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We have shown, that the possibility of the existence of the mixed phase ofthe non-uniform chiral (NCh) and the color superconducting (2SC) ground statedepends significantly on the choice of the parameters and type of theregularization scheme. Our calculations indicates, that in the 3d cut-offregularization scheme, the mixed region of the NCh and the 2SC phases existsfor a broad set of NJL model parameters. However, in the Schwingerregularization scheme, if parameters are fitted to the physical quantities inthe vacuum, then, the mixed region of the NCh and the 2SC phases does notexists.

Non-uniform chiral and 2SC color superconducting phases, taking into account the non-zero current quark mass