The Gluon Propagator on a Large Volume, at $\beta=6.0$

TL;DR

This study provides a high-statistics lattice analysis of the gluon propagator at $eta=6.0$, confirming its functional form and determining the critical exponent with high precision, while discussing implications for continuum limit behavior.

Contribution

It offers a detailed lattice measurement of the gluon propagator at a large volume and fixed $eta$, accurately determining the critical exponent and volume dependence.

Findings

Exponent $oldsymbol{oxed{ ext{η} = 0.532(12)}}$ determined precisely.

Mass parameter $oldsymbol{M^2}$ remains non-zero in the infinite volume limit.

Functional form of the propagator fits well with previous models.

Abstract

We present the results of a high statistics lattice study of the gluon propagator, in the Landau gauge, at $\beta=6.0$. As suggested by previous studies, we find that, in momentum space, the propagator is well described by the expression $G(k^2)= \Big[ M^2 + Z\cdot k^2(k^2/\Lambda^2)^\eta\Big]^{-1} $. By comparing $G(k^2)$ on different volumes, we obtain a precise determination of the exponent $\eta=0.532(12)$, and verify that $M^2$ does not vanish in the infinite volume limit. The behaviour of $\eta$ and $M^2$ in the continuum limit is not known, and can only be studied by increasing the value of $\beta$.