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 $D_{s}^*\bar{D}_s^*$ and $D^*\bar{D}^*$ 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).Comment: 4 pages, 4 figures. More references and discussions added, typos corrected. Accepted by Phys. Rev.