Comments on the Vacuum Orientations in QCD

Abstract

We study the QCD vacuum orientation angles in correlation with the strong CP phases. A vacuum alignment equation of the dynamical chiral symmetry breaking is derived based on the anomalous Ward identity. It is emphasized that a chiral rotation of the quark field causes a change of the vacuum orientation and a change in the definition of the light pseudoscalar generators. As an illustration of the idea, $\text{h}\to 2\text{p}$ decays are carefully studied in different chiral frames. Contrary to the claim in Ref.[7], the $\theta$-term does not directly contribute to the CP-violating processes.

Comments: 11 pages