Quark masses, mixings, and CP violation from spontaneous breaking of flavor $SU(3)^{3}$

TL;DR

This paper proposes a model where spontaneous breaking of a flavor symmetry explains quark masses, mixings, and CP violation without hierarchical parameters, providing a dynamical origin for observed flavor phenomena.

Contribution

It introduces a scalar potential invariant under flavor symmetry that dynamically explains quark flavor structure and CP violation without fine-tuning.

Findings

Reproduces quark mass hierarchies

Explains quark mixing angles and CP phase

No hierarchical parameters needed

Abstract

A ${\cal G}_{\cal F}=SU(3)_{Q}\times SU(3)_{u}\times SU(3)_{d}$ invariant scalar potential breaking spontaneously the quark flavor symmetry can explain the standard model flavor puzzle. The approximate alignment in flavor space of the vacuum expectation values of the up and down ``Yukawa fields'' is explained as a dynamical effect, and the observed quark mixing angles, the weak CP violating phase, and hierarchical quark masses can be reproduced without introducing hierarchical parameters.