Quark-lepton mass relations from modular flavor symmetry

• Published in: The journal of high energy physics Vol. 2024; no. 2; pp. 160 - 28
• Main Authors: Chen, Mu-Chun, King, Stephen F., Medina, Omar, Valle, José W. F.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 22.02.2024; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Clebsch-Gordan coefficients; Discrete Symmetries; Elementary Particles; Fermions; Flavor (particle physics); Flavour Symmetries; Invariants; Leptons; Mathematical models; Neutrinos; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry; Theories of Flavour; Thermal expansion; Discrete Symmetries; Theories of Flavour; Flavour Symmetries
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2024)160

A bstract The so-called Golden Mass Relation provides a testable correlation between charged-lepton and down-type quark masses, that arises in certain flavor models that do not rely on Grand Unification. Such models typically involve broken family symmetries. In this work, we demonstrate that realistic fermion mass relations can emerge naturally in modular invariant models, without relying on ad hoc flavon alignments. We provide a model-independent derivation of a class of mass relations that are experimentally testable. These relations are determined by both the Clebsch-Gordan coefficients of the specific finite modular group and the expansion coefficients of its modular forms, thus offering potential probes of modular invariant models. As a detailed example, we present a set of viable mass relations based on the Γ 4 ≅ S 4 symmetry, which have calculable deviations from the usual Golden Mass Relation.