The common origin of the family mass hierarchy and CP violation from flavor-dependent vacuum for quarks and leptons

Abstract

We rewrite the Yukawa interactions of the Standard Model in terms of flavor-dependent vacuum structure to address the family mass hierarchy and CP violation in both the quark sector and lepton sector. It is realized that Yukawa terms only include the same number of degrees of freedom as phenomenological observables with no requirement of extra particle or any new symmetry. The quark and lepton mass hierarchy arises as a natural result of the close-to-flat vacuum in flavor space. The CP violations in CKM mixing and PMNS mixing are explained as general quantum phases between weak gauge eigenstates and Yukawa interaction states. The mechanism is proven by reproduction of all current quark/lepton mass data and the CKM/PMNS mixing parameters.