Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory

TLDR

The study introduces the first fourth‑order chiral perturbation theory nucleon‑nucleon potential. The potential incorporates charge dependence up to next‑to‑leading order in the isospin‑violation scheme. The fourth‑order potential reproduces NN data below 290 MeV with accuracy comparable to high‑precision phenomenological models, demonstrating that fourth order is both necessary and sufficient, and offers a solid basis for exact few‑body calculations and microscopic nuclear structure studies.

Abstract

We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge dependence is included up to next-to-leading order of the isospin-violation scheme. The accuracy for the reproduction of the nucleon-nucleon $(NN)$ data below $290\text{\ensuremath{-}}\text{MeV}$ lab energy is comparable to the one of phenomenological high-precision potentials. Since $NN$ potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a $NN$ potential reliable up to $290\phantom{\rule{0.3em}{0ex}}\text{MeV}$. The new potential provides a promising starting point for exact few-body calculations and microscopic nuclear structure theory (including chiral many-body forces derived on the same footing).