Screening of the topological charge in a correlated instanton vacuum

TL;DR

This paper investigates how fermion-induced interactions screen the topological charge in a correlated instanton vacuum, providing a new method to compute the $ ext{η'}$ mass and suggesting applications for lattice QCD.

Contribution

It introduces a novel approach to study topological charge screening in a correlated instanton vacuum, differing from the random instanton model, and offers a practical method for $ ext{η'}$ mass calculation.

Findings

Screening of topological charge is confirmed in the correlated instanton vacuum.

The method allows $ ext{η'}$ mass calculation without Dirac operator inversion.

Results align with chiral Ward identities and low energy theorems.

Abstract

Screening of the topological charge due to he 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 $\eta'$ 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. \cite{Novikov-etal}. We also propose to evaluate the topological susceptibility in the Witten-Veneziano formula not in an infinite box in an world $without$ fermions but in an infinitesimal box in a world $with$ fermions.