CP-violating theta parameter in the domain model of the QCD vacuum

Abstract

A nonzero CP-violating θ parameter is treated in the domain model which assumes a clusterlike vacuum structure whose units are characterized, in particular, by a topological charge which is not necessarily an integer number. In the present paper we restrict consideration to rational values of the charge. The model has previously been shown to manifest confinement, spontaneous chiral symmetry breaking and the absence of an axial U(1) Goldstone boson. We find that the specific structure of the minima of the free energy density of the domain ensemble forces a 2π periodicity of observables in θ for any number of light quarks, that vacuum doubling occurs at θ=π for any Nf>1 and any value of topological charge q. These features are in agreement with expectations based on anomalous Ward identities and large Nc effective theories. We find also additional values of θ depending on q for which vacuum doubling occurs.