A Systematic Extended Iterative Solution for QCD

TL;DR

This paper introduces a systematic extended iterative approach for Euclidean QCD that incorporates nonperturbative effects while maintaining renormalizability, using rational approximations and Dyson-Schwinger equations.

Contribution

It develops a novel method combining rational approximations with perturbative corrections to address nonperturbative effects in QCD systematically.

Findings

Allows nonperturbative effects to self-reproduce in Dyson-Schwinger equations.

Restricts self-consistency to superficially divergent vertices.

Enables loop calculations with nonperturbative integrands.

Abstract

An outline is given of an extended perturbative solution of Euclidean QCD which systematically accounts for a class of nonperturbative effects, while allowing renormalization by the perturbative counterterms. Proper vertices Gamma are approximated by a double sequence Gamma[r,p], with r the degree of rational approximation w.r.t. the QCD mass scale Lambda, nonanalytic in the coupling g, and p the order of perturbative corrections in g-squared, 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 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 superficially divergent vertices. An interesting aspect of the scheme is that rational-function sequences for the propagators allow subsequences describing short-lived excitations. The method is calculational, in that it allows known techniques of loop computation to be used while dealing with integrands of truly nonperturbative content.