Asymptotic behaviour of the gluon propagator from lattice QCD

TL;DR

This study uses high-statistics lattice QCD calculations to analyze the gluon propagator in Landau gauge, revealing that asymptotic scaling at three loops is not achieved and providing an estimate for  MS .

Contribution

It introduces a scheme-independent test for asymptotic scaling and provides a refined estimate of  MS  from lattice data.

Findings

Asymptotic scaling at three loops is not observed.

An effective  MS  estimate is 353  2^{+25}_{-10} MeV.

Scheme independence test suggests the true  MS  may be smaller.

Abstract

We study the flavorless gluon propagator in the Landau gauge from high statistics lattice calculations. Hypercubic artifacts are efficiently eliminated by taking the $\sum p_\mu^4 \to 0$ limit. The propagator is fitted to the three-loops perturbative formula in an energy window ranging form $\sim$ 2.5 GeV up to $\sim$ 5.5 GeV. $\alpha_s$ is extracted from the best fit in a continuous set of renormalisation schemes. The fits are very good, with a $\chi^2$ per d.o.f smaller than 1. We propose a more stringent test of asymptotic scaling based on scheme independence of the resulting $\Lambda_{\bar MS}$. This method shows that asymptotic scaling at three loops is not reached by the gluon propagator although we use rather large energies. We are only able to obtain an effective flavorless three-loops estimate $\Lambda_{\bar MS}^{(3)}= 353 \pm 2 ^{+25}_{-10} $ MeV. We argue that the real asymptotic value for $\Lambda_{\bar MS}$ should plausibly be smaller.