Nonholomorphic $A_4$ modular invariance for fermion masses and mixing in SU(5) GUT

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 non-supersymmetric models, we propose the first renormalizable $SU(5)$ grand unified theory incorporating level 3 nonholomorphic modular symmetry, ${\Gamma }_3\simeq A_4$. 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 $m_{\beta \beta }$ values align with current neutrinoless double-beta decay experiments, and the effective neutrino mass $m_{\beta }$ 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 ${\varphi }_3\sim (3,3,-1/3)$ and a scalar octet ${\varphi }_5\sim (8,2,1/2)$ belonging to the $45_H$ Higgs, while proton decay constraints require a highly suppressed Yukawa couplings.

arXiv comment27 pages, 5 figures

References in corpus (48)

• Evidence for oscillation of atmospheric neutrinos
• Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
• Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry
• Proton stability in grand unified theories, in strings, and in branes
• A SUSY SU(5) Grand Unified Model of Tri-Bimaximal Mixing from A4
• NuFit-6.0: Updated global analysis of three-flavor neutrino oscillations
• Finite Modular Groups and Lepton Mixing
• Flavor structures of charged fermions and massive neutrinos
• Unified Models of Neutrinos, Flavour and CP Violation
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• Search for narrow resonances decaying to dijets in proton-proton collisions at sqrt(s) = 13 TeV
• NEXO: Neutrinoless double beta decay search beyond $10^{28}$ year half-life sensitivity
• Neutrino Masses and Mixing from Double Covering of Finite Modular Groups
• Determining the neutrino mass with Cyclotron Radiation Emission Spectroscopy - Project 8
• $SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry
• Search for proton decay via $p\to e^{+}{\pi }^0$ and $p\to {\mu }^{+}{\pi }^0$ with an enlarged fiducial volume in Super-Kamiokande I-IV
• Direct neutrino-mass measurement based on 259 days of KATRIN data
• A SUSY GUT of Flavour with S4 x SU(5) to NLO
• S4 Flavor Symmetry of Quarks and Leptons in SU(5) GUT
• Towards a complete $A_4\times SU(5)$ SUSY GUT
• Modular $S_3$ invariant flavor model in SU(5) GUT
• Simple Finite Non-Abelian Flavor Groups
• Yukawa Sector of Minimal SO(10) Unification
• The Design, Construction, and Commissioning of the KATRIN Experiment
• Heavy and light scalar leptoquarks in proton decay
• Automorphic Forms and Fermion Masses
• Neutrino masses and tribimaximal mixing in the minimal renormalizable supersymmetric SU(5) grand unified model with A4 flavor symmetry
• A4xSU(5) SUSY GUT of Flavour with Trimaximal Neutrino Mixing
• $SU(5)$ GUTs with $A_4$ modular symmetry
• Twin Modular $S_4$ with $SU(5)$ GUT
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• SUSY S4 x SU(5) revisited
• Modular $S_4\times SU(5)$ GUT
• SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry
• The symmetry approach to quark and lepton masses and mixing
• Toward minimal renormalizable SUSY SU(5) Grand Unified Model with tribimaximal mixing from A4 Flavor symmetry
• Scalar leptoquark in SU(5)
• Polyharmonic Maass forms for PSL(2, Z)
• Phenomenological Implications of an SU(5) x S4 x U(1) SUSY GUT of Flavour
• Approaching Minimal Flavour Violation from an SU(5) x S4 x U(1) SUSY GUT
• Neutrino phenomenology in the flavored NMSSM without domain wall problems
• Flavor physics in SU(5) GUT with scalar fields in the 45 representation
• Type II seesaw supersymmetric neutrino model for ${\theta }_{13}\ne 0$
• Gauge coupling unification and proton decay via 45 Higgs boson in SU(5) GUT
• Hybrid seesaw neutrino model in SUSY $SU(5)\times {\mathbb{A}}_4$
• Fermion Masses and Mixing in Pati-Salam Unification with $S_3$ Modular Symmetry
• Flavour in $SU(5)$ Finite Grand Unified Models
• Proton Decay and Gauge Coupling Unification in an Extended SU(5) GUT with 45-Dimensional Higgs

Cited by in corpus (1)

• Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maaß form