$Z^{+}(4430)$ as a resonance in the $D_1(D_1^{\mathrm{\prime }})D^{\ast }$ channel

We study the possibility that the $Z^{+}(4430)$ state observed by Belle is a $D_1{D}^{\ast }$ (or $D_1^{\mathrm{\prime }}{D}^{\ast }$) resonance in S-wave. Focusing on its decays, We find that the open-charm decay into $D^{\ast }{D}^{\ast }\pi$ is dominant. Furthermore, we use the re-scattering mechanism to study its hidden-charm decays and find that the re-scattering effects are significant in $D_1{D}^{\ast }$ channel but not in $D_1^{\mathrm{\prime }}{D}^{\ast }$ channel. For the $J^P=1^{-}$ candidate, with chosen parameters, we can get $\mathrm{\Gamma }(Z^{+}\to {\psi }^{\mathrm{\prime }}{\pi }^{+})\mathrm{/}\mathrm{\Gamma }(Z^{+}\to J\mathrm{/}\psi {\pi }^{+})\approx 5.3$, which tends to account for why the $Z^{+}(4430)$ is difficult to be found in $J\mathrm{/}\psi {\pi }^{+}$. However, the $0^{-}$ candidate can not be ruled out by our calculations.