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

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.