Numerical Study of the Ghost-Gluon Vertex in Landau gauge

TL;DR

This paper numerically investigates the ghost-gluon vertex in Landau gauge for SU(2) lattice gauge theory, confirming its nonrenormalization and analyzing effects like Gribov copies across different lattice setups.

Contribution

It provides the first nonperturbative verification that the ghost-gluon vertex remains approximately constant and equal to one for momenta above 1 GeV in SU(2) Landau gauge lattice simulations.

Findings

pproximately constant nd equal to 1 for ll studied momenta above 1 GeV.

onfirmed nonrenormalization of the ghost-gluon vertex in Landau gauge.

valuated the running coupling constant rom lattice data.

Abstract

We present a numerical study of the ghost-gluon vertex and of the corresponding renormalization function \widetilde{Z}_1(p^2) in minimal Landau gauge for SU(2) lattice gauge theory. Data were obtained for three different lattice volumes (V = 4^4, 8^4, 16^4) and for three lattice couplings \beta = 2.2, 2.3, 2.4. Gribov-copy effects have been analyzed using the so-called smeared gauge fixing. We also consider two different sets of momenta (orbits) in order to check for possible effects due to the breaking of rotational symmetry. The vertex has been evaluated at the asymmetric point (0;p,-p) in momentum-subtraction scheme. We find that \widetilde{Z}_1(p^2) is approximately constant and equal to 1, at least for momenta p > ~ 1 GeV. This constitutes a nonperturbative verification of the so-called nonrenormalization of the Landau ghost-gluon vertex. Finally, we use our data to evaluate the running coupling constant \alpha_s(p^2).