$Z^+(4430)$ as a resonance in the $D_1(D_1^\prime)D^*$ channel

Abstract

We study the possibility that the $Z^+(4430)$ state observed by Belle is a $D_1D^*$ (or $D_1'D^*$) resonance in S-wave. Focusing on its decays, We find that the open-charm decay into $D^*D^*\pi$ 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 $D_1D^*$ channel but not in $D_1'D^*$ channel. For the $J^P=1^-$ candidate, with chosen parameters, we can get $\Gamma(Z^+\to\psi'\pi^+)/\Gamma(Z^+\to J/\psi\pi^+)\thickapprox 5.3$, which tends to account for why the $Z^+(4430)$ is difficult to be found in $J/\psi\pi^+$. However, the $0^-$ candidate can not be ruled out by our calculations.