The Strong Coupling Constant from the Lattice 3-Gluon Vertex

TL;DR

This paper calculates the QCD strong coupling constant from the lattice 3-gluon vertex, demonstrating a method that aligns with continuum schemes without requiring lattice perturbation theory, and provides a precise value for the coupling at the Z boson mass.

Contribution

It introduces a novel lattice computation of the QCD coupling from the 3-gluon vertex that avoids lattice perturbation theory for scheme matching.

Findings

Coupling runs according to 2-loop asymptotic formula for momenta > 2 GeV

Precise determination of the Lambda parameter in QCD

Estimated lpha^{MSbar}(M_Z) = 0.115  0.003  0.008

Abstract

We compute the QCD running coupling on the lattice as defined from the 3-gluon vertex. We present the results of an exploratory study at $\beta=6.0$ on a $16^4$ lattice, which show that for momenta larger than 2 \Gev, the coupling runs according to the 2-loop asymptotic formula, allowing a precise determination of the $\Lambda$ parameter. Our renormalization procedure corresponds to a momentum subtraction scheme in the continuum and, most remarkably, one does not need lattice perturbation theory to match the results to MSbar scheme. We obtain $\alpha^{\MSB}(M_Z) = 0.115 \pm 0.003 \pm 0.008$.