  We propose a Gribov-Zwanziger type action for the Landau-DeWitt gauge that
preserves, for any gauge group, the invariance under background gauge
transformations. At zero temperature, and to one-loop accuracy, the model can
be related to the Gribov no-pole condition. We apply the model to the
deconfinement transition in SU(2) and SU(3) Yang-Mills theories and compare the
predictions obtained with a single or with various (color dependent) Gribov
parameters that can be introduced in the action without jeopardizing its
background gauge invariance. The Gribov parameters associated to color
directions orthogonal to the background can become negative, while keeping the
background effective potential real. In some cases, the proper analysis of the
transition requires the potential to be resolved in those regions.
