Strangeness $S = -3$ and $-4$ baryon-baryon interactions in relativistic chiral effective field theory

The strangeness $S=-3$ and $-4$ baryon-baryon interactions are investigated in the relativistic chiral effective field theory at leading order. First, the potentials are derived from the $S=-1$ sector assuming that the corresponding low-energy constants are related to each other via SU(3) flavor symmetry. The comparison with the state-of-the-art lattice QCD simulations, show, however, that SU(3) flavor symmetry breaking effects can not be neglected. In order to take into account these effects, we redetermine two sets of low-energy constants by fitting to the lattice QCD data in the $\Xi\Sigma$ and $\Xi\Xi$ channels respectively. The fitting results demonstrate that the lattice QCD $S$-waves phase shifts for both channels can be described rather well. Without any additional free low-energy constants, the predicted phase shifts for the ${}^3D_1$ channel and the mixing angle $\varepsilon_1$ are also in qualitative agreement with the lattice QCD data for the $S=-3$ channel, while the results for the $S=-4$ channel remain to be checked by future lattice QCD simulations. With the so-obtained low-energy constants, the $S$-wave scattering lengths and effective ranges are calculated for these two channels at the physical point. Finally, in combination with the $S=0$ and $-2$ results obtained in our previous works, we study the evolution of the irreducible representation $27$ in the baryon-baryon interactions as a function of increasing strangeness. It is shown that the attraction decreases dramatically as strangeness increases from $S=0$ to $S=-2$, but then remains relatively stable until $S=-4$. The results indicate that the existence of bound states in the $\Xi\Sigma$ and $\Xi\Xi$ channels is rather unlikely.