Interpreting $Z_c\mathbf{(}3900\mathbf{)}$ and $Z_c\mathbf{(}4025\mathbf{)}/Z_c\mathbf{(}4020\mathbf{)}$ as charged tetraquark states

In the framework of the color flux-tube model with a four-body confinement potential, the lowest charged tetraquark states $[Qq][{\overline{Q}}^{\prime }{\overline{q}}^{\prime }](Q=c,b,q=u,d,s)$ are studied by using the variational method, the Gaussian expansion method. The results indicate that some compact resonance states with three-dimensional spatial structures can be formed. These states cannot decay into two color singlet mesons $Q{\overline{q}}^{\prime }$ and ${\overline{Q}}^{\prime }q$ through the breakdown and recombination of color flux tubes but into $Q{\overline{Q}}^{\prime }$ and $q{\overline{q}}^{\prime }$. The four-body confinement potential is a crucial dynamical mechanism for the formation of these compact resonance states. The decay process is similar to that of a compound nucleus but due to the multibody color confinement. The newly observed charged states $Z_c(3900)$ and $Z_c(4025)/Z_c(4020)$ can be interpreted as the $S$-wave tetraquark states $[cu][\overline{c}\overline{d}]$ with quantum numbers $I{J}^P=11^{+}$ and $12^{+}$, respectively.

Figure 1

The tetrahedral structure of the states $[cu][\overline{c}\overline{d}]$.