Tetraquark states in the quark model

We perform systematical investigations of heavy flavor tetraquark systems, including fully heavy $QQ\bar{Q}\bar{Q}$ ($Q=b,c$), doubly heavy $Q{Q}^{(\mathrm{\prime })}\bar{q}\bar{q}$ ($q=u,d$), and singly heavy $Qs\bar{q}\bar{q}$ tetraquark systems, within the framework of quark potential model. We employ the Gaussian expansion method and complex scaling method to solve the four-body Hamiltonian and identify bound and resonant states. We further calculate the root mean square radii to study the spatial configurations of tetraquarks. Our calculations reveal a rich spectrum of tetraquark states exhibiting diverse spatial configurations. In particular, we find good candidates for experimental states $X(6900)$, $X(7200)$, $T_{cc}(3875{)}^{+}$, and $T_{\bar{c}\bar{s}0}^{\ast }(2870)$. The fully charmed tetraquark resonances $X(6900)$ and $X(7200)$ are compact teraquark states, while doubly charmed tetraquark bound state $T_{cc}(3875{)}^{+}$ and charm-strange tetraquark resonance $T_{\bar{c}\bar{s}0}^{\ast }(2870)$ are meson molecules. Additionally, more tetraquark bound and resonant states are predicted and may be searched for in future experiments.