High-quality two-nucleon potentials up to fifth order of the chiral expansion

Abstract

We present $\mathit{NN}$ potentials through five orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-next-to-leading order (${\mathrm{N}}^{4}\mathrm{LO}$). The construction may be perceived as consistent in the sense that the same power counting scheme as well as the same cutoff procedures are applied in all orders. Moreover, 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 by Hoferichter, Ruiz de Elvira, and coworkers. In fact, the uncertainties of these LECs are so small that a variation within the errors leads to effects that are essentially negligible, reducing the error budget of predictions considerably. The $\mathit{NN}$ potentials are fit to the world $\mathit{NN}$ data below the pion-production threshold of the year 2016. The potential of the highest order (${\mathrm{N}}^{4}\mathrm{LO}$) reproduces the world $\mathit{NN}$ data with the outstanding ${\ensuremath{\chi}}^{2}$/datum of 1.15, which is the highest precision ever accomplished for any chiral $\mathit{NN}$ potential to date. The $\mathit{NN}$ potentials presented 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 consistent order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our family of potentials is nonlocal and, generally, of soft character. This feature is reflected in the fact that the predictions for the triton binding energy (from two-body forces only) converges to about 8.1 MeV at the highest orders. This leaves room for three-nucleon-force contributions of moderate size.