Non-perturbative treatment of the linear covariant gauges by taking into account the Gribov copies.

In this paper, a proposal for the restriction of the Euclidean functional integral to a region free from infinitesimal Gribov copies in linear covariant gauges is discussed. An effective action, akin to the Gribov-Zwanziger action of the Landau gauge, is obtained which implements the aforementioned restriction. Although originally non-local, this action can be cast in local form by introducing auxiliary fields. As in the case of the Landau gauge, dimension two condensates are generated at the quantum level, giving rise to a refinement of the action which is employed to obtain the tree-level gluon propagator in linear covariant gauges. A comparison of our results with those available from numerical lattice simulations is also provided.

Glueball masses from an infrared moment problem.

We set up an infrared-based moment problem to obtain estimates of the masses of the scalar, pseudoscalar, and tensor glueballs in Euclidean Yang-Mills theories using the refined Gribov-Zwanziger (RGZ) version of the Landau gauge, which takes into account nonperturbative physics related to gauge copies. Employing lattice input for the mass scales of the RGZ gluon propagator, the lowest order moment problem approximation gives the values m(0++) ≈ 1.96 GeV, m(2++) ≈ 2.04 GeV, and m(0-+) ≈ 2.19 GeV in the SU(3) case, all within a 20% range of the corresponding lattice values. We also recover the mass hierarchy m(0++) < m(2++) < m(0-+).