The two-nucleon system at next-to-next-to-next-to-leading order Original Research Article

We consider the two-nucleon system at next-to-next-to-next-to-leading order (N3LO) in chiral effective field theory. The two-nucleon potential at N3LO consists of one-, two- and three-pion exchanges and a set of contact interactions with zero, two and four derivatives. In addition, one has to take into account various isospin-breaking and relativistic corrections. We employ spectral function regularization for the multi-pion exchanges. Within this framework, it is shown that the three-pion exchange contribution is negligibly small. The low-energy constants (LECs) related to pion–nucleon vertices are taken consistently from studies of pion–nucleon scattering in chiral perturbation theory. The total of 26 four-nucleon LECs has been determined by a combined fit to some np and pp phase shifts from the Nijmegen analysis together with the nn scattering length. The description of nucleon–nucleon scattering and the deuteron observables at N3LO is improved compared to the one at NLO and NNLO. The theoretical uncertainties in observables are estimated based on the variation of the cut-offs in the spectral function representation of the potential and in the regulator utilized in the Lippmann–Schwinger equation.