Hunting for the prospective $T_{cc}$ family based on the diquark-antidiquark configuration

Inspired by the first $T_{cc}$ observation at the LHCb Collaboration, the spectroscopic properties of the entire isoscalar and isovector $T_{cc}$ family are systematically investigated by means of multiple sorts of relativized and nonrelativistic diquark formalisms, which include the Godfrey-Isgur relativized diquark model, the modified Godfrey-Isgur relativized diquark model incorporating the color screening effects, the nonrelativistic diquark model with the Gaussian type hyperfine potential, and the nonrelativistic diquark model with the Yukawa type hyperfine potential. In terms of the $1S$-wave double-charm tetraquark state with $I(J^P)=0(1^+)$, the predicted masses of most diquark-antidiquark scenarios are somewhat higher than the observed value of the $T_{cc}(3875)^+$ structure. In light of the diquark-antidiquark configuration, this work unveils the mixing angles of the orbitally excited isovector $T_{cc}$ states and the magic mixing angles of the ideal heavy-light tetraquarks for the first time. As the advancement of the experimental detection capability, these phenomenological predictions will effectively boost the hunting for the prospective low-lying $T_{cc}$ states in the future.