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

TL;DR

This study uses a chiral quark model to analyze the possibility of $Z^+(4430)$ being a molecular state, finding it unlikely, but suggesting potential partner states and exploring bottom system molecules.

Contribution

It provides a detailed theoretical investigation of the molecular nature of $Z^+(4430)$ using the resonating group method within a chiral quark model, challenging previous molecular assumptions.

Findings

Preliminary results do not support $Z^+(4430)$ as a molecular state.

If $Z^+(4430)$ is molecular, partner states with opposite G-parity may exist.

Possible molecular states in bottom systems with specific quantum numbers.

Abstract

We investigated the bound state problem of the S wave charged $D_1 \bar{D}^*$ ($D_1' \bar{D}^*$) 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 $\psi'\pi^+\pi^0$ channel. For the bottom systems, we found the existence of both $I^G$=$1^+$ and $I^G$=$1^-$ $B_1 \bar{B}^*$ ($B_1' \bar{B}^*$) molecules is possible.