Towards unification of lepton and quark mass matrices from double covering of modular $A_4$ flavor symmetry

TL;DR

This paper explores a unified approach to quark and lepton masses using a double covering of modular $A_4$ flavor symmetry, identifying a common solution for the modulus parameter in the normal hierarchy case.

Contribution

It introduces a novel unification framework based on double covering of modular $A_4$ symmetry and performs a comprehensive numerical analysis to find a common modulus solution.

Findings

Found a narrow common $ au$ region within 5$\sigma$ for normal hierarchy.

Did not find a common $ au$ solution for inverted hierarchy.

Demonstrated the potential of modular symmetry in flavor physics.

Abstract

We study quark and lepton masses and mixings in a double covering of modular $A_4$ flavor symmetry in which we search for common solution of a single modulus $\tau$, applying chi-square numerical analysis under the as minimum framework as possible. We have found the common region of $\tau$ within $5\sigma$ interval that is narrow in case of normal hierarchy, but not found in case of inverted hierarchy.