Is there still a strong CP problem?

Abstract

The role of a chiral U(1) phase in the quark mass in QCD is analysed from first principles. In operator formulation, there is a parity symmetry and the phase can be removed by a change in the representation of the Dirac gamma matrices. Moreover, these properties are also realized in a Pauli-Villars regularized version of the theory. In the functional integral scenario, attempts to remove the chiral phase by a chiral transformation are thought to be obstructed by a nontrivial Jacobian arising from the fermion measure and the chiral phase may therefore seem to break parity. But if one starts from the regularized action with the chiral phase also present in the regulator mass term, the Jacobian for a combined chiral rotation of quarks and regulators is seen to be trivial and the phase can be removed by a combined chiral rotation. This amounts to a taming of the strong CP problem.