Strong decays of the vector tetraquark states with the masses about 4.5 GeV via the QCD sum rules

We suppose that there exist three vector hidden-charm tetraquark states with the $J^{PC}=1^{--}$ at the energy about $4.5\mathrm{GeV}$, and investigate the two-body strong decays systematically. We obtain thirty QCD sum rules for the hadronic coupling constants based on rigorous quark-hadron duality, then obtain the partial decay widths, therefore the total widths approximately, which are compatible with the experimental data of the $Y\left(4500\right)$ from the BESIII collaboration. The $Y\left(4500\right)$ may be one vector tetraquark state having three main Fock components, or consists of three different vector tetraquark states. We can search for the typical decays $Y\to \frac{{\overline{D}}_1^0{D}^0-{\overline{D}}^0{D}_1^0}{\sqrt{2}}$, $\frac{{\overline{D}}_1^{-}{D}^{+}-{\overline{D}}^{-}{D}_1^{+}}{\sqrt{2}}$, $\frac{{\overline{D}}_0^0{D}^{⁎0}-{\overline{D}}^{⁎0}{D}_0^0}{\sqrt{2}}$, $\frac{{\overline{D}}_0^{-}{D}^{⁎+}-{\overline{D}}^{⁎-}{D}_0^{+}}{\sqrt{2}}$, ${\eta }_c\omega$, $J/\psi \omega$ to diagnose the nature of the $Y\left(4500\right)$.