Analysis of strong decays of the $Z_c(4600)$ with the QCD sum rules

In this article, we tentatively assign the $Z_c(4600)$ to be the $[dc{]}_P[\bar{u}\bar{c}{]}_A-[dc{]}_A[\bar{u}\bar{c}{]}_P$ type vector tetraquark state and study its two-body strong decays with the QCD sum rules based on solid quark-hadron duality, the predictions for the partial decay widths $\mathrm{\Gamma }(Z_c^{-}\to J\mathrm{/}\psi {\pi }^{-})=41.4_{-14.9}^{+20.5}\mathrm{M}\mathrm{e}\mathrm{V}$, $\mathrm{\Gamma }(Z_c^{-}\to {\eta }_c{\rho }^{-})=41.6_{-22.2}^{+32.7}\mathrm{M}\mathrm{e}\mathrm{V}$, $\mathrm{\Gamma }(Z_c^{-}\to J\mathrm{/}\psi a_0^{-}(980))=10.2_{-6.7}^{+11.3}\mathrm{M}\mathrm{e}\mathrm{V}$, $\mathrm{\Gamma }(Z_c^{-}\to {\chi }_{c0}{\rho }^{-})=3.5_{-3.0}^{+6.7}\mathrm{M}\mathrm{e}\mathrm{V}$, $\mathrm{\Gamma }(Z_c^{-}\to D^{\ast 0}{D}^{\ast -})=39.5_{-19.3}^{+29.6}\mathrm{M}\mathrm{e}\mathrm{V}$, $\mathrm{\Gamma }(Z_c^{-}\to D^0{D}^{-})=6.6_{-3.0}^{+4.6}\mathrm{M}\mathrm{e}\mathrm{V}$ and $\Gamma(Z_c^-\to D^{*0} D^{-})=1.0^{+1.0}_{-0.6},\rm{MeV}$ can be confronted to the experimental data in the future to diagnose the nature of the $Z_c(4600)$.