# An approach to QCD perturbative and non-perturbative beta functions

## TL;DR

This paper derives an all-order perturbative and non-perturbative beta function for QCD using the partition function's global properties, potentially addressing the strong CP problem.

## Contribution

It introduces a novel method to compute both perturbative and non-perturbative QCD beta functions from the partition function's global properties.

## Key findings

- Perturbative beta function has a simple, consistent expression.
- Non-perturbative theta angle is approximately zero.
- Results may provide a solution to the strong CP problem.

## Abstract

Using the global properties of the QCD partition function we determine an all order perturbative beta function in the background gauge field method to find out that it has a simple expressions whose properties and consequences align with other recent results in the QCD literature. We further compute the non-perturbative beta functions for the coupling constant and the theta angle in the background of an instanton field with winding number $n$. We solve for the theta angle in the non-perturbative region to determine that it is approximately zero. By extrapolating to the full QCD beta functions our result may constitute a solution to the strong CP problem.