Gluons, light and heavy quarks and their interactions in the instanton vacuum
The instanton size $\rho$ and inter-instanton distance $R$ are the main parameters of Instanton Liquid Model (ILM) of the QCD vacuum. Various estimates show that $\rho\approx1/3$ fm and $R\approx1$ fm, and the corresponding packing parameter $\kappa=\rho^{4}/R^{4}\approx0.01$. The strength of the light quark-instanton interaction is sizable and close to that of the gluon-instanton one since the dynamical light quark mass $M_{q}$ and dynamical gluon mass $M_{g}$ are given by $M_{q}\approx M_{g}\approx 360$ MeV$\sim\kappa^{1/2}\rho^{-1}$. On the other hand, the strength of the heavy quark-instanton interaction is weak - the direct instanton contribution to the heavy quark mass $\Delta M_{Q}^{{\rm dir}}\approx70$ MeV$\sim\kappa\rho^{-1}.$ The instantons are responsible for mutual interactions among colored particles which are crossing the field of the same instanton, like t'Hooft-like interactions of $N_{f}$ light quarks ($N_{f}$ is the light quark flavors number). The light quark propagators in the instanton field have zero modes, which give dominant contributions. Within ILM we are able to derive the light quarks determinants and the light quarks partition function. These tools perfectly describe the light quark physics and its most important and basic phenomena - the spontaneous breaking of the chiral symmetry (SBChS) in details. These one allows us to find the properties of light and heavy quarks interactions and get SBChS traces in light-heavy and heavy-heavy quarks systems. So, we need to find heavy $Q\bar{Q}$ quarkonia spectra and their wave functions. Here we have interplay of two scales: short ($\sim(M_{Q}v)^{-1}\leq0.15$ fm) perturbative QCD and large ($\sim(M_{Q}v^{2})^{-1}\sim0.5$ fm) nonperturbative QCD scales, where $v$ is the velocity in $Q\bar{Q}$. We calculate the heavy quarks correlators with perturbative corrections within ILM.