Prospects for compact hexaquarks under the limitation imposed by quark confinement

The limitation of flavor constituents for compact multiquarks is crucial for understanding the strong interaction at the low energy scale. Utilizing the MIT bag model that incorporates perturbative interactions and confinement energy $E_{\rm CON}$, we derive a critical bag radius $R_c=5.61\,$GeV$^{-1}$ from the condition $E_{\rm CON} < 0$ at zero temperature and zero baryon density, which aligns with the string-breaking distance of 1.2--1.4$\,$fm. Applying this framework to 6-, 7-, and 8-quark systems, we find the bag radii $R_0$ to be highly sensitive to relativistic effects from light quarks, leading to the exclusion of most heavy-light flavor configurations (e.g., $n^3\bar{c}^3$, $n^3\bar{n}\bar{c}^2$) due to positive $E_{\rm CON}$ and radii exceeding the critical radius. Color-spin wavefunctions are constructed using Young tableaux to evaluate interaction matrices and OZI-superallowed decays. Broad decay widths in fully heavy systems for OZI-superallowed modes could arise from wavefunction overlaps due to heavy flavor symmetry, suggesting possible narrow widths for $nnb\bar{b}\bar{b}\bar{b}$ and $nnn\bar{b}\bar{b}\bar{b}$ hexaquarks. This phenomenological approach provides insights into the limitations on multiquarks imposed by confinement. It recommends experimental searches at LHCb for these states.