Lattice evidence for the family of decoupling solutions of Landau gauge Yang–Mills theory

Abstract

We show that the low-momentum behavior of the lattice Landau-gauge gluon and ghost propagators is sensitive to the lowest non-trivial eigenvalue (λ1) of the Faddeev–Popov operator. If the gauge fixing favors Gribov copies with small λ1 the ghost dressing function rises more rapidly towards zero momentum than on copies with large λ1. This effect is seen for momenta below 1 GeV, and interestingly also for the gluon propagator at momenta below 0.2 GeV: For large λ1 the gluon propagator levels out to a lower value at zero momentum than for small λ1. For momenta above 1 GeV no dependence on Gribov copies is seen. Although our data is only for a single lattice size and spacing, a comparison to the corresponding (decoupling) solutions from the DSE/FRGE study of Fischer, Maas and Pawlowski (2009) [22] yields already a good qualitative agreement.