Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system

TL;DR

This paper applies the subtracted kernel method to chiral NN interactions up to NNLO, demonstrating systematic improvements and renormalization group invariance in nucleon-nucleon scattering calculations.

Contribution

It introduces a recursive subtraction-based renormalization approach for chiral NN interactions and shows its invariance under scale changes, with improved power counting schemes.

Findings

Phase shifts show systematic improvement with order

SKM is renormalization group invariant

Modified power counting enhances convergence

Abstract

We apply the subtracted kernel method (SKM), a renormalization approach based on recursive multiple subtractions performed in the kernel of the scattering equation, to the chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading-order (NNLO). We evaluate the phase-shifts in the 1S0 channel at each order in Weinberg's power counting scheme and in a modified power counting scheme which yields a systematic power-law improvement. We also explicitly demonstrate that the SKM procedure is renormalization group invariant under the change of the subtraction scale through a non-relativistic Callan-Symanzik flow equation for the evolution of the renormalized NN interactions.