Renormalization group invariance in pionless effective field theory for the NN system

TL;DR

This paper demonstrates that a recursive subtractive renormalization scheme applied to pionless EFT for NN interactions achieves full renormalization group invariance, ensuring consistent phase-shift predictions across scales.

Contribution

It introduces a systematic multi-subtraction renormalization method for pionless EFT that maintains RG invariance in NN scattering calculations.

Findings

The renormalization scheme is fully RG invariant.

Phase-shift fits are stable under scale evolution.

The method improves consistency in EFT calculations.

Abstract

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.