Mass spectrum of the $Ω\barΩ$ states

TL;DR

The paper addresses the mass spectrum of ${\rm Ω}{\rm ̄Ω}$ baryonium with $J^{PC}=0^{-+},1^{--},0^{++},1^{++}$ using QCD sum rules. It employs interpolating currents built from the ${\rm Ω}$ baryon and analyzes two-point correlators with an OPE including condensates up to dimension 12, followed by a Borel transform to extract ground-state masses. The results yield four states at $m_{0^{-+}}=(3.22\pm0.07)$ GeV, $m_{1^{--}}=(3.28\pm0.08)$ GeV, $m_{0^{++}}=(3.46\pm0.09)$ GeV, and $m_{1^{++}}=(3.54\pm0.11)$ GeV, with the first two below the double-${\rm Ω}$ threshold and the latter two above it, indicating bound versus resonance-like behavior. The work also discusses decay channels and experimental accessibility at BESIII, Belle II, and LHCb, and compares with lattice-QCD predictions for ${\rm ΩΩ}$ to highlight annihilation effects in the baryonium system.

Abstract

In this study, we investigate the mass spectrum of the $Ω\barΩ$ states with quantum numbers $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, and $1^{++}$ within the framework of QCD sum rules. Employing suitably constructed interpolating currents, the analyses are carried out with the operator product expansion (OPE) including condensate contributions up to dimension $12$. Our results indicate the existence of four possible baryonium states with masses $m_{0^{-+}}=(3.22\pm0.07)$ GeV, $m_{1^{--}}=(3.28\pm0.08)$ GeV, $m_{0^{++}}=(3.46\pm0.09)$ GeV, and $m_{1^{++}}=(3.54\pm0.11)$ GeV. For the $0^{-+}$ and $1^{--}$ states, the predicted masses lie below the corresponding dibaryon thresholds, suggesting possible bound-state configurations. In contrast, the $0^{++}$ and $1^{++}$ states are found above the respective thresholds, implying resonance-like behavior. Potential decay channels for these baryonium candidates are discussed, with emphasis on those accessible to current experimental facilities such as BESIII, Belle II, and LHCb.

Figures (8)

• Figure 1: (a) The ratios of $R^{OPE}_{0^{-+}}$ and $R^{PC}_{0^{-+}}$ as functions of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$, where blue lines represent $R^{OPE}_{0^{-+}}$ and red lines denote $R^{PC}_{0^{-+}}$. (b) The mass $m_{0^{-+}}$ as a function of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$.
• Figure 2: (a) The ratios of $R^{OPE}_{1^{--}}$ and $R^{PC}_{1^{--}}$ as functions of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$, where blue lines represent $R^{OPE}_{1^{--}}$ and red lines denote $R^{PC}_{1^{--}}$. (b) The mass $m_{1^{--}}$ as a function of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$.
• Figure 3: (a) The ratios of $R^{OPE}_{0^{++}}$ and $R^{PC}_{0^{++}}$ as functions of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$, where blue lines represent $R^{OPE}_{0^{++}}$ and red lines denote $R^{PC}_{0^{++}}$. (b) The mass $m_{0^{++}}$ as a function of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$.
• Figure 4: (a) The ratios of $R^{OPE\;,B}_{0^{+-}}$ and $R^{PC\;,B}_{0^{+-}}$ as functions of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$, where blue lines represent $R^{OPE\;,B}_{0^{+-}}$ and red lines denote $R^{PC\;,B}_{0^{+-}}$. (b) The mass $M^{B}_{0^{+-}}$ as a function of the Borel parameter $M_B^2$ for different values of $\sqrt{s_0}$.
• Figure 5: In the figure, the curves from bottom to top correspond to $\sqrt{s_0}$ values of 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, and 3.8 GeV, respectively..