Asymptotic scaling of the gluon propagtor on the lattice

TL;DR

This study investigates the high-energy behavior of the gluon propagator on the lattice, providing evidence that it reaches three-loop asymptotic scaling between 5.6 and 9.5 GeV, and estimates the QCD scale parameter 1MS.

Contribution

The paper presents high-statistics lattice simulations at high energies, demonstrating the gluon propagator's asymptotic scaling and refining the 1MS parameter estimate.

Findings

Gluon propagator reaches three-loop asymptotic scaling between 5.6 and 9.5 GeV.

Estimated 1MS value is 319 b1 14 MeV, consistent with previous results.

A four-loop correction is necessary for a full fit across 2.8 to 9.5 GeV energy range.

Abstract

We pursue the study of the high energy behaviour of the gluon propagator on the lattice in the Landau gauge in the flavorless case (n_f=0). It was shown in a precedin g paper that the gluon propagator did not reach three-loop asymptotic scaling at an energy scale as high as 5 GeV. Our present high statistics analysis includes also a simulation at $\beta=6.8$ ($a\simeq 0.03$ fm), which allows to reach $\mu \simeq 10$ GeV. Special care has been devoted to the finite lattice-spacing artifacts as well as to the finite volume effects, the latter being acute at $\beta=6.8$ where the volume is bounded by technical limits. Our main conclusion is a strong evidence that the gluon propagator has reached three-loop asymptotic scaling, at $\mu$ ranging from 5.6 GeV to 9.5 GeV. We buttress up this conclusion on several demanding criteria of asymptoticity, including scheme independence. Our fit in the 5.6 GeV to 9.5 GeV window yields $\Lambda^{\bar{{\rm MS}}} = 319 \pm 14 ^{+10}_{-20}$ MeV, in good agreement with our previous result, $\Lambda^{\bar{{\rm MS}}} = 295 \pm 20 $ MeV, obtained from the three gluon vertex, but it is significantly above the Schr\"odinger functional method estimate : $238 \pm 19$ MeV. The latter difference is not understood. Confirming our previous paper, we show that a fourth loop is necessary to fit the whole ($2.8 \div 9.5$) GeV energy window.