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Strong decays of newly observed $D_{sJ}$ states in a constituent quark model with effective Lagrangians

The strong decay properties of the newly observed states $D_{sJ}(3040)$, $D_{sJ}(2860)$ and $D_{sJ}(2710)$ are studied in a constituent quark model with quark-meson effective Lagrangians. We find that the $D_{sJ}(3040)$ could be identified as the low mass physical state $|2{P_1}>_L$ ($J^P=1^+$) from the $D_{s}(2^1P_1)$-$D_{s}(2^3P_1)$ mixing. The $D_{sJ}(2710)$ is likely to be the low-mass mixed state $|(SD)>_L$ via the $1^3D_1$-$2^3S_1$ mixing. In our model, the $D_{sJ}(2860)$ cannot be assigned to any single state with a narrow width and compatible partial widths to $DK$ and $D^*K$. Thus, we investigate a two-state scenario as proposed in the literature. In our model, one resonance is likely to be the $1^3D_3$ ($J^P=3^-$), which mainly decays into $DK$. The other resonance seems to be the $|1{D_2}'>_H$, i.e. the high-mass state in the $1^1D_2$-$1^3D_2$ mixing with $J^P=2^-$, of which the $D^*K$ channel is its key decay mode. We also discuss implications arising from these assignments and give predictions for their partner states such as $|(SD)'>_H$, $|2{P'_1}>_H$, $2^3P_0$ and $2^3P_2$, which could be helpful for the search for these new states in future experiment.