Texture zeros of quark mass matrices at fixed point $\tau=\omega$ in modular flavor symmetry

TL;DR

This paper explores how specific quark mass matrix textures, particularly the NNI form, naturally emerge at the fixed point τ=ω in modular flavor symmetry models, using multi-Higgs fields and residual symmetries.

Contribution

It demonstrates the realization of NNI quark mass matrices at τ=ω in A4, S4, and A5 modular flavor models with different Higgs field configurations and symmetry considerations.

Findings

NNI form realized at τ=ω in A4 and S4 models with two Higgs pairs.

Four Higgs pairs needed for NNI form in A5 models.

Texture zeros originate from residual Z3 symmetry of SL(2,Z).

Abstract

We study systematically derivation of the specific texture zeros, that is the nearest neighbor interaction (NNI) form of the quark mass matrices at the fixed point $\tau=\omega$ in modular flavor symmetric models. We present models that the NNI forms of the quark mass matrices are simply realized at the fixed point $\tau=\omega$ in the $A_4$ modular flavor symmetry by taking account multi-Higgs fields. Such texture zero structure originates from the $ST$ charge of the residual symmetry $Z_3$ of $SL(2,Z)$. The NNI form can be realized at the fixed point $\tau = \omega$ in $A_4$ and $S_4$ modular flavor models with two pairs of Higgs fields when we assign properly modular weights to Yukawa couplings and $A_4$ and $S_4$ representations to three generations of quarks. We need four pairs of Higgs fields to realize the NNI form in $A_5$ modular flavor models.