A Nonperturbative Calculation of Basic Chiral QCD Parameters Within Zero Modes Enhancement Model of the QCD Vacuum. II

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 (up to the sign, by definition, the bag constant) have been calculated from first principles within a recently proposed zero modes enhancement (ZME) model of the true QCD vacuum. Our unique input data was chosen to be the pion decay constant in the chiral limit as given by the chiral perturbation theory at the hadronic level (CHPTh). In order to analyze our numerical results we set a scale by two different ways. In both cases we obtain almost the same numerical results for all chiral QCD parameters. Phenomenological estimates of these quantites as well as vacuum energy density are in good agreement with our numerical results. Complementing them by the numerical value of the instanton contribution to the vacuum energy density, we predict new, more realistic values for the vacuum energy density, the bag constant and the gluon condensate.Comment: 22 pages in total , 8 figures, 4 tables ; RevTex package use

How to calculate the quantum part of the truly nonperturbative Yang-Mills vacuum energy density in the axial gauge QCD

Using the effective potential approach for composite operators, we have formulated a general method how to calculate the truly nonperturbative vacuum energy density in the axial gauge QCD quantum models of its ground state. It is defined as integrated out the truly nonperturbative part of the full gluon propagator over the deep infrared region (soft momentum region). The nontrivial minimization procedure makes it possible to determine the value of the soft cutoff in terms of the corresponding nonperturbative scale parameter which is inevitably presented in any nonperturbative model for the full gluon propagator. If the chosen Ansatz for the full gluon propagator is a realistic one, then our method uniquely determines the truly vacuum energy density, which is always finite, automatically negative and it has no imaginary part (stable vacuum). We illustrate it by considering the Abelian Higgs model of dual QCD ground state. We have explicitly shown that the vacuum of this model without string contributions is unstable against quantum corrections.Comment: 12 pages, no figures, no tables, typos correcte

A general solution for the quark propagator in two-dimensional covariant gauge QCD

We have investigated a closed set of equations for the quark propagator, which has been obtained earlier within a new, nonperturbative approach to two-dimencional covariant gauge QCD. It is shown that this theory implies quark confinement (the quark propagator has no poles, indeed), as well as dynamical breakdown of chiral symmetry (a chiral symmetry preserving solution is forbidden). The above-mentioned set of equations can be exactly solved in the chiral limit. We develop an analytical formalism, the so-called chiral perturbation theory at the fundamental quark level, which allows one to find solution for the quark propagator in powers of the light quark masses. Each correction satisfies the differential equation, which can be formally solved. We develop also an analytical formalism which alows one to find solution for the quark propagator in the inverse powers of the heavy quark masses. IT coincides with free heavy quark propagator up to terms of order $1/m_Q^3$, where $m_Q$ is the heavy quark mass. So this solution automatically possesses the heavy quark flavor symmetry up to terms of order $1/m_Q$. At the same time, we have found a general solution for the heavy quark propagator, which by no means can be reduced to the free one.Comment: 12 pages, two figures, no tables, typos are correcte

A Nonperturbative Calculation of Basic Chiral QCD Parameters Within Zero Modes Enhancement Model of the QCD Vacuum. I

A new zero modes enhancement (ZME) model of the true QCD vacuum is breifly described. It makes possible to analytically investigate and calculate numerically low-energy QCD structure from first principles. Expressions of 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 (up to the sign, by definition, the bag constant), suitable for numerical calculations, have been derived. Solution to the Schwinger-Dyson (SD) equation for the quark propagator in the infrared (IR) domain on the basis of the ZME effect in QCD was used for this purpose. There are only two independent quantities (free parameters) by means of which calculations must be done within our approach. The first one is the integration constant of the above mentioned quark SD equation of motion. The second one is a scale at which nonperturbative effects begin to play a dominant role.Comment: 17 pages, two figures added, minor change