Nuclear and neutron matter in the relativistic Brueckner-Hartree-Fock theory with a next-to-leading-order covariant chiral nuclear force

The symmetric nuclear matter and pure neutron matter are investigated by the relativistic Brueckner-Hartree-Fock (RBHF) theory with the covariant chiral nuclear forces up to the next-to-leading order (NLO). A fitting scheme to ensure the naturalness of the low-energy constants is proposed, which plays a crucial role in the proper description of nuclear matter. With a momentum cutoff of Λ = 590 MeV, the empirical saturation energy and density, as well as the incompressibility coefficient at the saturation density, are reproduced well. The equations of state show less dependence on the momentum cutoff and become softer at densities above the saturation density, in comparison with the previous leading-order results. Given the good description of the saturation properties of nuclear matter, the present work encourages future studies of finite nuclei in the framework of the RBHF theory with the NLO covariant chiral nuclear forces.