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

Abstract

The cross sections of $e^{+}{e}^{-}\to \pi Z_c(3900)\to \pi \pi J/\psi$ and $e^{+}{e}^{-}\to \pi Z_c(3900)\to \pi D{\bar{D}}^{\ast }$ 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 $M=(4232\pm 5)$ MeV/$c^2$, $\Gamma =(65\pm 21)$ MeV. The ratio $\frac{\mathcal{B}(Z_c(3900)\to D{\bar{D}}^{\ast })}{\mathcal{B}(Z_c(3900)\to \pi J/\psi )}$ is determined to be $(16\pm 6)$. 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 $e^{+}{e}^{-}\to \pi Z_c(3900)$ line shape.