# Calculation of the non-perturbative strong coupling from first principles

## TL;DR

This paper develops a first-principles approach to calculate the non-perturbative strong coupling in pure Yang-Mills theory, using a screened momentum-subtraction scheme that aligns well with lattice data and reveals an IR fixed point.

## Contribution

It introduces a self-contained, predictive framework based on Slavnov-Taylor and Nielsen identities for the non-perturbative running of the strong coupling from first principles.

## Key findings

- Excellent agreement with lattice data.
- Identification of a finite IR stable fixed point at g=9.40.
- Analytical expression for IR behavior of the beta function.

## Abstract

The success of the screened massive expansion is investigated in the framework of a screened momentum-subtraction scheme for the running of the strong coupling in pure Yang-Mills theory. By the exact Slavnov-Taylor and Nielsen identities, a very predictive and self-contained set of stationary conditions are derived for the optimization of the fixed-coupling expansion, yielding explicit analytical one-loop expressions for the propagators, the coupling and the beta function, from first principles. An excellent agreement is found with the lattice data. In the proposed screened renormalization scheme, a monotonic running coupling emerges which saturates in the IR at the finite IR stable fixed point $g=9.40$ where the beta function crosses the zero. A simple analytical expression is derived for the leading behavior of the beta in the IR.