Masses of tetraquark states in the hidden charm sector above $D-D^*$ threshold

Abstract

In the diquark-diantiquark composition, we study the masses of hidden charm tetraquark systems ($cq\bar{c}\bar{q}$, $cs\bar{c}\bar{s}$ and $cs\bar{c}\bar{q}$) using a linear confinement potential. In this study, we have factorized the four body system into three subsequent two body systems. To remove degeneracy in the S and P wave masses of mesons and tetraquark states, the spin-spin, spin orbit and tensor components of the confined one gluon exchange interactions are employed. In this attempt, we have been able to assign the $\psi(4230)$ as pure $cq\bar{c}\bar{q}$ tetraquark state. $\psi(4360)$ and $\psi(4390)$ as pure $cs\bar{c}\bar{q}$ tetraquark states. According to our analysis $\psi(4260)$ is an admixture of $^1P_1$ and $^5P_1$ $cq\bar{c}\bar{q}$ tetraquark state. Additionally, we have been able to predict the radiative decay width $\Gamma_{(\psi \rightarrow J/\psi \gamma)}$, leptonic decay width $\Gamma_{e^+e^-}$ and hadronic decays of $1^{--}$ tetraquark stat