Accurate Relativistic Chiral Nucleon-Nucleon Interaction up to Next-to-Next-to-Leading Order.

We construct a relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory. We show that a good description of the np phase shifts up to T_{lab}=200  MeV and even higher can be achieved with a χ[over ˜]^{2}/d.o.f. less than 1. Both the next-to-leading-order results and the next-to-next-to-leading-order results describe the phase shifts equally well up to T_{lab}=200  MeV, but for higher energies, the latter behaves better, showing satisfactory convergence. The relativistic chiral potential provides the most essential inputs for relativistic ab initio studies of nuclear structure and reactions, which has been in need for almost two decades.