New Angle on the Strong CP and Chiral Symmetry Problems from a Rotating Mass Matrix

TL;DR

This paper proposes that a rotating fermion mass matrix with changing orientation in generation space can address the strong CP problem and offer new insights into chiral symmetry breaking, aligning with observed fermion properties.

Contribution

It introduces the concept that a rotating mass matrix can resolve the strong CP problem without contradicting quark mass observations and provides a novel perspective on chiral symmetry breaking.

Findings

Rotating mass matrices can eliminate the need for a nonzero theta term.

Rotation explains how zero eigenvalues do not imply zero physical masses.

Supports previous ideas linking rotation to fermion mixing and mass hierarchy.

Abstract

It is shown that when the mass matrix changes in orientation (rotates) in generation space for changing energy scale, then the masses of the lower generations are not given just by its eigenvalues. In particular, these masses need not be zero even when the eigenvalues are zero. In that case, the strong CP problem can be avoided by removing the unwanted $\theta$ term by a chiral transformation in no contradiction with the nonvanishing quark masses experimentally observed. Similarly, a rotating mass matrix may shed new light on the problem of chiral symmetry breaking. That the fermion mass matrix may so rotate with scale has been suggested before as a possible explanation for up-down fermion mixing and fermion mass hierarchy, giving results in good agreement with experiment.