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Fermion Hierarchies in $SU(5)$ Grand Unification from $\Gamma_6^\prime$ Modular Flavor Symmetry

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arxiv 2307.01419 v1 pith:I6DTRN2X submitted 2023-07-04 hep-ph hep-th

Yoshihiko Abe , Tetsutaro Higaki , Junichiro Kawamura , Tatsuo Kobayashi This is my paper · ORCID
classification hep-phhep-th
keywords hierarchiessymmetrygammamodularprimefermionflavorquark
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abstract

We construct a model in which the hierarchies of the quark and lepton masses and mixing are explained by the $\Gamma_6^\prime$ modular flavor symmetry. The hierarchies are realized by the Froggatt-Nielsen-like mechanism due to the residual $Z^T_6$ symmetry, approximately unbroken at $\tau \sim i\infty.$ We argue that the $\Gamma_6^{(\prime)}$ symmetry is the minimal possibility to realize the up-type quark mass hierarchies, since the Yukawa matrix is symmetric. We find a combination of the representations and modular weights and then show numerical values of $\mathcal{O}(1)$ coefficients for the realistic fermion hierarchies.

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Cited by 1 Pith paper

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  1. Large and small hierarchies from finite modular symmetries

    hep-ph 2024-12 conditional novelty 6.0 of 10

    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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