Gluons in the QCD bound state problem - a way to exact solution

Abstract

The colored objects -- quarks and gluons -- being confined in a small volume $V\sim R_0^3,$ $R_0\sim 0.5$fm inside the QCD bound state get there not small masses $m_{q\bar q}\sim 1$GeV, $m_g\sim 0.5$GeV. This drastically simplifies the QCD dynamics, as now the probabilities e.g. of production of one extra massive valent gluon or extra $q\bar q$ pair, turned to be small due to a large gap between corresponding energy levels. The ordinary quantum mechanical perturbation theory calculations made in the paper shows that corresponding dimensionless transition amplitudes $Λ_{MH}=\frac{V_{MH}}{|E^{(0)}_M-E^{(0)}_H|}$ (from meson $q\bar q$ to the hybrid $q\bar qg$) have a value of 20--25% and the mixing of hybrid with glueball $(gg)$ is even smaller (of the order of 10--18%). Taking into account all such mixings with all highly lying Fock states is equivalent to the exact solution of QCD bound state problem. This can be done really summing the small perturbation theory results for these states contributions.