QCD Sum Rule Analysis of Triply Heavy $(Q\bar{Q})(Q\bar{q})$ Tetraquark States with $J^P=0^{\pm}$
Within the framework of QCD sum rules, we systematically investigate the mass spectra and possible decay patterns of the $(c\bar{c})(c\bar{q})$ and $(b\bar{b})(b\bar{q})$ tetraquark states with quantum numbers $J^{P}=0^{\pm}$. Based on two distinct color configurations, $[8_c]_{Q\bar{Q}} \otimes [8_c]_{Q\bar{q}}$ and $[1_c]_{Q\bar{Q}} \otimes [1_c]_{Q\bar{q}}$, we construct 18 interpolating currents for these states, and obtain stable sum rules for a subset of them. By calculating the corresponding two-point correlation functions, we extract their mass spectra. For the $(c\bar{c})(c\bar{q})$ system, we identify four possible tetraquark states: two with $J^{P}=0^+$, namely $T_{3c,0}(4760)$ and $T_{3c,0}(5000)$, and two with $J^{P}=0^-$, denoted as $T_{3c,0}(5040)$ and $T_{3c,0}(5370)$. For the $(b\bar{b})(b\bar{q})$ system, the extracted masses are found to lie in the ranges $13.72$--$14.02$ GeV for the $J^{P}=0^+$ states and $13.90$--$14.22$ GeV for the $J^{P}=0^-$ states. We further analyze their possible decay modes. Our results indicate that $T_{3c,0}(5000)$, $T_{3c,0}(5040)$, and $T_{3c,0}(5370)$ can decay into a charmonium state and a charmed meson, and are therefore expected to have appreciable decay widths. By contrast, $T_{3c,0}(4760)$ and all predicted $(b\bar{b})(b\bar{q})$ tetraquark states are expected to be relatively narrow, since the corresponding two-body strong decays via the fall-apart mechanism are kinematically forbidden. Therefore, $T_{3c,0}(4760)$ and all predicted $(b\bar{b})(b\bar{q})$ tetraquark states are promising candidates for experimental searches in final states containing a $D$ or a $\bar{B}$ meson, accompanied by light hadrons or a photon.