Renormalization Group Invariance in Pionless Effective Field Theory for the NN System

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 ¹ S ₀ 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?CSchwinger equation through a non-relativistic Callan?CSymanzik equation. The results show that such a systematic renormalization scheme with multiple subtractions is fully renormalization group invariant.