Relativistic chiral description of the $^1S_0$ nucleon-nucleon scattering

TL;DR

This paper develops a covariant relativistic chiral interaction for nucleon-nucleon scattering, successfully describing the challenging $^1S_0$ channel's features at leading order, including the virtual bound state pole and zero amplitude.

Contribution

It introduces a covariant, separable form factor for the scattering kernel, improving the description of the $^1S_0$ channel within relativistic chiral effective field theory.

Findings

Accurately describes the pole position of the virtual bound state.

Represents the zero amplitude at scattering momentum ~340 MeV.

Demonstrates the naturalness of the relativistic formulation.

Abstract

Recently, a relativistic chiral nucleon-nucleon interaction is formulated up to leading order which provides a good description of the phase shifts of $J\leq1$ partial waves [Chin. Phys. C 42 (2018) 014103]. Nevertheless, a separable regulator function that is not manifestily covariant was used in solving the relativistic scattering equation. In the present work, we first propose a covariant and separable form factor to regularize the kernel potential and then apply it to study the simplest but most challenging $^1S_0$ channel which features several low-energy scales. In addition to being self-consistent, we show that the resulting relativistic potential can describe quite well the unique features of the $^1S_0$ channel at leading order, in particular the pole position of the virtual bound state and the zero amplitude at the scattering momentum $\sim 340$ MeV, indicating that the relativistic formulation might be more natural from the point of view of effective field theories.