The ground states of hidden-charm tetraquarks and their radial excitations

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 qcq̄c̄(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 qcq̄c̄(q=$u/d$) system, theoretical predictions support assigning Zc(3900) and $Z(4430)$ as the ground and the first radially excited states with their quantum numbers to be JPC=1⁺⁻. Besides, the broad structure Zc(4200) may be also a partner of Zc(3900), and arise from the higher state with JPC=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 scs̄c̄ system, $X(4140)$ and $X(4274)$ structures can be interpreted as this type of tetraquark states with JPC=1⁺⁺. In addition, $X(4350)$ can also be described as a scs̄c̄ tetraquark with JPC=0⁺⁺. With regard to qcs̄c̄(q=$u/d$) system, we find two potential candidates for this type of tetraquark, which are Zcs(4000) and Zcs(4220) structures. The masses of these two structures are in agreement with theoretical predictions of the 1⁺ state.