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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 $Γ(Z_c(3900)^0 \to γη_c(2S))$ and $Γ(Z_c(3900)^0 \to γχ_{c0})$ are predicted to be of order 10 keV and the cross sections for $σ(e^+ e^- \to π^0 Z_c(3900) \to π^0 γη_c(2S))$ and $σ(e^+ e^- \to π^0 Z_c(3900) \to π^0 γχ_{c0})$ are of order 0.1 pb at 4.23 GeV, which may be accessible for the BESIII and forthcoming BelleII.