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Nonholomorphic A4 modular invariance for fermion masses and mixing in SU(5) GUT

Mohamed Amin Loualidi1, Mohamed Miskaoui2, and Salah Nasri1,*

  • *Contact author: snasri@uaeu.ac.ae, salah.nasri@cern.ch
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Phys. Rev. D 112, 015008 – Published 9 July, 2025

DOI: https://doi.org/10.1103/1py2-cmfx

Abstract

Addressing the fermion flavor structures using modular invariance is a challenging task in the framework of quark-lepton unification. Building on recent applications of modular symmetry in nonsupersymmetric models, we propose the first renormalizable SU(5) grand unified theory incorporating level 3 nonholomorphic modular symmetry, Γ3≃A4. This framework constrains Yukawa couplings to polyharmonic Maaß forms, significantly reducing the number of free parameters while enhancing the predictive power of the models. We present a comprehensive analysis of fermion masses and mixing while tackling key grand unified theory (GUT) queries such as gauge coupling unification and proton decay. Beyond the minimal SU(5) framework, the Higgs sector incorporates the 45H dimensional Higgs field crucial in differentiating the masses of down quarks and charged leptons, and the fermion sector is extended with three right-handed neutrinos enabling neutrino masses via the type-I seesaw mechanism. We analyze two benchmark models with distinct modular weight and A4 charge assignments. The predicted effective Majorana mass mββ values align with current neutrinoless double-beta decay experiments, and the effective neutrino mass mβ is within the reach of future beta decay searches. The predicted sum of neutrino masses, ∑mi, satisfies the upper bound set by recent cosmological observations. The gauge coupling unification is achieved through a light scalar triplet ϕ3∼(3,3,−1/3) and a scalar octet ϕ5∼(8,2,1/2) belonging to the 45H Higgs, while proton decay constraints require that the contribution of the 45H Higgs to the up-quark mass matrix remains highly suppressed.

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Phys. Rev. D 112, 015008– Published 9 July, 2025
  • Received 20 March 2025
  • Accepted 19 May 2025
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