Combined fit to the cross sections of $e^+e^- \rightarrow \pi Z_c(3900) \rightarrow \pi\pi J/\psi$ and $e^+e^- \rightarrow \pi Z_c(3900) \rightarrow \pi D\bar{D}^{*}$

TL;DR

This paper reports measurements of cross sections for $e^+e^- ightarrow ext{pi} Z_c(3900)$ decays into $ ext{pi} ext{pi} J/ ext{psi}$ and $ ext{pi} Dar{D}^*$, performing combined fits to determine the structure's properties and exploring the possibility of multiple resonances.

Contribution

The study provides a combined fit to the cross sections with one Breit-Wigner function and explores the potential for a second structure, offering new insights into the $Z_c(3900)$ resonance.

Findings

Mass of the structure: 4232 MeV/$c^2$

Width of the structure: 65 MeV

Branching ratio: (16±6)

Abstract

The cross sections of $e^+e^- \rightarrow \pi Z_c(3900) \rightarrow \pi\pi J/\psi$ and $e^+e^- \rightarrow \pi Z_c(3900) \rightarrow \pi D\bar{D}^{*}$ have been measured by BESIII experiment. We try to perform a combined fit to the cross sections with one Breit-Wigner function, the fit results show the structure's mass and width are $M=(4232\pm5)$ MeV/$c^2$, $\Gamma=(65\pm21)$ MeV. The ratio $\frac{\mathcal{B}(Z_c(3900)\rightarrow D\bar{D}^{*})}{\mathcal{B}(Z_c(3900)\rightarrow\pi J/\psi)}$ is determined to be $(16\pm6)$. We also try to fit the cross sections with two Breit-Wigner functions, while we can't come to any definitive conclusions about the second structure. More measurements are desired to improve the understanding of $e^+e^- \rightarrow \pi Z_c(3900)$ line shape.