  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 heavy-baryon 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 heavy-baryon expansion, the
nonperturbatively 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 heavy-baryon
formulation and present numerical results for two-nucleon phase shifts at
leading order in the low-momentum expansion.
