Revisiting charmonium hybrid spectroscopy

TL;DR

This work investigates charmonium hybrids within a constituent gluon framework, treating the state as a $c\bar{c}g$ system with a transverse-electric gluon to predict the spectrum and open-charm decays. Using a nonrelativistic Hamiltonian with flux-tube confinement and one-gluon exchange, the authors obtain a lowest multiplet at $m_{0^{-+}}=4.189$ GeV, $m_{1^{-+}}=4.231$ GeV, $m_{1^{--}}=4.276$ GeV, and $m_{2^{-+}}=4.316$ GeV, and identify a crucial selection rule that suppresses decays to two identical spatial mesons, steering dominant decays toward $S$-wave plus $P$-wave charmed-meson pairs. The predicted widths show strong sensitivity to threshold openings, with the $1^{--}$ state near $D\bar{D}_1$ potentially several tens of MeV wide, while the $0^{-+}$ and $1^{-+}$ hybrids are expected to be narrow; the $2^{-+}$ state is closely tied to the $D\bar{D}_2^*$ threshold. The work also discusses experimental search strategies, including potential identification of the $1^{--}$ state around $4.27$ GeV in $e^+e^-$ collisions and the production of $(0,1,2)^{-+}$ hybrids via $\Upsilon$ annihilation, offering concrete channels to distinguish hybrids from conventional charmonium and highlighting ongoing tension with a pure hybrid interpretation for the $Y(4230)$ resonance. Overall, the study provides actionable predictions for current and upcoming facilities (BESIII, Belle II, Super Tau-Charm) to probe gluonic excitations in heavy quarkonia.

Abstract

Hadrons with explicit gluonic degrees of freedom, such as charmonium hybrids, are key to understanding nonperturbative behavior of strong interaction, yet they remain experimentally elusive. Within a constituent gluon model treating the hybrid as a $c\bar{c}g$ three-body system with a transverse electric gluon, we predict the masses of the lightest hybrid multiplet ($J^{PC}=1^{--}, 0^{-+}, 1^{-+}, 2^{-+}$) to lie in the range $4.19$--$4.32$ GeV. By analyzing their decay patterns, we provide specific, experimentally testable signatures to guide the search for these exotic states at current and future facilities.

Figures (4)

• Figure 1: The lowest $c\bar{c}g$ hybrid multiplet spectrum and charmed meson pair mass thresholds.
• Figure 2: Decay width of the $1^{--}$ hybrid as a function of its mass. The shaded band on the mass axis indicates $\pm25$ MeV around our nominal value for the $1^{--}$ hybrid mass. The vertical dashed line marks the $D\bar{D}_1$ threshold.
• Figure 3: Decay width of the $2^{-+}$ hybrid as a function of its mass. The shaded band on the mass axis indicates $\pm25$ MeV around our nominal value for the $2^{-+}$ hybrid mass. The vertical dashed line marks the $D\bar{D}_2^*$ threshold.
• Figure 4: Production of a charmonium hybrid through annihilation decay of $\Upsilon$ states: (a) $\gamma H_{c\bar{c}}$ and (b) $X H_{c\bar{c}}$, where $X$ denotes possible single or multiple hadrons.