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 $T_{\mathrm{lab}}=200\mathrm{MeV}$ and even higher can be achieved with a ${\tilde{\chi }}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ 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 $T_{\mathrm{lab}}=200\mathrm{MeV}$, 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.

• Received 21 November 2021
• Revised 25 February 2022
• Accepted 21 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.142002