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$D_{s3}^*(2860)$ and $D_{s1}^*(2860)$ as the 1D $c\bar{s}$ states

In this article, we take the $D_{s3}^*(2860)$ and $D_{s1}^*(2860)$ as the $1^3{\rm D}_3$ and $1^3{\rm D}_1$ $c\bar{s}$ states, respectively, study their strong decays with the heavy meson effective theory by including the chiral symmetry breaking corrections. We can reproduce the experimental data ${\rm Br}\left(D_{sJ}^*(2860)\to D^*K\right)/{\rm Br}\left(D_{sJ}^*(2860)\to D K\right) =1.10 \pm 0.15 \pm 0.19$ with suitable hadronic coupling constants, the assignment of the $D_{sJ}^*(2860)$ as the $D_{s3}^*(2860)$ is favored, the chiral symmetry breaking corrections are large. Furthermore, we obtain the analytical expressions of the decay widths, which can be confronted with the experimental data in the future to fit the unknown coupling constants. The predictions of the ratios among the decay widths can be used to study the decay properties of the $D_{s3}^*(2860)$ and $D_{s1}^*(2860)$ so as to identify them unambiguously. On the other hand, if the chiral symmetry breaking corrections are small, the large ratio $R=1.10 \pm 0.15 \pm 0.19$ requires that the $D_{sJ}^*(2860)$ consists of at least four resonances $D_{s1}^*(2860)$, $D_{s2}^*(2860)$, $D_{s2}^{*\prime}(2860)$, $D_{s3}^*(2860)$.