Spectrum of $J^{PC} = 0^{\pm\pm}$ Gluonic Hidden-Charm Tetraquark States

TL;DR

The paper investigates gluonic hidden-charm and hidden-bottom tetraquark states with quantum numbers JPC = 0±±, modeled as a diquark–antidiquark core plus a valence gluon in the color configuration bar3_c cq ⊗ 8_c_G ⊗ 3_c_bar cbar q. Using a comprehensive QCD sum-rule analysis up to dimension eight in the operator product expansion, the authors construct eight interpolating currents for the targeted JPC and extract masses from the two-point correlator after a Borel transform. They find six charm-sector and six bottom-sector hidden-tetraquark–hybrid states with masses in the ranges $5.14\le m_X\le 5.58$ GeV and $11.15\le m_X\le 11.29$ GeV, respectively, and discuss production and decay channels to guide experimental searches. The results suggest these states could be accessible at current and future facilities, providing a probe of explicit gluonic degrees of freedom in multiquark systems and offering a path to distinguish tetraquark hybrids from glueball candidates; the bottom-sector states, while heavier and harder to observe, remain within experimental reach at heavy-flavor facilities.

Abstract

We investigate gluonic hidden-charm tetraquark states composed of two valence quarks, two valence antiquarks and an explicit valence gluon. In the color configuration $[\bar{3}_c]_{c q}\otimes[8_c]_{G}\otimes[3_c]_{\bar{c}\bar{q}}$, a complete set of eight interpolating currents is constructed for states with quantum numbers $^{PC}=0^{++}$, $0^{-+},$ $0^{--}$, and $0^{+-}$. The corresponding mass spectra are systematically analysed within the QCD sum rule framework, including nonperturbative condensate contributions up to dimension eight. Our numerical analysis indicates the possible existence of six gluonic hidden-charm tetraquark states exhibiting stable behaviour in the adopted Borel windows. By replacing the charm quark with the bottom quark, masses for the corresponding hidden-bottom partners are also estimated. Possible production mechanisms and dominant decay channels are discussed, providing phenomenological guidance for experimental searches. These predicted states may be accessible at current and forthcoming facilities, including Belle II, PANDA, SuperB and LHCb, and thus offer an opportunity to probe explicit gluonic degrees of freedom in multiquark systems and deepen our understanding of nonperturbative QCD.

Figures (13)

• Figure 1: The typical Feynman diagrams associated with the correlation function are shown, where the thick solid line represents the heavy quark, the thin solid line denotes the light quark, and the wavy line corresponds to the gluon.
• Figure 2: (a) The ratios ${R_{0^{++}}^{B,\;OPE}}$ and ${R_{0^{++}}^{B,\;PC}}$ as functions of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$, where blue lines represent ${R_{0^{++}}^{B,\;OPE}}$ and red lines denote ${R_{0^{++}}^{B,\;PC}}$. (b) The mass $M_{0^{++}}^{B}$ as a function of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$.
• Figure 3: Similar captions as in Fig. \ref{['fig0++B']}, but for the current in Eq. (\ref{['current-0++C']}).
• Figure 4: Similar captions as in Fig. \ref{['fig0++B']}, but for the current in Eq. (\ref{['current-0-+B']}).
• Figure 5: Similar captions as in Fig. \ref{['fig0++B']}, but for the current in Eq. (\ref{['current-0-+C']}).