Radiative decays of the charmed mesons in a modified relativistic quark model

In the present work, we perform systematic estimations for the radiative decays of the charmed mesons in a modified relativistic quark model. Our estimations indicate that the branching ratios of the process of $D_2^0(1^3P_2) \to D^{\ast 0}(1^3S_1) \gamma$, $D_3^0(1D_3) \to D_2^0(1^3P_2) \gamma$, $D_2^0(2D_2^\prime) \to D_1^{0}(2P_1) \gamma$, $D_3^0(2^3D_3) \to D_2^0(2^3P_2) \gamma$, and $D^{\ast 0}(1^3S_1) \to D^0(1^1S_0) \gamma$ are of the order of $10^{-2}$, which are sizable to be detected experimentally. Moreover, the branching ratios of some channels, for example, $D_1^0(1P_1) \to D(1^1S_0)^0 \gamma$, $D^0(3^1S_0) \to D_1^{\prime 0}(2P^\prime_{1}) \gamma$ and $D^0(3^3S_1) \to D_2^0(2^3P_2) \gamma$ are estimated to be of the order of $10^{-3}$, which may be accessible with the accumulation of data in future experiments.