The lowest hidden charmed tetraquark state from QCD sum rules

Abstract

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 $M_{Z_c}=\left(3.82_{-0.08}^{+0.08}\right)\mathrm{GeV}$, 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 $G_{Z_{c}DD}$ 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 ${\Gamma }_{Z_c}\approx 21\mathrm{MeV}$. The present predictions can be confronted with the experimental data in the futures at the BESIII, LHCb and Belle-II.

Comments: 15 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1312.1537, arXiv:1312.2652