Mass spectra of four quark states in hidden charm sector

Abstract

Masses of the low lying four quark states in the hidden charm sector ($cq\bar{c}\bar{q};q\in u,d$) are calculated within the framework of a non-relativistic quark model. The four body system is considered as two two-body systems such as diquark-antidiquark ($Qq-\bar{Q}\bar{q}$) and quark antiquark-quark antiquark ($Q\bar{q}-\bar{Q}q$) molecular-like four quark states. Here, Cornell type potential has been used for describing the two body interactions among $Q-q$, $\bar{Q}-\bar{q}$, $Q-\bar{q}$, $Qq-\bar{Q}\bar{q}$ and $Q\bar{q}-\bar{Q}q$, with appropriate string tensions. Our present analysis suggests the following exotic states, $X(3823)$, $Z_c(3900)$, $X(3915)$, $Z_c(4025)$, $\psi (4040)$, $Z_1(4050)$ and $X(4160)$ as $Q\bar{q}-\bar{Q}q$ molecular-like four quark states while $Z_c(3885)$, $X(3940)$ and $Y(4140)$ as the diquark-antidiquark four quark states. We have been able to assign the $J^{PC}$ values for many of the recently observed exotic states according to their structure. Apart from this, we have identified the charged state $Z(4430)$ recently confirmed by LHCb as the first radial excitation of $Zc(3885)$ with G=+1 and $Y(4360)$ state as the first radial excitation of $Y(4008)$ with $G=-1$ and the state $\psi (4415)$ as the first radial excitation of the $\psi (4040)$ state.