  In this work, we choose 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 the quantum numbers $J^{PC}=1^{--}$. And we obtain the lowest
vector tetraquark masses and make possible assignments of the existing $Y$
states. There indeed exists a hidden-charm tetraquark state with the
$J^{PC}=1^{--}$ at the energy about $4.75\,\rm{GeV}$ as the first radial
excitation to account for the BESIII data.
