Topological structure of chiral QCD vacuum

Abstract

Using the trace anomaly relation, low-energy theorem and Witten-Veneziano formula, we have developed an analytical formalism which allows one to calculate the gluon condensate, the topological susceptibility and the mass of the ${\eta }^{\prime }$ meson in the chiral limit as functions of the non-perturbative vacuum energy density. It is used for numerical evaluation of the chiral QCD topology within the QCD vacuum model consisting mainly of the quantum component given by the recently proposed zero modes enhancement (ZME) model and the classical component given by the the random instanton liquid model (RILM). We sum up both contributions into the total, nonperturbative vacuum energy density. A very good agreement with the phenomenological values of the topological susceptibility, the mass of the ${\eta }^{\prime }$ meson in the chiral limit and the gluon condensate has been obtained. This puts the above mentioned QCD vacuum model on a firm phenomenological ground.

References and typos corrected. Some clarification is added, 13 pages, 9 Tables. To appear in Phys.Rev. D. Some expressions as well as some numbers in Tables 2-5 were corrected

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• The color gauge invariance and a possible origin of a mass gap in QCD
• The Contribution of the Light Quark Condensate to the Pion-Nucleon Sigma Term
• Can instantons saturate the large mass of the ${\eta }^{\prime }$ meson in the chiral limit?
• Structure of the Yang-Mills vacuum in the zero modes enhancement quantum model