$D^{\ast }{\bar{D}}_1(2420)$ and $D{\bar{D}}^{\prime \ast }(2600)$ interactions and the charged charmonium-like state $Z(4430)$

Abstract

The $D^{\ast }{\bar{D}}_1(2420)$ and $D{\bar{D}}^{\prime \ast }(2600)$ interactions are studied in a one-boson-exchange model. Isovector bound state solutions with spin parity $J^P=1^{+}$ are found from the $D^{\ast }{\bar{D}}_1(2420)$ interaction, which may be related to the observed charged charmonium-like state $Z(4430)$. There is no bound state solution found from the $D{\bar{D}}^{\prime \ast }(2600)$ interaction.

6 pages, 1 tables, 2 figures