$\Lambda \Lambda N$-$\Xi NN$ $S$ wave resonance

Abstract

We use an existing model of the $\Lambda \Lambda N-\Xi NN$ three-body system based in two-body separable interactions to study the $(I,J^P)=(1/2,1/2^{+})$ three-body channel. For the $\Lambda \Lambda$, $\Xi N$, and $\Lambda \Lambda -\Xi N$ amplitudes we have constructed separable potentials based on the most recent results of the HAL QCD Collaboration. They are characterized by the existence of a resonance just below or above the $\Xi N$ threshold in the so-called $H$-dibaryon channel, $(i,j^p)=(0,0^{+})$. A three-body resonance appears {2.3} MeV above the $\Xi d$ threshold. We show that if the $\Lambda \Lambda -\Xi N$ $H$-dibaryon channel is not considered, the $\Lambda \Lambda N-\Xi NN$ $S$ wave resonance disappears. Thus, the possible existence of a $\Lambda \Lambda N-\Xi NN$ resonance would be sensitive to the $\Lambda \Lambda -\Xi N$ interaction. The existence or nonexistence of this resonance could be evidenced by measuring, for example, the $\Xi d$ cross section.

Comments: 11 pages, 5 figures. To be published in Chinese Physics C