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Inspired by the great progresses in the observations of charmonium-like states in recent years, we perform a systematic analysis about the ground states and the first radially excited states of qcqc (q=u/d and s) tetraquark systems. Their mass spectra, root mean square (r. m. s. ) radii and radial density distributions are investigated within the framework of relativized quark model. By comparing numerical results with experimental data, some potential candidates for hidden-charm tetraquark states are suggested. For the qcqc (q=u/d) system, theoretical predictions support assigning Z₂ (3900) and Z (4430) as the ground and the first radially excited states with their quantum numbers to be J^PC=1^+-. Besides, the broad structure Z₂ (4200) may be also a partner of Z₂ (3900), and arise from the higher state with J^PC=1^+-. Theoretical predictions also indicate that the possible assignments for X (3930), X (4050) and X (4250) are low lying 0^++ states. As for the scsc system, X (4140) and X (4274) structures can be interpreted as this type of tetraquark states with J^PC=1^++. In addition, X (4350) can also be described as a scsc tetraquark with J^PC=0^++. With regard to qcsc (q=u/d) system, we find two potential candidates for this type of tetraquark, which are Z₂ₒ (4000) and Z₂ₒ (4220) structures. The masses of these two structures are in agreement with theoretical predictions of the 1^+ state.
Yu et al. (2024) studied this question.