OZI-Superallowed Decays in Hexaquarks

• OZI-superallowed decays are rapid, unsuppressed strong decay modes in multiquark systems that occur when the wavefunction strongly overlaps with baryon–antibaryon states.
• The MIT bag model and Young tableaux techniques are employed to construct color–spin wavefunctions, enabling predictions of decay widths and flavor viability.
• Experimental searches target bottom-rich hexaquark states by leveraging confinement criteria, heavy-flavor symmetry, and suppressed color-singlet overlaps to yield narrow decay signatures.

OZI-superallowed decays are rapid strong decay channels in multiquark systems, particularly hexaquarks, whose rates are unsuppressed by the Okubo–Zweig–Iizuka (OZI) rule due to the intrinsic color–spin configuration of the initial state. Unlike generic strong decays sensitive to string breaking or quark–antiquark pair creation, OZI-superallowed decays can proceed directly when the multiquark wavefunction has a large overlap with hadronic substructures (e.g. baryon–antibaryon pairs), resulting in significant partial widths. Their phenomenology is deeply intertwined with quark confinement dynamics, the construction of color–spin wavefunctions, and heavy-flavor symmetry. Systematic studies using the MIT bag model and group-theoretical techniques such as Young tableaux provide a framework for evaluating these decays and predicting which flavor configurations are phenomenologically viable under confinement constraints (Zhang et al., 5 Oct 2025).

1. Conceptual Basis of OZI-Superallowed Decays

OZI-superallowed decays are characterized by strong decay channels that are permitted by the OZI rule and occur without suppression, provided that the multiquark color–spin wavefunction has substantial overlap with a configuration separable into two color-singlet hadrons. For hexaquarks, this means the internal wavefunction possesses a large component that matches a baryon–antibaryon state, enabling the system to decay immediately into two free hadrons.

Contrary to typical OZI-forbidden processes, which inhibit disconnected quark-line topologies and thus lead to suppressed branching fractions, in OZI-superallowed scenarios the decay proceeds via the “superallowed” channel with maximal amplitude, dictated primarily by wavefunction overlap rather than dynamical rearrangement or pair creation thresholds.

2. Wavefunction Construction via Color–Spin and Young Tableaux Methods

The evaluative framework for OZI-superallowed decays centers on the explicit construction of complete color–spin wavefunctions. In the six-quark sector, this is achieved by:

• Decomposing the hexaquark into three-quark and three-antiquark sub-clusters,
• Expressing the full wavefunction as a linear combination of color and spin basis states, systematically organized by Young tableaux.

The general form is: $$|\psi\rangle = c^1 |(qqq)^1 \otimes (\bar{q}\bar{q}\bar{q})^1\rangle + c^8 |(qqq)^8 \otimes (\bar{q}\bar{q}\bar{q})^8\rangle + \ldots$$ where superscripts denote color singlet (1) and octet (8) components.

Young tableaux are employed to enumerate and construct all possible color and spin configurations. The key coefficient $|c^1|^2$ indicates the probability of the hexaquark existing in a color-singlet baryon–antibaryon configuration. In fully heavy systems, heavy-flavor symmetry typically enforces high $|c^1|^2$ values, while configurations with more light quarks tend toward smaller overlaps.

Appendices in (Zhang et al., 5 Oct 2025) tabulate the explicit bases ($\phi_1, ..., \phi_6$ for color; $\chi_1, ..., \chi_{20}$ for spin), which are the building blocks for the wavefunctions relevant to OZI-superallowed decay.

3. Decay Widths and the Role of Wavefunction Overlap

The partial width of a two-body $S$-wave OZI-superallowed decay channel is estimated as: $\Gamma_i = \gamma_i \alpha k \cdot |c^1_i|^2$ where $k$ is the momentum determined by the mass difference and phase space, $\gamma_i$ is a model-dependent dynamical factor, $\alpha$ the effective strong coupling, and $|c^1_i|^2$ is the color-singlet overlap probability in channel $i$.

For fully heavy systems (such as $bbb\bar{b}\bar{b}\bar{b}$), the heavy quark symmetry induces wavefunctions with large $|c^1|^2$, leading to broad decay widths of OZI-superallowed modes. In contrast, in bottom-rich systems with light quarks (e.g., $nnb\bar{b}\bar{b}\bar{b}$ and $nnn\bar{b}\bar{b}\bar{b}$), the overlap $|c^1|^2$ is suppressed (as low as 0.1–3%), potentially yielding much narrower decay widths despite their superallowed status.

