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

TL;DR

This paper proposes a novel framework where the family mass hierarchy and CP violation in quarks and leptons originate from a flavour-dependent vacuum structure, explaining observed data without extra particles or symmetries.

Contribution

It introduces a flavor-dependent vacuum approach that naturally accounts for mass hierarchies and CP violation, aligning with experimental observations without additional degrees of freedom.

Findings

Reproduces current quark and lepton mass data.

Explains CKM and PMNS mixing patterns.

Provides a unified origin for mass hierarchy and CP violation.

Abstract

We rewrite the Yukawa interactions of the standard model in terms of flavour-dependent vacuum structure to address the family mass hierarchy and CP violation in both the quark sector and lepton sector. It is realized for the first time that the Lagrangian only includes the same number of degrees of freedom as phenomenological observables with no requirement of extra particles or any new symmetry. The quark and lepton mass hierarchy arises as a natural result of the close-to-flat vacuum in flavour space. The CP violation in CKM and PMNS is explained as a general quantum phase 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 flavour mixings.