass matrices may arise solely due to the proximity of the modulus $\tau$ to a point of residual symmetry. This mechanism does not require flavon fields, and modular weights are not analogous to Froggatt-Nielsen charges. Instead, we show that hierarchies depend on the decomposition of field representations under the residual symmetry group. We systematically go through the possible fermion field representation choices which may yield hierarchical structures in the vicinity of symmetric points, for the four smallest finite modular groups, isomorphic to $S_3$, $A_4$, $S_4$, and $A_5$, as well as for their double covers. We find a restricted set of pairs of representations for which the discussed mechanism may produce viable fermion (charged-lepton and quark) mass hierarchies. We present two lepton flavour models in which the charged-lepton mass hierarchies are naturally obtained, while lepton mixing is somewhat fine-tuned. After formulating the conditions for obtaining a viable lepton mixing matrix in the symmetric limit, we construct a model in which both the charged-lepton and neutrino sectors are free from fine-tuning.
Forward citations
Cited by 6 Pith papers
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Stringy Constraints on Modular Flavor Models
Heterotic one-loop threshold corrections imply upper bounds on the modulus in modular flavor models, ruling out tau near i infinity for typical dilaton and beta-function values and disfavoring tau = i at large volume.
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Modular Flavor Symmetries and Fermion Mass Hierarchies
In modular flavor models, fermion mass hierarchies require the modulus to sit near the critical points i, i∞, or ω; the paper classifies the near-critical mass patterns for reducible 2⊕1 matter assignments.
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Large and small hierarchies from finite modular symmetries
Using finite modular symmetries, radiative stabilization of multiple moduli can simultaneously generate large and small hierarchies, such as Im τ1 ≈ 3 and Im τ2 ≈ 15.
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CPon Dark Matter
A light scalar from spontaneous CP violation, the CPon, can be a viable dark matter candidate with a mass between about 10 meV and 1 MeV and a suppression scale above 10^12 GeV.
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Modular Symmetry with Weighton
A systematic classification of modular weighton models at levels 3, 4 and 5, with two T' benchmark fits that reproduce quark and lepton hierarchies, each requiring one admitted cancellation.
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Quark and lepton masses
A review of fermion mass and mixing data and of the main theoretical attempts to explain them, from GUTs to string theory, without claiming a new result.
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