Ground states and first radial excitations of vector tetraquark states with explicit P-waves via QCD sum rules*

In this study, we chose the diquark-antidiquark type four-quark currents with an explicit P -wave between the diquark and antidiquark pairs to study the ground states and first radial excitations of the hidden-charm tetraquark states with quantum numbers . We also obtained the lowest vector tetraquark masses and made possible assignments of the existing states. There indeed exists a hidden-charm tetraquark state with at an energy of approximately 4.75 GeV as the first radial excitation that accounts for the BESIII data.