Radiative decays of the neutral $Z_c(3900)$

We study the radiative decays of the $Z_c(3900)^0$ in a hadronic molecule picture, where the $Z_c(3900)$ is treated as a $D \bar{D}^\ast +c.c$ hadronic molecule. The partial widths of $\Gamma(Z_c(3900)^0 \to \gamma \eta_c(2S))$ and $\Gamma(Z_c(3900)^0 \to \gamma \chi_{c0})$ are predicted to be of order 10 keV and the cross sections for $\sigma(e^+ e^- \to \pi^0 Z_c(3900) \to \pi^0 \gamma \eta_c(2S))$ and $\sigma(e^+ e^- \to \pi^0 Z_c(3900) \to \pi^0 \gamma \chi_{c0})$ are of order 0.1 pb at 4.23 GeV, which may be accessible for the BESIII and forthcoming BelleII.