Systematic study of $Z_c^{+}$ family from quark model's perspective

Abstract

Inspired by the present experimental status of charged charmonium-like states $Z_c^{+}$, the tetraquark states $[cu][\bar{c}\bar{d}]$ are systematically studied in a color flux-tube model with a multi-body confinement potential. The investigation indicates that charged charmonium-like states $Z_c^{+}(3900)$ or $Z_c^{+}(3885)$, $Z_c^{+}(3930)$, $Z_c^{+}(4020)$ or $Z_c^{+}(4025)$, $Z_1^{+}(4050)$, $Z_2^{+}(4250)$, and $Z_c^{+}(4200)$ can be uniformly described as tetraquark states $[cu][\bar{c}\bar{d}]$ with the quantum numbers $n^{2S+1}{L}_J$ and $J^P$ of $1^3{S}_1$ and $1^{+}$, $2^3{S}_1$ and $1^{+}$, $1^5{S}_2$ and $2^{+}$, $1^3{P}_1$ and $1^{-}$, $1^5{D}_1$ and $1^{+}$, and $1^3{D}_1$ and $1^{+}$, respectively. The predicted lowest charged tetraquark state $[cu][\bar{c}\bar{d}]$ with $0^{+}$ and $1^1{S}_0$ has a energy of $3780\pm 10$ MeV in the model. The tetraquark states are compact three-dimensional spatial configurations similar to a rugby ball, the higher orbital angular momentum $L$ between the diquark $[cu]$ and antidiquark $[\bar{c}\bar{d}]$, the more prolate of the states. The multibody color flux-tube, a collective degree of freedom, plays an important role in the formation of those charge tetraquark states. However, the two heavier charged states $Z_c^{+}(4430)$ and $Z_c^{+}(4475)$ can not be explained as tetraquark states $[cu][\bar{c}\bar{d}]$ in this model approach.

Comments: 6 pages, 5 tables