Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order

TL;DR

This paper develops a finite-cutoff chiral effective field theory approach for nucleon-nucleon scattering, demonstrating explicit perturbative renormalization at next-to-leading order and confirming its numerical validity through phase shift calculations.

Contribution

It introduces a novel scheme where leading-order interactions are summed to all orders while higher-order corrections are iterated once, with a rigorous proof of renormalizability and reduced cutoff dependence.

Findings

Power-counting breaking terms are absorbed into low energy constants.

Cutoff dependence is minimized by perturbative subtraction of regulator artifacts.

Numerical phase shifts support the scheme's validity for nucleon-nucleon scattering.

Abstract

We present a study of two-nucleon scattering in chiral effective field theory with a finite cutoff to next-to-leading order in the chiral expansion. In the proposed scheme, the contributions of the lowest-order interaction to the scattering amplitude are summed up to an arbitrary order, while the corrections beyond leading order are iterated only once. We consider a general form of the regulator for the leading-order potential including local and non-local structures. The main objective of the paper is to address formal aspects of renormalizability within the considered scheme. In particular, we provide a rigorous proof, valid to all orders in the iterations of the leading-order potential, that power-counting breaking terms originating from the integration regions with momenta of the order of the cutoff can be absorbed into the renormalization of the low energy constants of the leading contact interactions. We also demonstrate that the cutoff dependence of the scattering amplitude can be reduced by perturbatively subtracting the regulator artifacts at next-to-leading order. The obtained numerical results for phase shifts in $P$- and higher partial waves confirm the applicability of our scheme for nucleon-nucleon scattering.