Can the state $Y(4626)$ be a $P$-wave tetraquark state $[cs][\bar{c}\bar{s}]$?

Abstract

Stimulated by the state $Y(4626)$ recently reported by Belle Collaboration, we utilize a multiquark color flux-tube model with a multibody confinement potential and one-glue-exchange interaction to make an exhaustive investigation on the diquark-antidiquark state $[cs][\bar{c}\bar{s}]$. Numerical results indicate that the appearance of the states $[cs][\bar{c}\bar{s}]$ like a dumb-bell, the larger the orbital excitation $L$, the more distinguished the shape. The mixing of the color configurations ${\left[[cs{]}_{{\bar{3}}_c}[\bar{c}\bar{s}{]}_{3_c}\right]}_1$ and ${\left[[cs{]}_{6_c}[\bar{c}\bar{s}{]}_{{\bar{6}}_c}\right]}_1$ in the ground states is strong while the color configuration ${\left[[cs{]}_{{\bar{3}}_c}[\bar{c}\bar{s}{]}_{3_c}\right]}_1$ is absolutely predominant in the excited states. The main component of the state $Y(4626)$ can be interpreted as a $P$-wave state $[cs][\bar{c}\bar{s}]$. Its hidden-bottom partner is predicted in the model calculation. The states $X(4140)$, $X(4274)$, $X(4350)$, $X(4500)$ and $X(4700)$ are also discussed.