Prospects for compact hexaquarks under the limitation imposed by quark confinement

TL;DR

This work probes the feasibility of compact hexaquarks under confinement by employing the MIT bag model and introducing a critical radius $R_c$ with $R_c = 5.61\ \mathrm{GeV}^{-1}$, aligning with the lattice/string-breaking scale $r_c \approx 1.2$–$1.4$ fm. The mass spectrum is built from the bag-model terms $M = \sum_i \omega_i + E_{ m CON} + E_{ m CMI} + E_{ m BD}$, with a variational $R_0$ setting the confinement and perturbative parameters, while color-spin wavefunctions derived from Young tableaux quantify OZI-superallowed decays via overlaps $|c^1|^2$. The study finds that many heavy-light 6-, 7-, and 8-quark configurations violate the confinement scale (large $R_0$ or positive $E_{ m CON}$), whereas certain fully heavy states and some bottom-rich configurations can be compact; decay widths are driven by the wavefunction overlaps and phase space, yielding broad decays for many fully heavy states but potential narrow widths for selected partially heavy systems. These results offer a confinement-based framework to identify promising targets for experimental searches (e.g., at LHCb) and to connect multiquark spectroscopy with fundamental QCD confinement scales, while highlighting the sensitivity to light-quark content through non-linear $R_0$ behavior.

Abstract

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.

Figures (2)

• Figure 1: The curve of bag confinement energy $E_{\rm{CON}}$ (\ref{['equ:bconf']}) as a function of bag radius $R$, with particular hadronic states labeled as sphere dots, including heavy quarkoniums, doubly heavy baryon, tetraquarks and pentaquarks.
• Figure 2: The plots of bag radii $R_0$ of hexaquark family labeled with gray triangles, and their confinement energy $E_{\rm{CON}}(R_0)$ denoted by red sphere dots, arising upon number $N_c$ of charm ($N_s$ of strange, $N_n$ of non-strange light) quarks in flavor configurations. The critical bag radius $R_c=5.61\,\rm{GeV}^{-1}$ aligns with zero $E_{\rm{CON}}$ by a short-dashed line.