Recently the nucleon-nucleon interaction derived using time-ordered perturbation theory in manifestly Lorentz-invariant chiral effective field theory was shown to yield promising results for peripheral neutron-proton scattering. In this work we study low partial waves at next-to-leading order by treating the potential nonperturbatively in the scattering equation. Reasonable description of the phase shifts in the $S$ and $P$ waves as well as the deuteron properties is observed, which can be regarded as a feasibility study for the application of our formalism to the few- and many-body calculations.

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• Chiral perturbation theory
• Nuclear forces
• Nucleon-nucleon interactions