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

## TL;DR

This paper extends the analytical method for the QCD running coupling to an all-order beta function inspired by supersymmetric theories, providing a finite value at zero momentum without relying on dimensional parameters.

## Contribution

It introduces a novel approach to determine the QCD running coupling using an all-order beta function, resulting in a finite infrared value independent of dimensional parameters.

## Key findings

- The analytically improved coupling at zero momentum is 0.30642.
- The method is compatible with asymptotic freedom.
- The approach extends existing analytical methods to a supersymmetry-inspired beta function.

## Abstract

The analytical method of QCD running coupling constant is extended to a model with an all-order beta function which is inspired by the famous Novikov-Shifman-Vai\-n\-s\-htein-Zakharov beta function of N=1 supersymmetric gau\-g\-e theories. In the approach presented here, the running coupling is determined by a transcendental equation with non-elementary integral of the running scale $\mu$. In our approach $\alpha_{an}(0)$, 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 QCD running coupling constant. The new "analytically im\-p\-roved" running coupling constant is also compatible with the property of asymptotic freedom.