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

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.