Distinguishing cusp effects and near-threshold-pole effects

Abstract: We make use of a unitarized coupled-channel model to analyze the mass distribution data of final states in production processes of $X(4260)$. By analyzing the analytical structures of the decay amplitudes, we find that the line shape of $Z_c(3900)$ signal is related to the combined effect of a pair of near-threshold "shadow" poles and the $(D\bar{D}^*)^\pm$ thresholds, in which the third-sheet pole might provide a dominant contribution. As all the coupled channels effects are tuning off, the trajectories of these two poles suggest that the $Z_c(3900)$ might originate from the attractive interaction of $(D^\bar{D}^)^\pm$ through a long-distance interaction, $e.g.$ $\pi$-exchange interaction, as a "deuteron-like" state. There is no nearby pole structure corresponding to the $Z_c(4025)$ signal in the $(D^\bar{D}^)^\pm$ mass distribution.