Scalar Triple-Heavy Tetraquark States With Quark Content $cc\bar{c}\bar{s}$

In this paper, we study the scalar triple-heavy tetraquark states with quark content $cc\bar{c}\bar{s}$, $\eta_{c}D_{s}$ molecular state and $[cc]_{A(T)}[\bar{c}\bar{s}]_{A(T)}$ compact tetraquark states, by the QCD sum rule method. First, we construct the needed interpolating currents, $J^{M}(x)$, $J^{T_{1}}(x)$, and $J^{T_{2}}(x)$. Then, we derive the sum rules for the masses and the current coupling constants. Finally, we numerically analyze these sum rules, and find $m_{M}=4.9392^{+0.0851}_{-0.0817}~\mbox{GeV}$, and $\lambda_{M}=2.8857^{+0.5729}_{-0.4928}\times10^{-2}~\mbox{GeV}^{5}$ for the mass and the current coupling constant of the $\eta_{c}D_{s}$ molecular state, $m_{T_{1}}=5.0774^{+0.0708}_{-0.0641}~\mbox{GeV}$, and $\lambda_{T_{1}}=1.0436^{+0.1862}_{-0.1573}\times10^{-1}~\mbox{GeV}^{5}$ for the mass and the current coupling constant of the $[cc]_{A}[\bar{c}\bar{s}]_{A}$ compact tetraquark state, $m_{T_{2}}=5.0679^{+0.0839}_{-0.0721}~\mbox{GeV}$, and $\lambda_{T_{2}}=2.0316^{+0.4119}_{-0.3119}\times10^{-1}~\mbox{GeV}^{5}$ for the mass and the current coupling constant of the $[cc]_{T}[\bar{c}\bar{s}]_{T}$ compact tetraquark state.