Modular binary octahedral symmetry for flavor structure of Standard Model

TL;DR

This paper explores the use of the modular binary octahedral group as a flavor symmetry in the Standard Model, constructing modular forms, classifying mass models, and identifying a minimal model that explains fermion masses and mixings with few parameters.

Contribution

It introduces the modular binary octahedral group as a new flavor symmetry, constructs relevant modular forms, and develops a minimal model explaining fermion masses and mixings.

Findings

Constructed vector-valued modular forms for all irreducible representations.

Classified all possible fermion mass models based on the group.

Identified a minimal modular invariant model fitting experimental data.

Abstract

We have investigated the modular binary octahedral group $2O$ as a flavor symmetry to explain the structure of Standard Model. The vector-valued modular forms in all irreducible representations of this group are constructed. We have classified all possible fermion masses models based on the modular binary octahedral group $2O$. A comprehensive numerical analysis is performed, and we present some benchmark quark/lepton masses models in well agreement with the experimental data. Notably we find a minimal modular invariant model for leptons and quarks, which is able to explain simultaneously the masses and mixing parameters of both quarks and leptons in terms of 14 real free parameters including the modulus $\tau$. The fermion mass hierarchies around the vicinity of the modular fixed points are explored.