In this article, we study the $S\bar{ S}$ type scalar tetraquark state $cq\bar{ c}\bar{ q}$ in details with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and obtain the value $M_{ Z_c}=\left(3.82^{ +0.08}_{ -0.08}\right)\,\rm{ GeV}$, which is the lowest mass for the hidden charmed tetraquark states from the QCD sum rules. Furthermore, we calculate the hadronic coupling constants $G_{ Z_c\eta_c\pi}$ and $G_{ Z_cDD}$ with the three-point QCD sum rules, then study the strong decays $ Z_c\to \eta_c\pi\, ,\, DD$, and observe that the total width $\Gamma_{ Z_c}\approx 21\,\rm{ MeV}$. The present predictions can be confronted with the experimental data in the futures at the BESIII, LHCb and Belle-II.
Categories: hep-ph