Aspects of the refined Gribov-Zwanziger action in linear covariant   gauges
  We prove the renormalizability to all orders of a refined Gribov-Zwanziger type action in linear covariant gauges in four-dimensional Euclidean space. In this model, the Gribov copies are taken into account by requiring that the Faddeev-Popov operator is positive definite with respect to the transverse component of the gauge field, a procedure which turns out to be analogous to the restriction to the Gribov region in the Landau gauge. The model studied here can be regarded as the first approximation of a more general nonperturbative BRST invariant formulation of the refined Gribov-Zwanziger action in linear covariant gauges obtained recently in [Phys. Rev. D 92, no. 4, 045039 (2015) and arXiv:1605.02610 [hep-th]]. A key ingredient of the set up worked out in [Phys. Rev. D 92, no. 4, 045039 (2015) and arXiv:1605.02610 [hep-th]] is the introduction of a gauge invariant field configuration $\mathbf{A}_{\mu}$ which can be expressed as an infinite non-local series in the starting gauge field $A_\mu$. In the present case, we consider the approximation in which only the first term of the series representing $\mathbf{A}_{\mu}$ is considered, corresponding to a pure transverse gauge field. The all order renormalizability of the resulting action gives thus a strong evidence of the renormalizability of the aforementioned more general nonperturbative BRST invariant formulation of the Gribov horizon in linear covariant gauges. 
M. A. L. Capri, D. Fiorentini, A. D. Pereira, R. F. Sobreiro, S. P.   Sorella, R. C. Terin
hep-th