Abstract We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone z 2 → 0 limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the ln ⁡ ( − z 2 ) -dependence at short distances z 2 . The UV terms cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF. We also show that our results may be used for a rather straightforward calculation of the one-loop matching relations for quasi-PDFs.

中文翻译：

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短距离的胶子伪分布：前向情况

摘要 我们介绍了伪 PDF 方法中胶子部分子分布函数 (PDF) 正在进行的晶格计算所必需的结果。我们给出了可能的双胶子相关函数的分类，并确定了那些包含确定光锥 z 2 → 0 限制中胶子 PDF 的不变振幅的函数。已经在坐标表示和明确的规范不变形式中执行了单循环计算。我们努力在短距离 z 2 处分离 ln ⁡ ( − z 2 ) 依赖的紫外 (UV) 和红外 (IR) 源。UV 项在缩减的 Ioffe 时间分布 (ITD) 中抵消，我们得到缩减的 ITD 和光锥 ITD 之间的匹配关系。使用内核形式，我们得到了简化 ITD 的晶格数据和归一化胶子 PDF 之间的直接联系。我们还表明，我们的结果可用于对准 PDF 的单循环匹配关系进行相当直接的计算。