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, $1P\mathrm{/}2S$-wave, $1D\mathrm{/}2P$-wave, and $2D\mathrm{/}3P\mathrm{/}4S$-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.