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).