Study on radiative decays of D^*_(sJ)(2860) and D^*_(s1)(2710) into D_s by means of LFQM

The observed resonance peak around 2.86 GeV has been carefully reexamined by the LHCb collaboration and it is found that under the peak there reside two states $D^*_{s1}(2860)$ and $D^*_{s3}(2860)$ which are considered as $1^3D_1(c\bar s)$ and $1^3D_3(c\bar s)$ with slightly different masses and total widths. Thus, the earlier assumption that the resonance $D^*_{s1}(2710)$ was a $1D$ state should not be right. We suggest to measure the partial widths of radiative decays of $D^*_{sJ}(2860)$ and $D^*_{s1}(2710)$ to confirm their quantum numbers. We would consider $D^*_{s1}(2710)$ as $2^3S_1$ or a pure $1^3D_1$ state, or their mixture and respectively calculate the corresponding branching ratios as well as those of $D^*_{sJ}(2860)$. The future precise measurement would provide us information to help identifying the structures of those resonances .