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In charmed $D$ and $D_s$ mesons sector, the matrix of a Hamiltonian in aquark potential model is computed in the $2^3S_1$ and $1^3D_1$ subspace. Themasses of four mixed states of $2^3S_1$ and $1^3D_1$ denoted with$D^*_1(2635)$, $D^*_1(2739)$, $D^*_{s1}(2715)$ and $D^*_{s1}(2805)$ areobtained. It is an off-diagonal part of the spin-orbit tensor interaction thatcauses the mixing between the $2^3S_1$ and $1^3D_1$ states. The mixing anglesbetween the $2^3S_1$ and $1^3D_1$ states are tiny. Under the mixing, a $^3P_0$model is employed to compute the hadronic decay widths of all OZI-allowed decaychannels of the four mixed states. The two light mixed states $D^*_1(2635)$ and$D^*_{s1}(2715)$ are close in mass to $D^*_J(2600)$ and $D^*_{s1}(2700)$, whilethe two heavy mixed states $D^*_1(2739)$ and $D^*_{s1}(2805)$ are lighter inmass than $D(2750)$ and $D^*_{s1}(2860)$. The mixing angles obtained fromdynamical interaction are inconsistent with the mixing angles obtained fromhadronic decay. Based on mass spectra and hadronic decay analyses,$D^*_J(2600)$, $D(2750)$, $D^*_{s1}(2700)$ and $D^*_{s1}(2860)$ are impossiblythe mixed states of $2^3S_1$ and $1^3D_1$ at the small mixing angles. Theinconsistence implies that $D^*_1(2760)$ and $D^*_{s1}(2860)$ have not beenproperly resolved from present experimental data, or there exist large unknownoff-diagonal interactions that result in large mixing angles.

Dynamical mixing between $2^3S_1$ and $1^3D_1$ charmed mesons