A Nonperturbative Calculation of Basic Chiral QCD Parameters within Dynamical Equations Approach to QCD at Low Energies

Abstract

Basic chiral QCD parameters (the pion decay constant, the quark and gluon condensates, the dynamically generated quark mass, etc) as well as the vacuum energy density have been calculated from first principles within a recently proposed dynamical equations approach to QCD at low energies. The zero modes enhancement (ZME) model of quark confinement and dynamical chiral symmetry breaking (DCSB) based on the solution to the Schwinger-Dyson (SD) equation for the quark propagator in the infrared (IR) domain was used for this purpose. There are only two independent quantities by means of which calculations should be done within our approach. Our unique input data was chosen to be the pion decay constant in the chiral limit given by the chiral perturbation theory at the hadronic level (CHPTh). Phenomenological estimates of these quantities, as well as the vacuum energy density, are in good agreement with our numerical results. The nonperturbative vacuum structure which emerges from the ZME model, appears to be well suited to describe quark confinement, DCSB, current-effective (dynamical)-constituent, as well as constituent-valence quark transformations, the Okubo-Zweig-Iizuka (OZI) rule, dimensional transmutation, etc. The importance of the instanton-type fluctuations in the true QCD vacuum for the ZME model is also emphasized. This allows to predict new, more realistic values for the vacuum energy density (apart from the sign, by definition, the bag constant) and the gluon condensate.