# How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?

## TL;DR

This paper investigates the infrared behavior of Landau gauge Yang-Mills correlators using a massive extension of the Faddeev-Popov Lagrangian, analyzing fixed points and scaling solutions through perturbative and nonperturbative methods.

## Contribution

It provides a detailed analysis of the existence and properties of scaling and decoupling solutions in the infrared regime of Yang-Mills theory within a massive extension framework.

## Key findings

- Decoupling fixed point is infrared stable and weakly coupled.
- Scaling fixed point is unstable and strongly coupled in most dimensions.
- Scaling exponents are derived as functions of spacetime dimension.

## Abstract

We study the Landau gauge correlators of Yang-Mills fields for infrared Euclidean momenta in the context of a massive extension of the Faddeev-Popov Lagrangian which, we argue, underlies a variety of continuum approaches. Standard (perturbative) renormalization group techniques with a specific, infrared-safe renormalization scheme produce so-called decoupling and scaling solutions for the ghost and gluon propagators, which correspond to nontrivial infrared fixed points. The decoupling fixed point is infrared stable and weakly coupled, while the scaling fixed point is unstable and generically strongly coupled except for low dimensions $d\to2$. Under the assumption that such a scaling fixed point exists beyond one-loop order, we find that the corresponding ghost and gluon scaling exponents are, respectively, $2\alpha_F=2-d$ and $2\alpha_G=d$ at all orders of perturbation theory in the present renormalization scheme. We discuss the relation between the ghost wave function renormalization, the gluon screening mass, the scale of spectral positivity violation, and the gluon mass parameter. We also show that this scaling solution does not realize the standard Becchi-Rouet-Stora-Tyutin symmetry of the Faddeev-Popov Lagrangian. Finally, we discuss our findings in relation to the results of nonperturbative continuum methods.