Dynamical mixing between $2^3{S}_1$ and $1^3{D}_1$ charmed mesons

Abstract

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 $D_1^{\ast }(2635)$, $D_1^{\ast }(2739)$, $D_{s1}^{\ast }(2715)$ and $D_{s1}^{\ast }(2805)$ 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 $D_1^{\ast }(2635)$ and $D_{s1}^{\ast }(2715)$ are close in mass to $D_J^{\ast }(2600)$ and $D_{s1}^{\ast }(2700)$, while the two heavy mixed states $D_1^{\ast }(2739)$ and $D_{s1}^{\ast }(2805)$ are lighter in mass than $D(2750)$ and $D_{s1}^{\ast }(2860)$. 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, $D_J^{\ast }(2600)$, $D(2750)$, $D_{s1}^{\ast }(2700)$ and $D_{s1}^{\ast }(2860)$ are impossibly the mixed states of $2^3{S}_1$ and $1^3{D}_1$ at the small mixing angles. The inconsistence implies that $D_1^{\ast }(2760)$ and $D_{s1}^{\ast }(2860)$ have not been properly resolved from present experimental data, or there exist large unknown off-diagonal interactions that result in large mixing angles.

arXiv comment8 pages, 1 figure, PDFLatex, to appear in Phys.Rev.D

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Cited by in corpus (2)

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