The line shape of the radiative open-charm decay of Y(4140) and Y(3930)

In this work, we study the radiative open-charm decays $Y(4140)\to {D}s^{\ast+} D_s^- \gamma$and$Y(3930)\to{D}^{\ast+} D^-\gamma$ under the assignments of $D_s^{\ast }{\bar{D}}_s^{\ast }$ and $D^{\ast }{\bar{D}}^{\ast }$ as molecular states for Y(4140) and Y(3930) respectively. Based on our numerical result, we propose the experimental measurement of the photon spectrum of $Y(4140)\to {D}s^{\ast+} D_s^- \gamma, D{s}^+D{s}^{*-}\gamma$and$Y(3930)\to D^{0}\bar{D}^0\gamma, D^{0}\bar{D}^{0}\gamma, D^{+}D^-\gamma, D^+D^{-}\gamma$ can further test the molecular assignment for Y(4140) and Y(3930).