Local position-space two-nucleon potentials from leading to fourth order of chiral effective field theory

Abstract

We present local, position-space chiral $NN$ potentials through four orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-leading order (${\mathrm{N}}^{3}\mathrm{LO}$, fourth order) of the $\mathrm{\ensuremath{\Delta}}$-less version of the theory. The long-range parts of these potentials are fixed by the very accurate $\ensuremath{\pi}N$ low-energy constants (LECs) as determined in the Roy-Steiner equations analysis. At the highest order (${\mathrm{N}}^{3}\mathrm{LO}$), the $NN$ data below 190 MeV laboratory energy are reproduced with the respectable ${\ensuremath{\chi}}^{2}/\mathrm{datum}$ of 1.45. A comparison of the ${\mathrm{N}}^{3}\mathrm{LO}$ potential with the phenomenological Argonne ${v}_{18}$ (AV18) potential reveals substantial agreement between the two potentials in the intermediate range ruled by chiral symmetry, thus providing a chiral underpinning for the phenomenological AV18 potential. Our chiral $NN$ potentials may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the order-by-order development of the potentials will make possible a reliable determination of the truncation error at each order. Our new family of local position-space potentials differs from existing potentials of this kind by a weaker tensor force as reflected in relatively low $D$-state probabilities of the deuteron (${P}_{D}\ensuremath{\lesssim}4.0$% for our ${\mathrm{N}}^{3}\mathrm{LO}$ potentials) and predictions for the triton binding energy above 8.00 MeV (from two-body forces alone). As a consequence, our potentials may lead to different predictions when applied to light and intermediate-mass nuclei in ab initio calculations and, potentially, help solve some of the outstanding problems in microscopic nuclear structure.

Topics & Concepts