Strong decays of the fully-charm tetraquark states with explicit P-waves via the QCD sum rules

We introduce a relative P-wave to construct the vector doubly-charm diquark $(\tilde{V})$, therefore, the scalar and tensor four-quark currents to investigate the decay widths of the fully-charm tetraquark states with the $J^{PC}=0^{++}$, $1^{+-}$ and $2^{++}$ via the QCD sum rules. We observe that the total width of the ground state $\tilde{V}\overline{\stackrel{~}{V}}$-type scalar tetraquark state is compatible with that of the $X(6552)$ within the uncertainties, and the branching ratios are quite different from that of the first radial excitation of the $A\bar{A}$-type scalar tetraquark state. Other predictions can be verified in the future experiments to shed light on the nature of the fully-charm tetraquark states.