Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory

We present the two- and three-pion-exchange contributions to the nucleon-nucleon interaction which occur at next-to-next-to-next-to-next-to-leading order (N4LO, fifth order) of chiral effective field theory and calculate nucleon-nucleon scattering in peripheral partial waves with L≥3 by using low-energy constants that were extracted from πN analysis at fourth order. While the net three-pion-exchange contribution is moderate, the two-pion exchanges turn out to be sizable and prevailingly repulsive, thus compensating the excessive attraction characteristic for next-to-next-to-leading order and N3LO. As a result, the N4LO predictions for the phase shifts of peripheral partial waves are in very good agreement with the data (with the only exception being the 1F3 wave). We also discuss the issue of the order-by-order convergence of the chiral expansion for the NN interaction.