Evidence for a two scale Infrared NPQCD dynamics from Pade couplant structures

We report our finding of a two scale cut off structure in the infrared nonperturbative dynamics of Pade couplant QCD, in the flavor states $N_{f} \le 8$. We argue that these two NPQCD momentum scales $Q_{c}(Y_{1})$ and $Q_{c}(Y_{2})$ can be identified as the scales of onset of chiral symmetry breaking and quark confinement in QCD, and as the cut off boundaries of a strongly interacting infrared quark gluon phase of Quantum Chromodynamics, intermediate between the hadronic phase of QCD and the weakly coupled perturbative QCD regime. We investigated the pattern of variation with flavor number $N_{f} \le 8$, of these domain boundaries of the intermediate nonperturbative infrared QCD, and found that the two scales are correlated, with a correlation factor $Q_{c}(Y_{2})/Q_{c}(Y_{1})$ that rises to a peak at $N_{f} = 2$ from $N_{f} = 0$, but falls off rapidly to zero for $4 \le N_{f} \le 8$. We concluded firmly that dynamical chiral symmetry breaking and quark confinement while being two distinct QCD phenomena caused by two independent component QCD forces $Y_{1}$ and $Y_{2}$, are nevertheless closely related phenomena of infrared nonperturbative QCD dynamics. Their correlation leads us to a finding that quark confinement is most favored in the $N_{f} = 2$ flavor state of QCD, but becomes rapidly less probable for $N_{f} \geq 4$, this finding being exactly as one observes in nature.