The electron, positron, and photon Parton Distribution Functions (PDFs) of the unpolarised electron have recently been computed at the next-to-leading logarithmic accuracy in QED, by adopting the \( \overline{\mathrm{MS}} \) factorisation scheme. We present here analogous results, obtained by working in a different framework that is inspired by the so-called DIS scheme. We derive analytical solutions relevant to the large-z region, where we show that the behaviour of the PDFs depends in a dramatic way on whether running-α effects are included to all orders, as opposed to being truncated to some fixed order. By means of suitable initial and evolution conditions, next-to-leading logarithmic accurate PDFs are obtained whose large-z functional forms are identical to those of their leading logarithmic counterparts.

通过采用\( \overline{\mathrm{MS}} \)因式分解，最近以 QED 中次领先的对数精度计算了未极化电子的电子、正电子和光子部分分布函数 (PDF)方案。我们在这里展示了类似的结果，这些结果是通过在受所谓的 DIS 方案启发的不同框架中工作而获得的。我们推导出与大z区域相关的解析解，我们表明 PDF 的行为以戏剧性的方式取决于运行-α效应是否包含在所有顺序中，而不是被截断为某个固定顺序。通过合适的初始条件和演化条件，获得次领先的对数精确 PDF，其大z 函数形式与它们的主要对数对应形式相同。