Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory

TL;DR

This paper calculates nucleon-nucleon interactions at fifth order in chiral effective field theory, showing improved agreement with experimental phase shifts for peripheral waves by including two- and three-pion exchange contributions.

Contribution

It provides the first detailed analysis of N4LO (fifth order) two- and three-pion exchange effects on peripheral nucleon-nucleon scattering, improving theoretical predictions.

Findings

Two-pion exchanges are sizeable and predominantly repulsive.

N4LO phase shifts agree well with experimental data.

Three-pion exchange contribution is moderate.

Abstract

We present the two- and three-pion exchange contributions to the nucleon-nucleon interaction which occur at next-to-next-to-next-to-next-to-leading order (N4LO, fifth order) of chiral effective field theory, and calculate nucleon-nucleon scattering in peripheral partial waves with L>=3 using low-energy constants that were extracted from pi-N analysis at fourth order. While the net three-pion exchange contribution is moderate, the two-pion exchanges turn out to be sizeable and prevailingly repulsive, thus, compensating the excessive attraction characteristic for NNLO and N3LO. As a result, the N4LO predictions for the phase shifts of peripheral partial waves are in very good agreement with the data (with the only exception of the 1F3 wave). We also discuss the issue of the order-by-order convergence of the chiral expansion for the NN interaction.