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

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 $\left(NN\right)$ data below $290\text{−}\text{MeV}$ 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 $290\text{MeV}$. 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).

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Figure 1

$np$ phase parameters below $300\text{−}\text{MeV}$ lab energy for partial waves with $J⩽2$. The solid line is the result at ${\mathrm{N}}^3\text{LO}$. The dotted and dashed lines are the phase shifts at NLO and NNLO, respectively, as obtained by Epelbaum et al. [37]. The solid dots show the Nijmegen multienergy $np$ phase shift analysis [38], and the open circles are the VPI single-energy $np$ analysis SM99 [39].