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 (NN) data below 290-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 2900. 3em{0ex}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).