Extended-soft-core baryon-baryon model ESC16. IV. $S=-3$ and $S=-4$ hyperon-hyperon interactions

Background: This paper presents the extended-soft-core (ESC) potentials ESC16 for baryon-baryon ($BB$) channels with total strangeness $S=-3$ and $-4$. For these channels no experimental scattering data exist, apart from very recently measured preliminary correlations. Also, there is no information from hypernuclei or hyperonic matter.

Purpose: The aim is to calculate the predictions of the ESC16 model for the $S=-3$ and $S=-4 BB$ channels.

Methods: The potential models for $S=-3$ and $-4$ are based on SU(3) extensions of potential models for the $S=0$ and $-1$ and $S=-2$ sectors, which are fitted to experimental data. Flavor SU(3) symmetry is broken “kinematically” by the masses of the baryons and the mesons. The fit to the $S=0$ and $-1$ sectors provides the necessary constraints to fix all free parameters, i.e., baryon-baryon-meson couplings and cutoff masses. The $S=-2$ systems are constrained by the $\mathrm{\Delta }{B}_{\mathrm{\Lambda }\mathrm{\Lambda }}$ value from the Nagara event and the requirement of $U_{\mathrm{\Xi }}\approx -10$ MeV.

Results: Various properties of the potentials are illustrated by giving results for scattering lengths, bound states, and phase parameters.

Conclusions: No $\mathrm{\Xi }\mathrm{\Xi }, \mathrm{\Xi }\mathrm{\Lambda }$, and $\mathrm{\Xi }\mathrm{\Sigma }$ bound states are predicted by the ESC16 model.

Figure 1

Thresholds in $\mathit{YY}$ channels for $S=-3$ and $-4$. The laboratory momenta $p_{\mathrm{\Lambda }}, p_{\mathrm{\Sigma }}$, and $p_{\mathrm{\Xi }}$ are given in $\mathrm{MeV}/c^2$.

Figure 2

ESC16 ${\mathrm{\Xi }}^0{\mathrm{\Xi }}^0({}^1{S}_0,I=1)$ and ${\mathrm{\Xi }}^0{\mathrm{\Xi }}^{-}({}^3{S}_1,I=0)$ phases.

Figure 3

ESC16 $\mathrm{\Lambda }\mathrm{\Xi }I=1/2$ phases.

Figure 4

ESC16 $I=1/2{}^1{S}_0\left({\mathrm{\Sigma }}^0{\mathrm{\Xi }}^0\right)$ phases and $\eta$ inelasticities.

Figure 5

ESC16 $I=1/2{}^3{C}_1\left({\mathrm{\Sigma }}^0{\mathrm{\Xi }}^0\right)$ phases and $\eta$ inelasticities.

Figure 6

ESC16 $I=3/2{\mathrm{\Sigma }}^{+}{\mathrm{\Xi }}^0$ phases.

Figure 7

Baryon-baryon $\left\{8\right\}$ and $\left\{27\right\}$ states.

Figure 8

Baryon-baryon antidecuplet $\left\{{10}^{*}\right\}$ and $\left\{10\right\}$ states.