In charmed $D$ and $D_s$ mesons sector, the matrix of a Hamiltonian in a quark potential model is computed in the $2^3{S}_1$ and $1^3{D}_1$ subspace. The masses of four mixed states of $2^3{S}_1$ and $1^3{D}_1$ denoted with $D_1^{*}(2635)$, $D_1^{*}(2739)$, $D_{s1}^{*}(2715)$ and $D_{s1}^{*}(2805)$ are obtained. It is an off-diagonal part of the spin-orbit tensor interaction that causes the mixing between the $2^3{S}_1$ and $1^3{D}_1$ states. The mixing angles between the $2^3{S}_1$ and $1^3{D}_1$ states are tiny. Under the mixing, a ${}^3{P}_0$ model is employed to compute the hadronic decay widths of all OZI-allowed decay channels 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 $D_{s1}^{*}(2700)$, while the two heavy mixed states $D_1^{*}(2739)$ and $D_{s1}^{*}(2805)$ are lighter in mass than $D(2750)$ and $D_{s1}^{*}(2860)$. The mixing angles obtained from dynamical interaction are inconsistent with the mixing angles obtained from hadronic decay. Based on mass spectra and hadronic decay analyses, $D_J^{*}(2600)$, $D(2750)$, $D_{s1}^{*}(2700)$, and $D_{s1}^{*}(2860)$ are impossibly the mixed states of $2^3{S}_1$ and $1^3{D}_1$ at the small mixing angles. The inconsistence implies that $D_1^{*}(2760)$ and $D_{s1}^{*}(2860)$ have not been properly resolved from present experimental data, or there exist large unknown off-diagonal interactions that result in large mixing angles.

• Received 1 June 2020
• Accepted 31 August 2020

DOI:https://doi.org/10.1103/PhysRevD.102.054013

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Published by the American Physical Society