Nonholomorphic $A_4$ modular invariance for fermion masses and mixing in SU(5) GUT
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915424651706368 |
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| author | Loualidi, Mohamed Amin Miskaoui, Mohamed Nasri, Salah |
| author_facet | Loualidi, Mohamed Amin Miskaoui, Mohamed Nasri, Salah |
| contents | 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 non-supersymmetric models, we propose the first renormalizable $SU(5)$ grand unified theory incorporating level 3 nonholomorphic modular symmetry, $Γ_3 \simeq A_4$. 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 GUT queries such as gauge coupling unification and proton decay. Beyond the minimal $SU(5)$ framework, the Higgs sector incorporates the $45_H$ 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 $A_4$ charge assignments. The predicted effective Majorana mass $m_{ββ}$ values align with current neutrinoless double-beta decay experiments, and the effective neutrino mass $m_β$ is within the reach of future beta decay searches. The predicted sum of neutrino masses, $\sum m_i$, satisfies the upper bound set by recent cosmological observations. The gauge coupling unification is achieved through a light scalar triplet $ϕ_3 \sim (3,3,-1/3)$ and a scalar octet $ϕ_5 \sim (8,2,1/2)$ belonging to the $45_H$ Higgs, while proton decay constraints require a highly suppressed Yukawa couplings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonholomorphic $A_4$ modular invariance for fermion masses and mixing in SU(5) GUT Loualidi, Mohamed Amin Miskaoui, Mohamed Nasri, Salah High Energy Physics - Phenomenology 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 non-supersymmetric models, we propose the first renormalizable $SU(5)$ grand unified theory incorporating level 3 nonholomorphic modular symmetry, $Γ_3 \simeq A_4$. 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 GUT queries such as gauge coupling unification and proton decay. Beyond the minimal $SU(5)$ framework, the Higgs sector incorporates the $45_H$ 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 $A_4$ charge assignments. The predicted effective Majorana mass $m_{ββ}$ values align with current neutrinoless double-beta decay experiments, and the effective neutrino mass $m_β$ is within the reach of future beta decay searches. The predicted sum of neutrino masses, $\sum m_i$, satisfies the upper bound set by recent cosmological observations. The gauge coupling unification is achieved through a light scalar triplet $ϕ_3 \sim (3,3,-1/3)$ and a scalar octet $ϕ_5 \sim (8,2,1/2)$ belonging to the $45_H$ Higgs, while proton decay constraints require a highly suppressed Yukawa couplings. |
| title | Nonholomorphic $A_4$ modular invariance for fermion masses and mixing in SU(5) GUT |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2503.12594 |