Dominant contributions to the nucleon-nucleon interaction at sixth order of chiral perturbation theory

We present the dominant two- and three-pion-exchange contributions to the nucleon-nucleon interaction at sixth order (next-to-next-to-next-to-next-to-next-to-leading order, N⁵LO) of chiral perturbation theory. Phase shifts with orbital angular momentum L≥4 are given parameter free at this order and allow for a systematic investigation of the convergence of the chiral expansion. The N⁵LO contribution is prevailingly repulsive and considerably smaller than the N⁴LO one, thus, showing the desired trend towards convergence. Using low-energy constants that were extracted from an analysis of πN scattering at fourth order, the predictions at N⁵LO are in excellent agreement with the empirical phase shifts of peripheral partial waves.