Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects

TL;DR

This study investigates how lattice spacing and volume affect gluon and ghost propagators, as well as the strong coupling constant, in pure SU(3) Yang-Mills theory, revealing mild volume dependence but significant lattice spacing effects in the infrared.

Contribution

It provides detailed lattice simulation data on propagators and coupling in SU(3) Yang-Mills theory, highlighting the impact of lattice spacing and volume on these quantities.

Findings

Propagators show mild dependence on volume for large lattices.

Gluon and ghost propagators are sensitive to lattice spacing in the infrared.

Strong coupling constant depends significantly on lattice spacing up to 1 GeV.

Abstract

The dependence of the Landau gauge two point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to $128^4$ and for two lattice spacings $0.10$ fm and $0.06$ fm corresponding to volumes of $\sim$ (13 fm)$^4$ and $\sim$ (8 fm)$^4$, respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing $a$ in the infrared region, with the gluon propagator having a stronger dependence on $a$ compared to the ghost propagator. In what concerns the strong coupling constant $\alpha_s (p^2)$, as defined from gluon and ghost two point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to $\sim 1$ GeV.