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arXiv 2006.01347hep-phhep-ex
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$2^3S_1$和$1^3D_1$粲介子的动力学混合

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

Hao Yu, Ze Zhao, Ailin Zhang

备注：
8 pages, 1 figure, PDFLatex, to appear in Phys.Rev.D
发表信息：
Phys. Rev. D 102, 054013 (2020)
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摘要：

在粲$D$和$D_s$介子扇区中，在$2^3S_1$和$1^3D_1$子空间中计算了夸克势模型中哈密顿量的矩阵。计算了$2^3S_1$和$1^3D_1$四种混合态的质量，记作$D^*_1(2635)$、$D^*_1(2739)$、$D^*_{s1}(2715)$和$D^*_{s1}(2805)$。它是自旋轨道张量相互作用的非对角部分，导致$2^3S_1$和$1^3D_1$态之间的混合。$2^3S_1$和$1^3D_1$态之间的混合角很小。在混合条件下，采用$^3P_0$模型计算了四个混合态的OZI允许衰变通道的强子衰变宽度。两个轻混合态$D^*_1(2635)$和$D^*_{s1}(2715)$的质量接近于$D^*_J(2600)$和$D^*_{s1}(2700)$，而两个重混合态$D^*_1(2739)$和$D^*_{s1}(2805)$的质量比$D(2750)$和$D^*_{s1}(2860)$轻。由动力学相互作用得到的混合角与由强子衰变得到的混合角不一致。根据质谱和强子衰变分析，$D^*_J(2600)$，$D(2750)$，$D^*_{s1}(2700)$和$D^*_{s1}(2860)$在小混合角下不可能是$2^3S_1$和$1^3D_1$的混合态.这种不一致性意味着$D^*_1(2760)$和$D^*_{s1}(2860)$还没有从现有的实验数据中得到正确的解决，或者存在导致大混合角的大的未知的非对角相互作用。

英文摘要：

In charmed $D$ and $D_s$ mesons sector, the matrix of a Hamiltonian in a quark potential model is computed in the $2^3S_1$ and $1^3D_1$ subspace. The masses of four mixed states of $2^3S_1$ and $1^3D_1$ denoted with $D^*_1(2635)$, $D^*_1(2739)$, $D^*_{s1}(2715)$ and $D^*_{s1}(2805)$ are obtained. It is an off-diagonal part of the spin-orbit tensor interaction that causes the mixing between the $2^3S_1$ and $1^3D_1$ states. The mixing angles between 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 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 $2^3S_1$ and $1^3D_1$ 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.

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