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 $D^*_1(2600)/D^*_{s1}(2700)$ and $D^*_1(2760)/D^*_{s1}(2860)$ are predominantly the $2^3S_1$ and $1^3D_1$ charmed/charmed-strange mesons, respectively, while $D_3^*(2760)/D_{s3}^*(2860)$ can be regarded as the $1^3D_3$ 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 $D^*_1(2600)/D^*_1(2760)$ and $D^*_{s1}(2700)/D^*_{s1}(2860)$.