A method for getting a finite $$\alpha $$ α in the IR region from an all-order beta function

Abstract The analytical method of the QCD running coupling constant is extended to a model with an all-order beta function which is inspired by the famous Novikov–Shifman–Vainshtein–Zakharov beta function of $$N=1$$ N = 1 supersymmetric gauge theories. In the approach presented here, the running coupling is determined by a transcendental equation with non-elementary integral of the running scale $$\mu $$ μ . In our approach $$\alpha _\text {an}(0)$$ α an ( 0 ) , which reads 0.30642, does not rely on any dimensional parameters. This is in accordance with results in the literature on the analytical method of the QCD running coupling constant. The new “analytically improved” running coupling constant is also compatible with the property of asymptotic freedom