Multibaryon states in the framework of an equivparticle model

Abstract

Within the framework of an equivparticle model employing mean-field approximation, we investigate systematically the mass spectra of color-singlet $N$-quark configurations with $N = 3, 6, 9, 12, 15$, and 18, which are assumed to be spherically symmetric with quarks occupying the 1s$_{1/2}$ state, i.e., compact multibaryon states. At a given quark number $N$, these states collectively form a single irreducible representation under SU(6) symmetry. Our analysis yields comprehensive mass formulae that characterize these SU(6) multiplets, providing a unified description of their mass spectra. In order to effectively constrain the parameter space of the model and improve the prediction accuracy, we carry out a Bayesian parameter inference based on the experimental masses of eight baryons and $D_{03}$. The posterior probability density functions and their correlations of the model parameters are examined, based on which we further predict the masses of various multibaryon states and provide their 68$\%$ and 90$\%$ credible intervals. In our prediction, H-dibaryon, $D_{03}$, and the dibaryon with $S = -6$ are all bound states relative to $\Lambda\Lambda$, $\Delta\Delta$ and $\Omega\Omega$ thresholds, while slight probabilities of other stable dibaryons (23.64$\%$ more stable than $\Omega^- \Xi^0$ for the state wtih $I = \frac{1}{2}$, $S = -5$ and 92.49$\%$ more stable than $\Xi^0\Xi^-$ for the state wtih $I = 0$, $S = -4$) and tribaryons (0.25$\%$ more stable than $\Xi^-\Xi^0\Xi^0$ for the state wtih $S = -6$, $I = 1/2$; 2.19$\%$ more stable than $\Lambda\Xi^0\Xi^-$ for the state wtih $S = -5$, $I = 0$; and 2.21$\%$ more stable than $\Lambda\Lambda\Xi^0$ for the state wtih $S = -4$, $I = 1/2$) are observed as well. For heavier compact multibaryon states, it is unlikely for them to be stable.