A systematic extended iterative solution for quantum chromodynamics

Abstract

An outline is given of an extended perturbative solution of Euclidean QCD which systematically accounts for a class of nonperturbative effects, while still allowing renormalization by the perturbative counterterms. Euclidean proper verticesΓ are approximated by a double sequenceΓ ^[r,p], wherer denotes the degree of rational approximation with respect to the spontaneous mass scaleΛ _QCD, nonanalytic in the couplingg ², whilep represents the order of perturbative corrections ing ² calculated fromΓ ^[r,0]-rather than from the perturbative Feynman rulesΓ ^(0)pert-as a starting point. The mechanism allowing the nonperturbative terms to reproduce themselves in the Dyson-Schwinger equations preserves perturbative renormalizability and is intimately tied to the divergence structure of the theory. As a result, it restricts the self-consistency problem for theΓ ^[r,0] rigorously — i.e. without decoupling approximations — to the seven superficially divergent vertices. An interesting aspect of the solution is that rational-function sequences for the QCD propagators contain subsequences describing short-lived elementary excitations. The method is calculational, in that it allows the known techniques of loop computation to be used while dealing with integrands of truly nonperturative content.