Going in quest of potential tetraquark interpretations for the newly observed $T_{\psi\psi}$ states in light of the diquark-antidiquark scenarios

Stimulated by the recent experimental progress on the $T_{\psi\psi}$ states, the fully charmed tetraquark spectroscopy is systemically investigated by dint of the Godfrey-Isgur relativized diquark model, the modified Godfrey-Isgur relativized diquark model with the color screening effects, and the nonrelativistic diquark model. The theoretical results of the diquark-antidiquark scenarios propose to interpret the $T_{\psi\psi}(6200)$, $T_{\psi\psi}(6600)$, $T_{\psi\psi}(6900)$, and $T_{\psi\psi}(7300)$ structures as the candidates of the $1S$-wave, $1P/2S$-wave, $1D/2P$-wave, and $2D/3P/4S$-wave fully charmed tetraquark states, respectively. On account of the deficiency of sufficient experimental information, e.g., the parities of the newly observed $T_{\psi\psi}$ states, there are uncertainties about the assignments of the $T_{\psi\psi}(6600)$, $T_{\psi\psi}(6900)$, and $T_{\psi\psi}(7300)$ states. It is demonstrated that the further experimental survey on the $cc\bar c\bar c$ states, implemented by the LHCb, ATLAS, CMS, and other collaborations, ought to be continued in the future.