Weinberg's approach to nucleon-nucleon scattering revisited

TL;DR

This paper introduces a new renormalizable approach to nucleon-nucleon scattering in chiral effective field theory that avoids heavy-baryon expansion, enabling consistent renormalization of the one-pion exchange potential.

Contribution

It presents a Lorentz-invariant formulation of chiral EFT for nucleon-nucleon scattering that reproduces known results and improves renormalization procedures.

Findings

Reproduces known results for pion-less and perturbative pions cases.

Allows renormalization of nonperturbative one-pion exchange by absorbing divergences into contact interactions.

Provides numerical phase shift results at leading order.

Abstract

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.