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

Zi-Xuan Ma, Qi Huang, Rui Chen, Li-Ming Wang, Xiao-Huang Hu, Yue Tan, Jun He, Hong-Xia Huang

TL;DR

The paper investigates whether light exotic $1^{-+}$ states can be interpreted as hybrids within a three-body $q\bar{q}g$ framework by incorporating a constituent gluon mass $m_g$. Using the Gauss Expansion Method in a chiral constituent quark model with three confinement forms, the authors compute both spectra and leading-order decay widths, finding that $m_g\approx 450$ MeV reproduces lattice and phenomenological results while suggesting that $\pi_1(1600)$ and $\eta_1(1855)$ cannot both be $1^{-+}$ hybrids. The study predicts an $\eta_1(1640)$ and identifies golden search channels $K_1(1270)\bar{K}$ and $K_1(1270)\pi$ for isospin-0 and isospin-$\frac{1}{2}$ hybrids, respectively, highlighting the role of gluon mass as the final piece in hybrid spectroscopy. It also shows that varying $m_g$ from $0.4$ to $0.8$ GeV causes only modest shifts in ground-state masses, underscoring the robustness of the framework and its predictive power for future experiments such as BESIII.

Abstract

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.

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

TL;DR

The paper investigates whether light exotic states can be interpreted as hybrids within a three-body framework by incorporating a constituent gluon mass . Using the Gauss Expansion Method in a chiral constituent quark model with three confinement forms, the authors compute both spectra and leading-order decay widths, finding that MeV reproduces lattice and phenomenological results while suggesting that and cannot both be hybrids. The study predicts an and identifies golden search channels and for isospin-0 and isospin- hybrids, respectively, highlighting the role of gluon mass as the final piece in hybrid spectroscopy. It also shows that varying from to GeV causes only modest shifts in ground-state masses, underscoring the robustness of the framework and its predictive power for future experiments such as BESIII.

Abstract

In this letter, we propose that a proper constituent gluon mass =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 with , we find the and may not be explained as hybrids, simultaneously, and the observed by BESIII may not be a hybrid. In addition, we predict an existence of a hybrid , which can be verified by searching the channel. Moreover, we suggest the and as the golden channels to search for an isospin-0 and an isospin- hybrids, respectively.

Paper Structure

This paper contains 11 sections, 33 equations, 4 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Model Setup
  3. Numerical results and discussions
  4. Summary
  5. Some details on the model
  6. Deriving the potential between quark and gluon
  7. A little more on the construction of spin-orbit wave function
  8. More details on the transition amplitude from a hybrid to two mesons
  9. Chiral constituent quark model
  10. More details on numerical calculation
  11. Impact of constituent gluon mass on the spectra of hybrid

Figures (4)

  • Figure 1: The coupling scheme of hybrid (left) and the interaction between quark and gluon (right). Here, in left panel, the T-type solid lines means that quark and antiquark couple first to form a $(q\bar{q})$ cluster, then gluon couples to this cluster to form the final hybrid.
  • Figure 2: Mass spectra of low-lying hybrid states with $I(J^{PC})=I(1^{-+})$, where the error bar line means a collection of different results obtained by different models or works. Here, the black lines, yellow bands, red lines, and blue lines correspond to the results in our work, the experimental data from Ref. ParticleDataGroup:2024cfk, the lattice QCD results referenced in Bernard:1981pgLacock:1996nyMILC:1997usnMcNeile:1998cpMei:2002ipBernard:2003jdDudek:2013yja, and in other phenomenological models Meyer:2015etaShastry:2022mhkBarnes:1982zsBarnes:1982txDonoghue:1983fyIddir:2007dqSzczepaniak:2001rgIshida:1991mxHorn:1977rqTan:2024grd, respectively.
  • Figure 3: Two kinds of coupling schemes. The left panel shows the wave function coupling mode of Eq. (\ref{['j-j']}), and the right panel shows the coupling mode of Eq. (\ref{['l-s']}).
  • Figure 4: Impact of different constituent gluon masses on the spectra of ground hybrid states with quantum number $1^{-+}$, where states are distinguished by compositeness and isospin, and the error bar line means a collection of different results obtained by different models or works. Here, the black lines denote our results, where the constituent gluon mass varies from 0.4 GeV to 0.8 GeV, the yellow bands reflect experimental data from Ref. ParticleDataGroup:2024cfk, the red lines correspond to lattice QCD results referenced in Bernard:1981pgLacock:1996nyMILC:1997usnMcNeile:1998cpMei:2002ipBernard:2003jdDudek:2013yja, and the blue lines represent results from other phenomenological models Meyer:2015etaShastry:2022mhkBarnes:1982zsBarnes:1982txDonoghue:1983fyIddir:2007dqSzczepaniak:2001rgIshida:1991mxHorn:1977rqTan:2024grd.