Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization

TL;DR

This paper develops a modified Weinberg approach using a symmetry-preserving regularization to improve the analysis of two-nucleon scattering, reducing regulator artifacts and enhancing the understanding of nucleon interactions.

Contribution

It introduces a Lorentz invariant, symmetry-preserving regularization method within baryon chiral perturbation theory for two-nucleon scattering, enabling better control of ultraviolet behavior and regulator artifacts.

Findings

Reduced regulator artifacts in phase shifts

Improved chiral extrapolations of scattering lengths

Enhanced analysis of deuteron binding energy

Abstract

We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz invariant formulation of baryon chiral perturbation theory. Using a symmetry preserving higher derivative form of the effective Lagrangian, we exploit the freedom of the choice of the renormalization condition and obtain an integral equation for the scattering amplitude with an improved ultraviolet behavior. The resulting formulation is used to quantify finite regulator artifacts in two-nucleon phase shifts as well as in the chiral extrapolations of the S-wave scattering lengths and the deuteron binding energy. This approach can be straightforwardly extended to analyze few-nucleon systems and processes involving external electroweak sources.