AI 中文总结
研究标量和自旋-2核子结构的色电和色磁匹配，构建RG一致实现，利用QCD迹恒等式等方法，明确分解成立假设，将夸克偶素匹配与核子结构分开，给出相关投影与表示关系。
AI 中文摘要
紧凑重夸克偶素通过多极相互作用与标量和自旋-2胶子算符耦合。在领先色电阶，相应的匹配系数满足\(C_2^\Phi=-C_S^\Phi\)；一个独立的色磁极化率在一般CP偶数、自旋无关、四维零导数阶的局部双胶子相互作用中打破了这种关系。我们在固定的\(MS\)规约下构建了一个RG一致的实现。QCD迹恒等式将仅胶子的标量匹配条件转换为不变基，并确定了在远离匹配标度的依赖标度基中重新表达相互作用时所需的相关夸克质量系数，而领先对数单态演化诱导了一个夸克自旋-2系数。在阈值对齐对称运动学中，规范自旋非翻转投影包含\(A_i(t)\)和组合\(3B_i(t)-D_i(t)\)。一个明确的Breit框架计算将此投影与非零类空\(t\)的非对角螺旋度表示相关联；非对角形式是运动学的而非额外的动力学自旋翻转。标量和自旋-2演化的线性将它们比率的色磁依赖性分解为\(R_{2/0}^{\Phi}(t;\rho_\Phi)=[(1+\rho_\Phi)/(1-\rho_\Phi)]R_{2/0}^{\Phi}(t;0)\)在仅胶子的四维匹配设置中。结果将依赖态的夸克偶素匹配与标量和引力核子结构分开，并明确说明了这种分解成立的假设。
英文摘要
Compact heavy quarkonium couples through the multipole interaction to scalar and spin-two gluonic operators. At leading chromoelectric order the corresponding matching coefficients satisfy $C_2^Φ=-C_S^Φ$; an independent chromomagnetic polarizability lifts this relation within the general CP-even, spin-independent, local two-gluon interaction at dimension four and zero derivative order. We construct an RG-consistent realization in a fixed $MS$ convention. The QCD trace identity converts the gluon-only scalar matching condition into an invariant basis and fixes the correlated quark-mass coefficient required when the interaction is re-expressed in the scale-dependent basis away from the matching scale, whereas leading-logarithmic singlet evolution induces a quark spin-two coefficient. In threshold-aligned symmetric kinematics, the canonical-spin non-flip projection contains $A_i(t)$ and the combination $3B_i(t)-D_i(t)$. An explicit Breit-frame calculation relates this projection to an off-diagonal helicity representation for nonzero spacelike $t$; the off-diagonal form is kinematic rather than an additional dynamical spin flip. Linearity of the scalar and spin-two evolution factorizes the chromomagnetic dependence of their ratio as $R_{2/0}^Φ(t;ρ_Φ)=[(1+ρ_Φ)/(1-ρ_Φ)]R_{2/0}^Φ(t;0)$ within the gluon-only dimension-four matching setup. The result separates state-dependent quarkonium matching from scalar and gravitational nucleon structure and states explicitly the assumptions under which this factorization holds.
Comments10 pages, 1 figure
