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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, establishing the desired trend towards convergence. Using low-energy constants that were extracted from an analysis of pi-N scattering at fourth order, the predictions at N5LO are in excellent agreement with the empirical phase shifts of peripheral partial waves.