# Chasing after flavor symmetries of quarks from bottom up

## TL;DR

This paper investigates the flavor symmetries of quarks within the Standard Model by assuming their existence in a beyond-Standard-Model theory, using a bottom-up approach to understand their properties.

## Contribution

It proposes a framework for understanding quark flavor structures through flavor symmetries, emphasizing rank-one and democratic matrices based on Dirac's naturalness.

## Key findings

- Flavor-symmetric Yukawa matrices can be represented by rank-one matrices.
- Democratic-type matrices play a special role in flavor symmetry models.
- The approach offers insights into the origin of quark mass hierarchies.

## Abstract

We explore a flavor structure of quarks in the standard model under the assumption that flavor symmetries exist in a theory beyond the standard model, and chase after their properties, using a bottom-up approach. We reacknowledge that a flavor-symmetric part of Yukawa coupling matrix can be realized by a rank-one matrix and a democratic-type one occupies a special position, based on Dirac's naturalness.