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 ((NLO)-L-4, 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 pi N 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 (NLO)-L-3. As a result, the (NLO)-L-4 predictions for the phase shifts of peripheral partial waves are in very good agreement with the data (with the only exception being the F-1(3) wave). We also discuss the issue of the order-by-order convergence of the chiral expansion for the NN interaction.