Distinguishing cusp effects and near-threshold-pole effects

TL;DR

This paper uses a unitarized coupled-channel model to analyze the origin of the $Z_c(3900)$ and $Z_c(4025)$ signals, revealing that $Z_c(3900)$ is linked to near-threshold poles and long-range interactions, while $Z_c(4025)$ lacks such pole structures.

Contribution

It introduces a detailed analysis of the $Z_c(3900)$ and $Z_c(4025)$ signals using a coupled-channel approach, highlighting the role of near-threshold poles and long-distance interactions.

Findings

$Z_c(3900)$ is associated with near-threshold shadow poles and threshold effects.

$Z_c(3900)$ may originate from long-range $(D^*ar{D}^*)^ ext{±}$ interactions.

No pole structure is found for $Z_c(4025)$ in the $(D^*ar{D}^*)^ ext{±}$ mass distribution.

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.