Propagators and running coupling from SU(2) lattice gauge theory

TL;DR

This study investigates the behavior of the running coupling and propagators in SU(2) lattice gauge theory, confirming a finite ghost-ghost-gluon vertex and an IR fixed point for the coupling.

Contribution

It provides numerical evidence for the finiteness of the ghost-ghost-gluon vertex and characterizes the infrared behavior of propagators and the running coupling in SU(2) lattice gauge theory.

Findings

Ghost propagator diverges faster than 1/p^2 at low momentum.

Gluon propagator appears finite in the infrared.

IR fixed point of the running coupling is approximately 5.

Abstract

We perform numerical studies of the running coupling constant alpha_R(p^2) and of the gluon and ghost propagators for pure SU(2) lattice gauge theory in the minimal Landau gauge. Different definitions of the gauge fields and different gauge-fixing procedures are used respectively for gaining better control over the approach to the continuum limit and for a better understanding of Gribov-copy effects. We find that the ghost-ghost-gluon-vertex renormalization constant is finite in the continuum limit, confirming earlier results by all-order perturbation theory. In the low momentum regime, the gluon form factor is suppressed while the ghost form factor is divergent. Correspondingly, the ghost propagator diverges faster than 1/p^2 and the gluon propagator appears to be finite. Precision data for the running coupling alpha_R(p^2) are obtained. These data are consistent with an IR fixed point given by lim_{p \to 0} alpha_R(p^2) = 5(1).