  We consider the NN interaction in pionless effective field theory (EFT) up to
next-to-next-to-leading order (NNLO) and use a recursive subtractive
renormalization scheme to describe NN scattering in the 1S0 channel. We fix the
strengths of the contact interactions at a reference scale, chosen to be the
one that provides the best fit for the phase-shifts, and then slide the
renormalization scale by evolving the driving terms of the subtracted
Lippmann-Schwinger equation through a non-relativistic Callan-Symanzik
equation. The results show that such a systematic renormalization scheme with
multiple subtractions is fully renormalization group invariant.
