Comment on the Nature of the $D_{s1}^*(2710)$ and $D_{sJ}^*(2860)$ Mesons

Two charm-strange mesons, the $D_{s1}^*(2710)$ and the $D_{sJ}^*(2860)$, have recently been observed by several experiments. There has been speculation in the literature that the $D_{s1}^*(2710)$ is the $2^3S_1(c\bar{s})$ state and the $D_{sJ}^*(2860)$ is the $1^3D_1(c\bar{s})$ state. In this paper we explore this and other explanations in the context of the relativized quark model and the pseudoscalar emission decay model. We conclude that the $D_{s1}^*(2710)$ is most likely the $1^3D_1 (c\bar{s})$ state and the $D_{sJ}^*(2860)$ is most likely the $1^3D_3 (c\bar{s})$ state with the $1D_2$ resonances also contributing to the observed signals and explaining the observed ratios of branching ratios to $D^*K$ and $DK$ final states. We point out that measuring the $D_{sJ}^*(2860)$ spin can support or eliminate this explanation and that there are six excited $D_s$ states in this mass region; the $2^3S_1$, $2^1S_0$, $1^3D_1$, $1^3D_3$ and two $1D_2$ states. Observing some of the missing states would help confirm the nature of the $D_{s1}^*(2710)$ and the $D_{sJ}^*(2860)$ states.