Leading order relativistic hyperon-nucleon interactions in chiral effective field theory

TL;DR

This paper develops a covariant chiral effective field theory for hyperon-nucleon interactions, introducing more low energy constants due to Lorentz invariance and fitting hyperon-nucleon scattering data with comparable accuracy to existing models.

Contribution

It applies a covariant power counting scheme to hyperon-nucleon interactions, expanding the number of low energy constants and using the Kadyshevsky equation for non-perturbative resummation.

Findings

Achieves a fit with chi-squared around 16 for hyperon-nucleon data.

Lorentz invariance increases the number of low energy constants at leading order.

Cannot simultaneously describe nucleon-nucleon and hyperon-nucleon data at leading order.

Abstract

We apply a recently proposed covariant power counting in nucleon-nucleon interactions to study strangeness $S=-1$ $\Lambda N-\Sigma N$ interactions in chiral effective field theory. At leading order, Lorentz invariance introduces 12 low energy constants, in contrast to the heavy baryon approach, where only five appear. The Kadyshevsky equation is adopted to resum the potential in order to account for the non-perturbative nature of hyperon-nucleon interactions. A fit to the $36$ hyperon-nucleon scattering data points yields $\chi^2\simeq 16$, which is comparable with the sophisticated phenomenological models and the next-to-leading order heavy baryon approach. However, one cannot achieve a simultaneous description of the nucleon-nucleon phase shifts and strangeness $S=-1$ hyperon-nucleon scattering data at leading order.