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A regularization scheme that explicitly separates vacuum contributions frommedium effects is applied to a Nambu--Jona-Lasinio model with diquarkinteractions and in $\beta-$equilibrium. We perform a comparison of thisproposed scheme with the more traditional one, where no separation of vacuumand medium effects is done. Our results point to both qualitative andquantitative important differences between these two methods, in specialregarding the phase structure of the model in the cold and dense nuclear mattercase.

Regularization issues for a cold and dense quark matter model in $\beta-$equilibrium