Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: Peripheral phases

Abstract

We study the nucleon-nucleon interaction up to next-to-next-to-leading order using time-ordered perturbation theory in the framework of manifestly Lorentz-invariant chiral effective field theory. We present the two-pion exchange contribution at one-loop level, which is consistent with the corresponding nonrelativistic expressions in the large-nucleon-mass limit. Using the Born series truncated at one-loop order, we calculate the phase shifts and mixing angles of the partial waves with the angular momentum l≥2. Comparing with the results of the nonrelativistic formulation, we find an improved description of the phase shifts for some D waves such as the D33 one. For the other partial waves, both approaches show globally similar results.