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 $[qc][\bar{s}\bar{c}]$ $\left([sc][\bar{q}\bar{c}]\right)$ 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 $I^GJ^{PC}=0^+0^{++}$, $1^+1^{+-}$, and $1^-2^{++}$, respectively, the $\chi_{c1}(4274)$ is an $[sc][\bar{s}\bar{c}]$ state with $I^GJ^{PC}=0^+1^{++}$, the $X(3940)$ is a $[qc][\bar{q}\bar{c}]$ state with $I^GJ^{PC}=1^-0^{++}$ 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.