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In this paper we take into account the existence of Gribov copies in afour-dimensional Yang-Mills theory in the Landau gauge with an effectiveLorentz symmetry breaking, induced by the Carroll-Field-Jackiw (CFJ) term. Theself consistent gap equation of the Gribov parameter is properly derived and,provided observational bounds to the amplitude of the CFJ parameter in the$SU(2)$ gauge theory, a qualitative analysis of the Gribov parameter and of thepoles of the propagator is developed.

Lorentz symmetry breaking in a Yang-Mills theory within the Gribov restriction