Proper constituent gluon mass as the final piece to construct hybrid mesons

In this letter, we propose that a proper constituent gluon mass $m_g$=450 MeV can be applied to identify the hybrids composed of quarks and gluons. By investigating the spectra and decay widths of the light hybrids $(q\bar{q}g)$ with $J^P=1^{-+}$, we find the $π_1(1600)$ and $η_1(1855)$ may not be explained as $1^{-+}$ hybrids, simultaneously, and the $η_1(1855)$ observed by BESIII may not be a hybrid. In addition, we predict an existence of a hybrid $η_1(1640)$, which can be verified by searching the $a_1(1260)π$ channel. Moreover, we suggest the $K_1(1270)\bar{K}$ and $K_1(1270)π$ as the golden channels to search for an isospin-0 and an isospin-$\frac{1}{2}$ hybrids, respectively.

💡 Research Summary

This paper presents a comprehensive study aimed at constructing the mass spectrum of hybrid mesons, which are exotic hadrons composed of a quark, an antiquark, and a valence gluon, as predicted by Quantum Chromodynamics (QCD). The central thesis is that introducing a proper constituent gluon mass is the final crucial piece needed to successfully describe these states within a phenomenological potential model framework.

The authors adopt a specific value for the constituent gluon mass, m_g = 450 MeV, motivated by recent non-perturbative studies of QCD, such as those invoking the Schwinger mechanism, which generate a gauge-invariant dynamical mass for gluons. They incorporate this gluon mass into a well-established chiral constituent quark model, whose parameters were previously fine-tuned to accurately reproduce the spectra of conventional mesons and baryons. The hybrid is treated as a genuine three-body (q, q̄, g) system. The interactions include confinement potentials (tested in screened, linear, and square-root forms to assess robustness), one-gluon exchange potentials, and specifically derived quark-gluon potentials. The Gaussian Expansion Method (GEM) is used to solve the Schrödinger equation for the spectra.

Focusing on the light hybrid mesons with exotic quantum numbers J^(PC) = 1^(-+), the calculations for the ground states show remarkable agreement with prior results from lattice QCD and other phenomenological models, regardless of the confinement form used. The predicted masses are approximately 1.6 GeV for the isospin-1 (qq̄g) state, 1.57-1.88 GeV for the pure isospin-0 (qq̄g) state, 1.9-2.2 GeV for the pure (ss̄g) state, and around 1.8 GeV for the isospin-1/2 (qs̄g) state.

A key analysis involves the mixing between the pure isoscalar qq̄g and ss̄g hybrid states to form physical particles. Using a mixing angle of about 28.8°, the resulting states are identified as η₁(1640) and η₁(1855). Under this hybrid assignment, the calculated partial decay width for η₁(1855) → ηη′ via the leading-order decay mechanism (where the constituent gluon splits into a quark-antiquark pair) is found to be nearly zero. This starkly contradicts the fact that the η₁(1855) was observed by the BESIII collaboration precisely in the J/ψ → γηη′ decay channel. This discrepancy leads the authors to suggest that the η₁(1855) is likely not a hybrid meson, opening the possibility for interpretations like a tetraquark state.

The paper also calculates two-body strong decay widths for the hybrid candidates. The results are qualitatively consistent with earlier works, identifying dominant decay channels: π₁(1600) → b₁(1235)π, the predicted η₁(1640) → a₁(1260)π. Furthermore, the authors propose “golden channels” for future experimental searches: K₁(1270)K̄ for an isospin-0 hybrid and K₁(1270)π for an isospin-1/2 hybrid.

Sensitivity tests show that varying the gluon mass from 0.4 to 0.8 GeV shifts the ground-state hybrid masses less than proportionally, due to the non-linear running coupling constant α_s, and the results remain within the broad consensus of other theoretical approaches. The study concludes that adopting a proper constituent gluon mass, grounded in non-perturbative QCD, allows for a unified description where the same model parameters successful for ordinary hadrons can be extended to predict the spectra of hybrid mesons, particularly their ground states. This provides a crucial step towards a coherent phenomenological understanding of exotic hadrons within the QCD framework.