4 November 1999 Ž . Physics Letters B 466 1999 305–312 Topology of the chiral QCD vacuum V. Gogohia a,b,1 , H. Toki b a HAS, CRIP, RMKI, Depart. Theor. Phys., P.O.B. 49, H-1525 Budapest 114, Hungary b ( ) Research Center for Nuclear Physics RCNP , Osaka UniÕersity, Mihogaoka 10-1, Ibaraki, Osaka 567-0047, Japan Received 19 August 1999; accepted 23 September 1999 Editor: R. Gatto 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 h X 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 Ž . Ž . zero modes enhancement ZME model and the classical component given by the random instanton liquid model RILM . We sum up both contributions into the total, non-perturbative vacuum energy density. A very good agreement with the phenomenological values of the topological susceptibility, the mass of the h X 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. q 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 11.15.Tk; 12.38.Lg 1. Introduction The nonperturbative QCD vacuum has a very rich wx dynamical and topological structure 1 . It is a very complicated medium and its dynamical and topologi- cal complexity means that its structure can be orga- Ž . nized at various levels quantum, classical and it can contain many different components and ingredients which may contribute to the vacuum energy density, the one of main characteristics of the QCD ground state. 1 E-mail: gogohia@rcnp.osaka-u.ac.jp cc: gogohia@rmki.kfki.hu wx In our previous work 2 we have formulated a Ž new, quantum model of the QCD ground state its . non-perturbative vacuum , the so-called zero modes Ž . enhancement ZME model. It is based on the exis- tence and importance of such kind of the non-per- turbative, topologically nontrivial quantum excita- tions of the gluon field configurations which can be effectively, correctly described by the q y4 -type be- haviour of the full gluon propagator in the deep infrared domain. It allows one to calculate the non- perturbative vacuum energy density from first princi- ples using the effective potential approach for com- wx Ž wx. posite operators 3 see also Ref. 4 . It gives the vacuum energy density in the form of the loop 0370-2693r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved. Ž . PII: S0370-2693 99 01106-5