Soft breaking of BRST invariance for introducing non-perturbative   infrared effects in a local and renormalizable way
  The possibility of introducing non-perturbative infrared effects leading to a modification of the long distance behavior of gauge theories through a soft breaking of the BRST invariance is investigated. The method reproduces the Gribov-Zwanziger action describing the restriction of the domain of integration in the Feynman path integral to the Gribov region and a model for the dynamical quark mass generation is presented. The soft symmetry breaking relies on the introduction of BRST doublets and massive physical parameters, which allow one to distinguish the infrared region from the ultraviolet one, within the same theory. 
L. Baulieu, S. P. Sorella