An accurate relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading order

We report on the construction of an accurate relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading (NNLO) order. We compare the so-obtained neutron-proton phaseshifts with the next-to-next-to-next-to-leading order (N³LO) nonrelativistic ones and we show that up to T_lab. = 200 MeV, the relativistic chiral nuclear force can describe the PWA93 phaseshifts and inelasticities as well as its N³LO nonrelativistic counterparts. As a result, the relativistic chiral nuclear force can be readily used for relativistic ab initio nuclear structure, reaction, as well astrophysical studies.