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 $D_2^0(1^3{P}_2)\to D^{\ast 0}(1^3{S}_1)\gamma$, $D_3^0(1D_3)\to D_2^0(1^3{P}_2)\gamma$, $D_2^0(2D_2^{\mathrm{\prime }})\to D_1^0(2P_1)\gamma$, $D_3^0(2^3{D}_3)\to D_2^0(2^3{P}_2)\gamma$, and $D^{\ast 0}(1^3{S}_1)\to D^0(1^1{S}_0)\gamma$ are of the order of ${10}^{-2}$, which are sizable to be detected experimentally. Moreover, the branching ratios of some channels, for example, $D_1^0(1P_1)\to D(1^1{S}_0{)}^0\gamma$, $D^0(3^1{S}_0)\to D_1^{\mathrm{\prime }0}(2P_1^{\mathrm{\prime }})\gamma$ and $D^0(3^3{S}_1)\to D_2^0(2^3{P}_2)\gamma$ are estimated to be of the order of ${10}^{-3}$, which may be accessible with the accumulation of data in future experiments.