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.
Categories: hep-ph nucl-th