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

Understand

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.