Comprehensive Analysis of Yukawa Hierarchies on $T^2/Z_N$ with Magnetic Fluxes

TL;DR

This paper systematically examines Yukawa hierarchies in magnetized orbifold models, revealing the potential and limitations of generating realistic fermion mass ratios, especially between the up and top quarks.

Contribution

It provides a comprehensive analysis of Yukawa sector configurations on various magnetized orbifolds, highlighting the challenges in achieving extremely hierarchical fermion masses.

Findings

Hierarchies of 10^{-2} to 10^{-3} are achievable via kinetic mixing.

Achieving the up-top quark mass ratio of 10^{-5} is very difficult on complex orbifolds.

The study clarifies the limitations of Yukawa hierarchy generation in these models.

Abstract

Based on the result of classification in our previous work, we exhaustively investigate Yukawa sector of $U(8)$ model on magnetized orbifolds $T^{2}/Z_{2}$, $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$ by evaluating ratios of the mass eigenvalues of the three states in all the possible configurations with one and two Higgs pairs where three generations are realized in fermions. Because of smearing effect via kinetic mixing, one can realize a hierarchy such as $10^{-2}$-$10^{-3}$, but it is very difficult to achieve the mass ratio between the up and top quarks ($m_{\text{up}}/m_{\text{top}} \sim 10^{-5}$) on the complicated magnetized orbifolds $T^{2}/Z_{N}\,(N=3,4,6)$.