4. Flavor Composition, Confinement, and Critical Bag Radius

OZI-superallowed decay phenomenology depends critically on both flavor composition and the dynamical constraints of confinement. The MIT bag model, incorporating perturbative interactions and a confinement energy $E_{\rm CON}$, yields a critical bag radius $R_c = 5.61\,{\rm GeV}^{-1}$ ($\sim 1.11\,{\rm fm}$), matching with lattice QCD string-breaking distances.

The compactness of hexaquark configurations is determined by whether their equilibrium radius $R_0$ satisfies $R_0 < R_c$ (ensuring $E_{\rm CON} < 0$). Systems with several light quarks tend to exceed this threshold, resulting in positive $E_{\rm CON}$ and thus exclusion as compact multiquarks. Heavy–light configurations such as $n^3\bar{c}^3$ or $n^3\bar{n}\bar{c}^2$ are excluded on this basis. In contrast, bottom-rich states with minimal light quark content can be compact and phenomenologically accessible, as summarized in the following table:

configuration	$R_0$ relative to $R_c$	decay width character
$bbb\bar{b}\bar{b}\bar{b}$	$R_0 < R_c$	broad ($|c^1|^2$ large)
$nnb\bar{b}\bar{b}\bar{b}$	$R_0 \lesssim R_c$	narrow ($|c^1|^2$ suppressed)
$nnn\bar{b}\bar{b}\bar{b}$	$R_0 \approx R_c$	narrow ($|c^1|^2$ suppressed)

This sensitivity enables potential identification of states with favorable experimental signatures, especially those featuring both compactness and narrow decay widths.

5. Experimental Signatures and Implications

The paper (Zhang et al., 5 Oct 2025) recommends targeted searches at LHCb for bottom-rich hexaquark states with expected narrow widths – specifically $nnb\bar{b}\bar{b}\bar{b}$ and $nnn\bar{b}\bar{b}\bar{b}$ – because their suppressed wavefunction overlap with the color-singlet baryon–antibaryon channel translates to experimentally distinguishable, comparatively long-lived resonances.

These states are predicted to have mass scales of $20$–$26$ GeV depending on constituent quark masses and bag radii. Fully heavy systems, while compact, will generally exhibit broad widths and may not produce narrow resonance signals.

6. Interplay with Heavy Flavor Symmetry and Model Limitations

Heavy-flavor symmetry is a central factor in determining wavefunction structure and decay properties. In fully heavy systems, the symmetry produces significant overlap with color-singlet configurations, thus favoring rapid and broad decay via OZI-superallowed channels. The presence of light quarks distorts this symmetry, enlarges the bag radius, and reduces the singular overlap, thereby offering narrower widths.

The bag model's limitation is mediated by the critical radius $R_c$, which acts as an exclusion criterion for many heavy–light configurations. The phenomenology rests on the maxims:

• Only configurations with $R_0 < R_c$ should be considered as candidates for compact multiquarks.
• Experimentally accessible states are those combining this confinement criterion with suppressed wavefunction overlap in relevant decay channels.

This suggests that future multiquark searches should prioritize flavor compositions optimized for both compactness and wavefunction suppression, as encoded in the group-theoretical analyses and bag model energetics.

7. Summary and Prospects

OZI-superallowed decays reveal critical intersections between quark model structure, group theory, and QCD confinement dynamics. Their analytic treatment via color–spin wavefunctions and bag-model energetics provides stringent criteria for viable hexaquark candidates, leading to concrete experimental proposals. The central formulas from (Zhang et al., 5 Oct 2025):

• Wavefunction: $$|\psi\rangle = c^1 |(qqq)^1 \otimes (\bar{q}\bar{q}\bar{q})^1\rangle + c^8 |(qqq)^8 \otimes (\bar{q}\bar{q}\bar{q})^8\rangle + ...$$
• Decay width: $\Gamma_i = \gamma_i \alpha k \cdot |c^1_i|^2$
• Critical radius: $$E_{\mathrm{CON}}(R_c) = 0 \rightarrow R_c = 5.61\,{\rm GeV}^{-1}$$

These equations summarize the theoretical infrastructure guiding the search and analysis of OZI-superallowed decay phenomenology in multiquark, and in particular, hexaquark systems.