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 $2{}^3{S}_1(c\overline{s})$ state and the $D_{sJ}^{*}(2860)$ is the $1{}^3{D}_1(c\overline{s})$ 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 $1{}^3{D}_1(c\overline{s})$ state and the $D_{sJ}^{*}(2860)$ is most likely the $1{}^3{D}_3(c\overline{s})$ 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 $2{}^3{S}_1$, $2{}^1{S}_0$, $1{}^3{D}_1$, $1{}^3{D}_3$ and two $1D_2$ states. Observing some of the missing states would help confirm the nature of the $D_{s1}^{*}(2710)$ and $D_{sJ}^{*}(2860)$ states.

Figure 1

The $D_s$ mass spectrum. The mixed $L_{J=L}$ states are described by Eq. (7) with the primed states in the figure corresponding to the primed mixed state in Eq. (7) and the following mixing angles: ${\theta }_{1P}^{c\overline{s}}=-37.5°$, ${\theta }_{2P}^{c\overline{s}}=-30.4°$, ${\theta }_{1D}^{c\overline{s}}=-38.5°$, ${\theta }_{2D}^{c\overline{s}}=-37.7°$ and ${\theta }_{1F}^{c\overline{s}}=-39.3°$.

Figure 2

Decay widths and the ratios $\mathrm{\Gamma }(D^{*}K)/\mathrm{\Gamma }(DK)$ of the $D_{s1}^{*}(2700{)}^{\pm }$ and the $D_{sJ}^{*}(2860{)}^{\pm }$ assuming they are linear combinations of the $2{}^3{S}_1$ and $1{}^3{D}_1$ $c\overline{s}$ states as a function of the $2{}^3{S}_1-1{}^3{D}_1$ mixing angle defined in the text. The shaded regions are the $1-\sigma$ ranges for the experimental measurements. (a) and (b) are for the $D_{s1}^{*}(2700)$ state and (c) and (d) for the $D_{sJ}^{*}(2860)$ state. In (a) and (c) the solid lines are for the total widths, the long-dashed line for $DK$, dot-dashed for $D^{*}K$, short-dashed for $D_s\eta$ and dash-dot-dot for $D_s^{*}\eta$ final states. [The $D_{s1}^{*}(2700)\to D_s^{*}\eta$ partial width is too small to show up in (a).]