Multibaryon states in the framework of an equivparticle model

TL;DR

This paper develops a unified SU(6) multiplet mass formula for multibaryon states using an equivparticle model, Bayesian inference, and predicts the stability of various multibaryons including the H-dibaryon.

Contribution

It introduces a comprehensive mass formula for multibaryons within an equivparticle framework and applies Bayesian methods to predict their stability, including potential bound states.

Findings

H-dibaryon and certain dibaryons are predicted to be bound states.

Bayesian inference constrains model parameters with experimental baryon masses.

Heavier multibaryons are unlikely to be stable.

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.