A Three-Coupled-Channel Analysis of $Z_c(3900)$ Involving $D{\bar{D}}^{\ast }$, $\ddot{I}€J/\ddot{I}ˆ$, and $\ddot{I}\hat{I}{\cdot }_c$

Abstract

In this work, we conduct a three-coupled-channel analysis of the $Z_c(3900)$ structure, focusing on the $D{\bar{D}}^{\ast }$, $J/\ddot{I}ˆ\ddot{I}€$, and $\ddot{I}\hat{I}{\cdot }_c$ channels, based on the one-boson exchange model. Drawing from previous study on the exotic state $T_{cc}$, we only utilize one more parameter to construct the interactions between the channels. Our model successfully reproduces the experimental line shapes of the invariant mass distribution at $\sqrt{s}=4.23$ and $4.26$ GeV for the three channels. Additionally, the finite-volume energy levels in our model show agreement with current LQCD conclusion. Detailed analysis suggests that the $Z_c(3900)$ peaks in the $\ddot{I}€J/\ddot{I}ˆ$ and $\ddot{I}\hat{I}{\cdot }_c$ distributions primarily arise from the triangle loop involving the $D_1\bar{D}{D}^{\ast }$ intermediate system. In the $D{\bar{D}}^{\ast }$ distribution, the threshold peak is generated by the cascade decay mechanism enhanced by a triangle diagram. Moreover, we find a virtual pole located far from the threshold, indicating that $Z_c(3900)$ peaks are not associated with physical pole. We conclude that the $Z_c(3900)$ peaks are predominantly caused by the threshold cusp.