# Alpha_s from the non-perturbatively renormalised lattice three-gluon vertex

## TL;DR

This paper presents a non-perturbative lattice QCD method to compute the running coupling constant, achieving precise results in the quenched approximation and potentially applicable to unquenched calculations.

## Contribution

It introduces a non-perturbative renormalisation scheme based on the three-gluon vertex, avoiding lattice perturbation theory for scheme matching, and demonstrates its effectiveness in quenched QCD.

## Key findings

- Coupling runs according to two-loop asymptotic formula in the studied momentum range.
- Lattice artifacts and finite-volume effects are well-controlled.
- Method can be extended to unquenched QCD calculations.

## Abstract

We compute the running QCD coupling on the lattice by evaluating two-point and three-point off-shell gluon Green's functions in a fixed gauge and imposing non-perturbative renormalisation conditions on them. Our exploratory study is performed in the quenched approximation at beta=6.0 on 16^4 and 24^4 lattices. We show that, for momenta in the range 1.8-2.3 Gev, our coupling runs according to the two-loop asymptotic formula, allowing a precise determination of the corresponding Lambda parameter. The role of lattice artifacts and finite-volume effects is carefully analysed and these appear to be under control in the momentum range of interest. Our renormalisation procedure corresponds to a momentum subtraction scheme in continuum field theory, and therefore lattice perturbation theory is not needed in order to match our results to the MSbar scheme, thus eliminating a major source of uncertainty in the determination of alpha_MSbar. Our method can be applied directly to the unquenched case.