A systematic extended iterative solution for quantum chromodynamics

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 vertices Gamma are approximated by a double sequence Gamma([r,p]), where r denotes the degree of rational approximation with respect to the spontaneous mass scale Lambda(QCD),nonanalytic in the coupling g(2), while p represents the order of perturbative corrections in g(2) calculated from Gamma([r,0]) - rather than from the perturbative Feynman rules Gamma((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 the Gamma([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 nonperturbative content.