Casimir operator dependences of nonperturbative fermionic QCD amplitudes

In eikonal and quenched approximations, it is argued that the strong coupling fermionic QCD Green’s functions and related amplitudes depart from a sole dependence on the [Formula: see text] quadratic Casimir operator, [Formula: see text], evaluated over the fundamental gauge group representation. Noted in nonrelativistic quark models and in a nonperturbative generalization of the Schwinger mechanism, an additional dependence on the cubic Casimir operator shows up, in contradistinction with perturbation theory and other nonperturbative approaches. However, it accounts for the full algebraic content of the rank-2 Lie algebra of [Formula: see text]. Though numerically subleading effects, cubic Casimir dependences, here and elsewhere, appear to be a signature of the nonperturbative fermionic sector of QCD.

CASIMIR SCALING AND MODELS OF CONFINEMENT IN QCD

Recent lattice calculations have demonstrated that the QCD static potential for sources in different representations of the gauge group is proportional to the eigenvalue of the corresponding quadratic Casimir operator with an accuracy of a few percent. We discuss the present theoretical status of this "Casimir scaling" phenomenon and stress its importance for the analysis of nonperturbative QCD vacuum models and other field theories. It is argued that Casimir scaling strongly advocates the property of Gaussian dominance of nonperturbative QCD vacuum. We also briefly discuss possible future tests to improve our understanding of the phenomenon.