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arXiv · 2307.01419

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

Yoshihiko Abe·Tetsutaro Higaki·Junichiro Kawamura·Tatsuo Kobayashi
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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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Yoshihiko Abe, Tetsutaro Higaki, Junichiro Kawamura, Tatsuo Kobayashi. 2023-07-04. Fermion Hierarchies in $SU(5)$ Grand Unification from $\Gamma_6^\prime$ Modular Flavor Symmetry. https://arxiv.org/abs/2307.01419

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