QCD sum rule study of the tensor $Δ^0Δ^0$ dibaryon state

TL;DR

This study uses QCD sum rules to investigate a tensor $Δ^{0}Δ^{0}$ dibaryon with $J^{P}=2^{+}$, constructing an appropriate tensor interpolating current and evaluating the two-point correlator with condensates up to dimension nine. By matching the hadronic and QCD representations and applying a Borel transform, the authors extract the mass $m_{ m Δ^{0}Δ^{0},2^{+}} = 2426^{+101}_{-108}$ MeV and the decay constant $f_{ m Δ^{0}Δ^{0}} = (2.30^{+0.49}_{-0.45}) imes 10^{-4}$ GeV$^8$, finding a central value about $38$ MeV below the $2 m_{ m Δ^{0}}$ threshold, which indicates a possible bound molecular configuration. The estimated size $r oughly 0.90$ fm suggests a compact hexaquark structure, potentially accessible to experiments. Overall, the results contribute a robust theoretical prediction for a tensor dibaryon and motivate searches for such exotic states in future experiments.

Abstract

We study the exotic $Δ^{0}Δ^{0}$ dibaryon state with quantum numbers $J^{P} = 2^{+}$ within the framework of QCD sum rules. A tensor interpolating current is constructed to determine the mass and residue of this state, including explicit calculations of contributions from quark, gluon, and mixed vacuum condensates up to dimension nine. The numerical analysis yields a mass of $m_{Δ^{0}Δ^{0}} = 2426^{+101}_{-108}~\mathrm{MeV}$ and a residue of $f_{Δ^{0}Δ^{0}} = \left( 2.30^{+0.49}_{-0.45} \right) \times 10^{-4}~\mathrm{GeV}^{8}$. The predicted mass lies about $38~\mathrm{MeV}$ below the $2m_{Δ^{0}}$ threshold, which indicates the possible existence of a bound molecular configuration. Consequently, the tensor $Δ^{0}Δ^{0}$ dibaryon may serve as a promising candidate for future experimental searches.

Figures (2)

• Figure 1: The left panel shows the variation of the $\Delta^0\Delta^0$ dibaryon mass with respect to $M^2$ at fixed $s_0$, while the right panel illustrates its dependence on $s_0$ at fixed $M^2$.
• Figure 2: The left panel shows the variation of the $\Delta^0\Delta^0$ dibaryon mass with respect to $M^2$ at fixed $s_0$, while the right panel illustrates its dependence on $s_0$ at fixed $M^2$.