Yukawa textures in modular symmetric vacuum of magnetized orbifold models

TL;DR

This paper investigates quark mass matrices derived from magnetized orbifold models, classifying Yukawa textures at specific modular fixed points and exploring conditions for realistic hierarchical quark masses and mixings.

Contribution

It classifies Yukawa textures at key modular fixed points and demonstrates how realistic quark mass hierarchies can emerge from these textures in magnetized orbifold models.

Findings

Yukawa matrices exhibit texture structures at fixed points

Realistic quark mass hierarchies are achievable near specific modular vacua

Illustrative examples reproduce observed quark mass ratios and mixing angles

Abstract

We study quark mass matrices derived from magnetized $T^2/\mathbb{Z}_2$ orbifold models. Yukawa matrices at three modular fixed points, $\tau=i, e^{2\pi i/3}$ and $i\infty$ are invariant under $S$, $ST$ and $T$-transformations. We study these invariances on $T^2/\mathbb{Z}_2$ twisted orbifold. We find that Yukawa matrices have a kind of texture structures although ones at $\tau=i\infty$ are not realistic. We classify Yukawa textures at $\tau=i$ and $e^{2\pi i/3}$. Moreover we investigate the conditions such that quark mass matrix constructed by Yukawa textures becomes approximately rank one matrix, which is favorable to lead to hierarchical masses between the third generation and the others. It is found that realistic quark mass matrices can be obtained around the $S$-invariant vacuum and $ST$-invariant vacuum. As an illustrating example, we show the realization of the quark mass ratios and mixing based on Fritzch and Fritzch-Xing mass matrices.