Helicity-dependent generalization of the JIMWLK evolution
Helicity-dependent generalization of the JIMWLK evolution
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JIMWLK 演化的螺旋度相关泛化
作者：
Florian Cougoulic;Y. Kovchegov
我们将 JIMWLK 演化方程推广到包括螺旋度分布的小 $x$ 演化。为了推导螺旋度 JIMWLK，我们使用 A.H. Mueller 为通常的非极化 JIMWLK 设计的方法，并将其应用于之前推导的螺旋度演化方程。我们获得了广义 JIMWLK 权泛函的函数演化方程。现在泛函是螺旋性无关项和螺旋性相关项的总和。新的演化方程的核由标准映象前阶 JIMWLK 核加上包含亚映象夸克和胶子场导数的新项组成。我们推导出的新内核可用于生成标准 JIMWLK 演化，并为风味单线算子构建小 $x$ 演化方程，该算子由任意数量的光锥威尔逊线以及包含亚演导螺旋性相关局部算子插入的威尔逊线（“极化威尔逊线”）组成。
We generalize the JIMWLK evolution equation to include the small-$x$ evolution of helicity distributions. To derive helicity JIMWLK, we use the method devised by A.H. Mueller for the usual unpolarized JIMWLK, and apply it to the helicity evolution equations derived earlier. We obtain a functional evolution equation for the generalized JIMWLK weight functional. The functional now is a sum of a helicity-independent term and a helicity-dependent term. The kernel of the new evolution equation consists of the standard eikonal leading-order JIMWLK kernel plus new terms containing derivatives with respect to the sub-eikonal quark and gluon fields. The new kernel we derive can be used to generate the standard JIMWLK evolution and to construct small-$x$ evolution equations for flavor-singlet operators made of any number of light-cone Wilson lines along with one Wilson line containing sub-eikonal helicity-dependent local operator insertions (a "polarized Wilson line").