Weinbergʼs approach to nucleon-nucleon scattering revisited

We propose a new, renormalizable approach to nucleon-nucleon scattering in chiral effective field theory based on the manifestly Lorentz invariant form of the effective Lagrangian without employing the non-relativistic expansion. For the pion-less case and for the formulation based on perturbative pions, the new approach reproduces the known results obtained by Kaplan, Savage and Wise. Contrary to the standard formulation utilizing the non-relativistic expansion, the non-perturbatively resummed one-pion exchange potential can be renormalized by absorbing all ultraviolet divergences into the leading S-wave contact interactions. We explain in detail the differences to the non-relativistic formulation and present numerical results for two-nucleon phase shifts at leading order in the low-momentum expansion.