The soft-gluon limit of the Landau gauge ghost-gluon vertex: results for pure Yang-Mills SU(3) theory from lattice simulations

Abstract

This work reports on the computation of the ghost-gluon vertex for the pure Yang-Mills SU(3) gauge group, using lattice simulations and the Landau gauge. The simulations access only one of the form factors that describes the vertex. The form factor is estimated using large statistical ensembles of gauge configurations, with two different lattice spacings and two different volumes to check for finite size effects. Moreover, the calculation shows the importance of using lattice perturbation theory, instead of its continuum version, to correct for the breaking of rotational symmetry. The measured bare lattice form factors are compatible, within errors, for all the ensembles. The form factor has a maximum at momentum $\sim 1$ GeV, is suppressed in the infrared and is compatible with a constant behaviour at high momenta, in good agreement with the corresponding lattice estimations for the SU(2) gauge group.