The QCD beta-function from global solutions to Dyson-Schwinger equations

TL;DR

This paper derives the QCD beta-function using global solutions to Dyson-Schwinger equations, revealing asymptotic freedom and exploring low-energy behavior and mass gap possibilities.

Contribution

It introduces a novel approach by transforming Dyson-Schwinger equations into an ODE for the gluon anomalous dimension, providing new insights into nonperturbative QCD.

Findings

QCD must exhibit asymptotic freedom beyond perturbation theory

Constraints on solutions imply specific low-energy behaviors

Analysis suggests the possibility of a mass gap in the theory

Abstract

We study quantum chromodynamics from the viewpoint of untruncated Dyson-Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This nonlinear equation is parameterized by a function P(x) which is unknown beyond perturbation theory. Still, very mild assumptions on P(x) lead to stringent restrictions for possible solutions to Dyson-Schwinger equations. We establish that the theory must have asymptotic freedom beyond perturbation theory and also investigate the low energy regime and the possibility for a mass gap in the asymptotically free theory.