Renormalization Group Invariance in the Subtractive Renormalization Approach to the NN Interactions

In this work, we apply the subtracted kernel method (SKM) to the chiral nucleon-nucleon ($NN$) interaction in the $^3P_0$ channel up to next-to-next-to-leading-order ($NNLO$). We demonstrate, by explicit numerical calculations, that the SKM procedure is renormalization group invariant under the change of the subtraction scale provided the driving-term of the subtracted scattering equation is evolved through a non-relativistic Callan-Symanzik (NRCS) flow-equation.