QED下次领头阶（NNLO）的电子部分子分布函数
The electron parton distribution functions at the NNLO in QED
AI总结：
本研究在QED NNLO阶下计算电子PDFs，推广$\Delta$因子化方案至所有阶，发现该方案可消除$\rm\overline{MS}$方案中的软对数增强，能降低计算复杂度，且NNLO PDFs对百GeV对撞机达$10^{-4}$精度必要。
AI中文摘要：
电子部分子分布函数（PDFs）是轻子对撞机共线因子化框架下截面计算的核心组成部分。我们在量子电动力学（QED）的次次领头阶（NNLO）下，采用两种不同的因子化方案计算这些分布函数：标准的$\rm\overline{MS}$方案，以及最初在次领头阶下定义、本工作中将其定义推广至所有阶的所谓$\Delta$方案。我们给出了两种因子化方案下与PDFs的大$z$行为相关的解析结果，由此表明$\rm\overline{MS}$电子PDF的软对数增强效应在$\Delta$方案中完全不存在。因此，$\Delta$方案是一种自然的选择，不仅能显著降低唯象应用中数值模拟的复杂度，还能大幅减少实现物理可观测量软重整化所需的解析计算的复杂度。我们指出，对于质心能量处于百GeV量级的对撞机，要达到$10^{-4}$或更高的相对精度目标，NNLO阶的PDFs是必不可少的。
英文摘要：
The electron Parton Distribution Functions (PDFs) are essential components in the calculations of cross sections within a collinear-factorisation framework at lepton colliders. We compute them at the next-to-next-to-leading order (NNLO) in QED by working in two different factorisation schemes, namely the standard $\overline{\rm MS}$ one and the so-called $Δ$ scheme, which was originally defined at the next-to-leading order, and which we generalise in this work by extending its definition to all orders. We present analytical results relevant to the large-$z$ behaviour of the PDFs in both factorisation schemes, and thus show how the soft-logarithm enhancement of the $\overline{\rm MS}$ electron PDF is completely absent in the $Δ$ scheme. The latter therefore constitutes a natural choice that helps significantly reduce the complexity not only of numerical simulations in phenomenological applications, but also that of analytical computations necessary to achieve the soft resummation of physical observables. We argue that NNLO PDFs are necessary to attain relative-precision targets of $10^{-4}$ or better, for colliders whose centre-of-mass energies are in the hundred-GeV range.
