Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points

TL;DR

This paper explores how magnetized orbifold models can naturally produce realistic quark and lepton mass hierarchies and mixing angles, identifying specific flavor models associated with residual modular symmetries at fixed points.

Contribution

It classifies flavor models based on zero-mode wave functions and residual symmetries, revealing 24 viable models near S-symmetric vacua and none for others.

Findings

24 realistic flavor models identified near S-symmetric vacuum

Large mass hierarchies achieved through residual symmetries

Lepton mixing angles are large, quark angles are small

Abstract

We study quark and lepton mass matrices derived from magnetized $T^2/\mathbb{Z}_2$ orbifold models. Quark and lepton masses have a large hierarchy. In addition, mixing angles are large in the lepton sector, while those are small in the quark sector. We find that this structure can be realized in certain flavor models, which are identified by the zero points of the zero-mode wave functions of fermions and Higgs modes. We classify such realistic flavor models. Fixed points $\tau=i$, $e^{2\pi i/3}$ and $i\infty$ of the modulus $\tau$ play a role in realizing a large mass hierarchy through our scenario, where residual $S$, $ST$, and $T$ symmetries remain and the lightest Higgs modes can correspond to eigenstates of residual symmetries at the leading order. As a result, we find that there are 24 flavor models in total which can be realistic in a vicinity of $S$-symmetric vacuum but no flavor models for $ST$ and $T$-symmetric vacua.