Hidden charm tetraquark states in a diquark model

The purpose of the present study is to explore the mass spectrum of the hidden charm tetraquark states within a diquark model. Proposing that a tetraquark state is composed of a diquark and an antidiquark, the masses of all possible $[qc][\bar{q}\bar{c}]$, $[sc][\bar{s}\bar{c}]$, and $[qc][\bar{s}\bar{c}]$ $([sc][\bar{q}\bar{c}])$ hidden charm tetraquark states are systematically calculated by use of an effective Hamiltonian, which contains color, spin, and flavor dependent interactions. Apart from the $X(3872)$, $Z(3900)$, ${\chi }_{c2}(3930)$, and $X(4350)$ which are taken as input to fix the model parameters, the calculated results support that the ${\chi }_{c0}(3860)$, $X(4020)$, $X(4050)$ are $[qc][\bar{q}\bar{c}]$ states with $I^G{J}^{PC}=0^{+}{0}^{++}$, $1^{+}{1}^{+-}$, and $1^{-}{2}^{++}$, respectively, the ${\chi }_{c1}(4274)$ is an $[sc][\bar{s}\bar{c}]$ state with $I^G{J}^{PC}=0^{+}{1}^{++}$, the $X(3940)$ is a $[qc][\bar{q}\bar{c}]$ state with $I^G{J}^{PC}=1^{-}{0}^{++}$ or $1^{-}{1}^{++}$, the $Z_{cs}(3985{)}^{-}$ is an $[sc][\bar{q}\bar{c}]$ state with $J^P=0^{+}$ or $1^{+}$, and the $Z_{cs}(4000{)}^{+}$ and $Z_{cs}(4220{)}^{+}$ are $[qc][\bar{s}\bar{c}]$ states with $J^P=1^{+}$. Predictions for other possible tetraquark states are also given.