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

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.