Modular Flavor Symmetries and Fermion Mass Hierarchies

2025/06/29 by Chen, Mu-Chun, Li, Xueqi, Liu, Xiang-Gan +1 · 1 citation
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph)

paper · doi:10.48550/arxiv.2506.23343

Abstract

We investigate fermion mass hierarchies in models with modular flavor symmetries. Several key conclusions arise from the observation that the determinants of mass matrices transform as 1-dimensional vector-valued modular forms. We demonstrate that, under some fairly general assumptions, achieving hierarchical fermion masses requires the vacuum expectation value of the modulus τ to be located near one of the critical points, i, i∞, or ω. We also revisit the universal near-critical behavior around these points and classify the resulting mass hierarchies for the critical points i and ω. We compare the traditional Froggatt--Nielsen mechanism with its modular variant. The knowledge and boundedness of Fourier and Taylor coefficients are crucial to the predictive power of modular flavor symmetries.

Citations

• Flavor Symmetries and Winding Modes
• Modular Symmetry with Weighton
• Multiple realizations of modular flavor symmetries and their phenomenology
• Comprehensive Bayesian Exploration of Froggatt-Nielsen Mechanism
• Solving the strong CP problem without axions
• The symmetry approach to quark and lepton masses and mixing
• Universal predictions of Siegel modular invariant theories near the fixed points
• Modular invariant holomorphic observables
• Neutrino Mass and Mixing with Modular Symmetry
• Modular binary octahedral symmetry for flavor structure of Standard Model
• Modular flavor symmetric models
• Neutrino Flavor Model Building and the Origins of Flavor and CP Violation: A Snowmass White Paper
• Growth of Fourier coefficients of vector-valued automorphic forms
• Modular Invariant Models of Leptons at Level 7
• Are neutrino masses modular forms?
• Anomaly-safe discrete groups
• Representations of the braid group B₃ and of SL(2,Z)

Cited by

• Flavour Physics Beyond the Standard Model

Related

• Aspects of Modular Flavor Symmetries
• CP phase in modular flavor models and discrete Froggatt-Nielsen models
• Quark masses and CKM hierarchies from S₄^′ modular flavor symmetry
• Multiple realizations of modular flavor symmetries and their phenomenology
• Modular Symmetry with Weighton