Double strange hybrid baryon

Abstract: We investigate the spectroscopic properties of the double strange hybrid baryon with quark content $ssqg$ within the framework of QCD sum rule. Using an interpolating current with explicit gluonic degrees of freedom, the two-point correlation function is analyzed in terms of two independent Lorentz structures, $\slashed{q}$ and $I$. The operator product expansion is carried out by including vacuum condensates up to dimension ten, and the corresponding sum rules are derived for both structures. By taking the average of the results obtained from the two Lorentz structures, we extract the masses and pole residues of the ground and first excited states. For the ground state, we obtain a mass of $\widetilde{M } = (1593.44\pm 130.29)~ \mathrm{MeV}$ and a residue of $$\widetilde{λ} = (2.57\pm 0.40) \times10^{-3} ~\mathrm{GeV}<sup>5$$. For the first excited state, the corresponding values are $M = (1897.47\pm 124.44)~ \mathrm{MeV}$ and $$λ= (2.88\pm 0.62) \times10^{-3} ~\mathrm{GeV}<sup>5$$. The obtained results provide theoretical predictions for the double strange hybrid baryon spectrum and may be useful for future experimental searches as well as further nonperturbative studies of hybrid hadrons.

• The paper derives robust QCD sum rules that extract masses and pole residues for both negative-parity (1/2-) and positive-parity (1/2+) double strange hybrid baryons.
• It employs a carefully constructed interpolating current with explicit gluonic fields and expands the OPE up to dimension-10 condensates.
• The predicted masses (~1593 MeV and ~1897 MeV) offer concrete targets for experimental searches in hadronic spectroscopy.

Spectroscopy of the Double Strange Hybrid Baryon: QCD Sum Rule Analysis

Introduction

This paper investigates the mass spectrum of double strange hybrid baryons with quark content $ssqg$, emphasizing the role of explicit gluonic excitations within baryonic systems. Hybrid baryons, unlike their mesonic counterparts, lack manifestly exotic quantum numbers ($J^{PC}$) and therefore present significant challenges for experimental identification due to potential strong mixing with conventional excited baryons of the same quantum numbers. The study addresses these challenges by performing a systematic QCD sum rule analysis to extract masses and pole residues for both the negative-parity ground state and the first positive-parity orbital excitation of the $ssqg$ hybrid baryon (2607.04237).

Theoretical Framework

The analysis is grounded on the two-point correlation function of a carefully constructed interpolating current that explicitly incorporates gluonic degrees of freedom:

$$\eta_H(x) = g_s \epsilon^{abc} [s^a(x)C\gamma^{\mu} s^b(x)] \gamma^{\nu}\gamma_5 [G_{\mu\nu} q(x)]^c$$

This current is tailored to couple to the desired $ssqg$ hybrid baryon states, capturing both negative-parity ground ($1/2^-$) and positive-parity orbitally excited ($1/2^+$) states.

The QCD sum rule methodology involves evaluating the correlation function on two levels:

• Hadronic (phenomenological) side: The correlator is saturated by the hybrid baryon ground and excited states, parameterized with their respective pole residues and masses. Both parity states are included due to the current's coupling structure.
• OPE (theoretical) side: The correlator is expanded using the operator product expansion up to dimension-10 condensates, integrating both perturbative and nonperturbative effects, including the effects of gluon and quark condensates relevant for explicitly gluonic modes in the state structure.

Matching both sides under the assumption of quark-hadron duality and isolating two independent Lorentz structures ($\slashed{q}$ and $I$), the analysis yields two coupled QCD sum rules. The masses and residues are subsequently extracted by numerically studying these sum rules.

Numerical Analysis and Results

The working windows for the auxiliary Borel parameter $M^2$ and continuum threshold $J^{PC}$0 are rigorously fixed by standard sum rule criteria: pole dominance, OPE convergence, and stability of predictions under reasonable variations of these parameters. The chosen ranges ensure the suppression of excited/continuum states as well as higher-dimension OPE terms, attaining reliable isolation of ground and excited $J^{PC}$1 hybrid baryon contributions.

Averaging results from both Lorentz structures, the following strong numerical results are obtained:

• Ground state ($J^{PC}$2) mass: $J^{PC}$3 MeV
• Ground state pole residue: $J^{PC}$4
• First excited state ($J^{PC}$5) mass: $J^{PC}$6 MeV
• Excited state pole residue: $J^{PC}$7

These predictions are robust against variation in the Borel mass and continuum threshold within the allowable windows and exhibit internal consistency between the two independent sum rules for each Lorentz structure.

A noteworthy point is that, within uncertainties, the predicted ground-state mass is significantly lower than the $J^{PC}$8 scale found in some recent analyses of light hybrid baryons, but marginally higher than early sum rule estimates, likely due to the specific structure of the interpolating current and the inclusion of strange quark content.

Implications and Discussion

From a theoretical perspective, these findings substantiate the expectation that QCD supports the existence of hybrid baryons with explicit gluonic degrees of freedom in the low-lying baryon spectrum. The paper's explicit computation up to dimension-10 operators strengthens the reliability of the predictions. It demonstrates that the hybrid $J^{PC}$9 configurations yield identifiable mass eigenstates distinct from those of conventional three-quark baryons, consistent with the QCD spectrum's anticipated richness.

On the practical side, these results furnish concrete targets for experimental searches. The predicted masses for the lowest double strange hybrid baryons provide a baseline for ongoing and future experimental programs (e.g., at JLab, PANDA/FAIR, or LHCb) that aim to resolve possible hybrid structures in the baryon sector. Precise pole residues will also be beneficial for modeling production rates and decay widths once such states are sought experimentally.

The analysis highlights the continued difficulties inherent in unambiguous identification of baryonic hybrids due to possible mixing with conventional baryonic states; however, the mass predictions serve as reference points for detailed experimental and theoretical studies—especially for channels where mixing effects are expected to be minimized due to flavor content.

Future Directions

Potential future developments include:

• Extension to other flavor combinations, particularly those involving heavy quarks, where mixing with ordinary excitations is suppressed and experimental identification is facilitated.
• Refinement using lattice QCD computations and comparison with QCD sum rule results for cross-validation.
• Detailed phenomenological studies of decay patterns and coupling strengths, leveraging the calculated pole residues.
• Systematic exploration of mixing effects with ordinary baryons through coupled-channel analysis or advanced theoretical formalisms.

Conclusion

This work delivers comprehensive QCD sum rule predictions for the spectrum of double strange hybrid baryons with explicit gluonic excitations, establishing their masses and pole residues for both ground and first excited states. The results, residing in the $ssqg$0–$ssqg$1 GeV mass range, form a crucial theoretical foundation for the ongoing exploration of hybrid baryons in experimental hadron spectroscopy and underline the importance of nonperturbative techniques in characterizing the gluonic components of hadronic matter (2607.04237).