Strangeness S=-2 baryon-baryon interaction at next-to-leading order in chiral effective field theory

Abstract

The strangeness $S=-2$ baryon-baryon interaction is studied in chiral effective field theory up to next-to-leading order. The potential at this order consists of contributions from one- and two-pseudoscalar-meson exchange diagrams and from four-baryon contact terms without and with two derivatives. SU(3) flavor symmetry is imposed for constructing the interaction in the $S=-2$ sector. Specifically, the couplings of the pseudoscalar mesons to the baryons are fixed by SU(3) symmetry and, in general, also the contact terms are related via SU(3) symmetry to those determined in a previous study of the $S=-1$ hyperon-nucleon interaction. The explicit SU(3) symmetry breaking due to the physical masses of the pseudoscalar mesons ($\pi$, $K$, $\eta$) is taken into account. It is argued that the $\Xi N$ interaction has to be relatively weak to be in accordance with available experimental constraints. In particular, the published values and upper bounds for the $\Xi^- p$ elastic and inelastic cross sections apparently rule out a somewhat stronger attractive $\Xi N$ force and, specifically, disfavor any near-threshold deuteron-like bound states in that system.