A Solution of the Strong CP Problem Transforming the theta-angle to the KM CP-violating Phase

TL;DR

This paper proposes a novel approach where a rotating fermion mass matrix eliminates the QCD theta-angle term via chiral transformations, linking strong and weak CP violations through the CKM matrix's phase.

Contribution

It introduces a scale-dependent rotating fermion mass matrix that removes the theta-angle term and naturally generates the CKM phase, unifying strong and weak CP violation explanations.

Findings

Theta-angle can be eliminated without zero quark masses.

The CKM phase arises from mass matrix rotation, matching observed CP violation levels.

Strong and weak CP violations are interconnected phenomena.

Abstract

It is shown that in the scheme with a rotating fermion mass matrix (i.e. one with a scale-dependent orientation in generation space) suggested earlier for explaining fermion mixing and mass hierarchy, the theta-angle term in the QCD action of topological origin can be eliminated by chiral transformations, while giving still nonzero masses to all quarks. Instead, the effects of such transformations get transmitted by the rotation to the CKM matrix as the KM phase giving, for $\theta$ of order unity, a Jarlskog invariant typically of order $10^{-5}$ as experimentally observed. Strong and weak CP violations appear then as just two facets of the same phenomenon.