Combined study of $2S$ and $1D$ open-charm mesons with natural spin-parity

In this paper, we perform a combined study of $2S$ and $1D$ open-charm mesons with natural spin-parity. Our results indicate that $D_1^{\ast }(2600)\mathrm{/}{D}_{s1}^{\ast }(2700)$ and $D_1^{\ast }(2760)\mathrm{/}{D}_{s1}^{\ast }(2860)$ are predominantly the $2^3{S}_1$ and $1^3{D}_1$ charmed/charmed-strange mesons, respectively, while $D_3^{\ast }(2760)\mathrm{/}{D}_{s3}^{\ast }(2860)$ can be regarded as the $1^3{D}_3$ charmed/charmed-strange mesons. In addition, some typical ratios of partial widths of the discussed natural states are predicted, by which future experiments can test these assignments, especially for the $2S$-$1D$ mixing scheme existing in $D_1^{\ast }(2600)\mathrm{/}{D}_1^{\ast }(2760)$ and $D_{s1}^{\ast }(2700)\mathrm{/}{D}_{s1}^{\ast }(2860)$.