A chiral quark model study of $Z^{+}(4430)$ in the molecular picture

Abstract

We investigated the bound state problem of the S wave charged $D_1{\bar{D}}^{\ast }$ ($D_1^{\prime }{\bar{D}}^{\ast }$) system in a chiral quark model by solving the resonating group method equation. Our preliminary study does not favor the molecular assumption of $Z^{+}(4430)$. On the contrary, if $Z^{+}(4430)$ is really a molecule, its partner with opposite $G$-parity should also exist and probably may be found in the ${\pi }^{+}{\eta }_c(2S)$, $J/\psi {\pi }^{+}{\pi }^0$, or ${\psi }^{\prime }{\pi }^{+}{\pi }^0$ channel. For the bottom systems, we found the existence of both $I^G$=$1^{+}$ and $I^G$=$1^{-}$ $B_1{\bar{B}}^{\ast }$ ($B_1^{\prime }{\bar{B}}^{\ast }$) molecules is possible.

Comments: 6 pages, 3 figures