Fermion regularization, fermion measure and axion fields

TL;DR

This paper discusses how fermion regularization and measure choices can preserve CP symmetry in QCD, allowing the theta term's CP violation to be neutralized by setting theta to zero.

Contribution

It demonstrates that Pauli-Villars regularization and parity symmetric fermion measures can eliminate CP violation from the fermion sector in QCD.

Findings

Fermion regularization preserves CP symmetry.

CP violation from the theta term can be neutralized.

Setting theta to zero removes CP violation.

Abstract

Axion fields were originally introduced to control CP violation due to the theta term in QCD. Pauli-Villars regularization, or the use of a parity symmetric fermion measure, however, preserves CP in the fermion sector. A CP violation arising from the theta term can then be neutralized in a natural way by setting theta equal to zero.