AI 中文总结
该研究推导了自旋-1强子中夸克自旋-轨道关联的两条规范不变求和规则，分别给出非极化靶及具有自旋-0、自旋-1/2靶无的张量极化依赖的关联，并估算了ρ介子和氘核的非极化自旋-轨道关联。
AI 中文摘要
夸克自旋-轨道关联探测强子内部夸克螺旋度与纵向动能轨道角动量的对齐情况，该关联由量子色动力学（QCD）算符定义：即宇称奇的夸克能量-动量张量的位置矩。该二阶张量的矩阵元可分解为无迹对称部分、反对称部分和迹部分；其中无迹对称部分与轴向广义部分子分布的矩匹配，反对称部分通过QCD运动方程与矢量和张量形状因子关联，迹部分被设为零。利用这些关联，我们推导了自旋-1强子中自旋-轨道关联的两条规范不变求和规则：一条给出非极化靶中的关联，另一条给出其张量极化依赖关系（自旋-0和自旋-1/2靶无此依赖）。我们分别利用现有格点输入和唯象学输入估算了ρ介子和氘核的非极化自旋-轨道关联。
英文摘要
The quark spin-orbit correlation probes the alignment of quark helicity with longitudinal kinetic orbital angular momentum inside a hadron. This correlation is defined by a QCD operator: the position moment of the asymmetric parity-odd quark energy-momentum tensor. The matrix element of this rank-two tensor decomposes into symmetric-traceless, antisymmetric, and trace parts. The symmetric-traceless part is matched to moments of axial generalized parton distributions. The QCD equations of motion relate the antisymmetric part to vector and tensor form factors and set the trace to zero. Using these relations, we derive two gauge-invariant sum rules for the spin-orbit correlation in a spin-$1$ hadron. One gives the correlation in an unpolarized target. The other gives its tensor-polarization dependence, which is absent for spin-$0$ and spin-$1/2$ targets. We estimate the unpolarized spin-orbit correlations for the $ρ$ meson and deuteron using existing lattice and phenomenological inputs, respectively.
Comments8 pages
