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

Abstract

A ${\mathcal{G}}_{\mathcal{F}}=SU(3{)}_Q\times SU(3{)}_u\times SU(3{)}_d$ 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.

Comments: 12 pages, 1 figure; Revised to match the published version in Phys.Rev.D. Note added explaining the mistake in our claim made in Phys.Rev.Lett.111:061601,2013 regarding the solution to strong CP problem through spontaneous breaking of the quark-flavor symmetry