Screening of the topological charge in a correlated instanton vacuum

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Abstract
Screening of the topological charge due to fermion-induced interactions is an important phenomenon, closely related with the resolution of the strong CP and U(1) problems. We study the mechanism of such screening in a ‘‘correlated instanton vacuum,’’ as opposed to the ‘‘random’’ one. Both scalar and pseudoscalar gluonic correlators are analyzed by means of an observable that minimizes finite size effects. Screening of the topological charge is established. This allows us to calculate the η’ mass without having to invert the Dirac operator. We suggest that this method might be used in lattice QCD calculations as well. Our results for the screening of the topological charge are in agreement with the chiral Ward identities, and the scalar gluonic correlator satisfies a low energy theorem first derived by Novikov et al. We also propose a modified Witten-Veneziano formula, in which the topological susceptibility is not defined for an infinite box in a world without fermions, but for a small box in the real world.