AI 中文总结
本论文发展微扰QCD的解析方法，涵盖角积分、一圈积分结构及横向动量展开等，以提升对撞机现象学和质子结构相关辐射修正与尺度演化的解析控制。
AI 中文摘要
在当代对撞机可达到的最短距离上，自然界的性质由粒子物理标准模型以非凡的精度描述。自2012年发现希格斯玻色子以来，研究进展已从寻找新共振转向对既有理论的精确研究。在此，描述夸克与胶子相互作用的量子色动力学（QCD）扮演着核心角色。涉及强子的对撞机观测量通过因子化在理论上变得可处理，因子化将编码在部分子分布中的普适长距离强子动力学与可在微扰论中计算的特定过程短距离系数分离开来。\n本论文发展了微扰QCD的解析方法，并将其应用于对撞机唯象学和质子结构。主要部分致力于角积分，这是相空间积分的关键构建模块。最初为费曼积分发展的方法，包括分部积分恒等式、区域展开、微分方程和维度平移，被改编应用于角积分并产生了若干新结果。还研究了一圈积分的解析结构，使用单值多对数消除了虚假支点割线，从而得到了半单举深度非弹性散射系数函数的紧凑表示。发展了横向动量高次幂的系统性展开，并将其应用于Drell-Yan过程，深化了对其因子化结构的理解。最后，探索了一种用于部分子分布演化的新半解析ansatz。总之，这些方法提高了对辐射修正、运动学依赖性以及在与电子-离子对撞机及其他对撞机实验相关过程中的尺度演化的解析控制能力。
英文摘要
Nature, at the shortest distances accessible to contemporary colliders, is described by the Standard Model of particle physics with remarkable precision. Since the discovery of the Higgs boson in 2012, progress has shifted from finding new resonances to precision studies of established theory. Here, quantum chromodynamics (QCD), describing the interactions of quarks and gluons, plays a central role. Collider observables involving hadrons are made theoretically accessible by factorization, which separates universal long-distance hadron dynamics encoded in parton distributions from process-specific short-distance coefficients calculable in perturbation theory. This thesis develops analytic methods for perturbative QCD with applications to collider phenomenology and proton structure. A major part is devoted to angular integrals, key building blocks of phase-space integrals. Methods originally developed for Feynman integrals, including integration-by-parts identities, expansion by regions, differential equations, and dimensional shifts, are adapted to angular integrals and yield several new results. The analytic structure of one-loop integrals is also studied, with spurious branch cuts removed using single-valued polylogarithms, leading to a compact representation of coefficient functions for semi-inclusive deep-inelastic scattering. A systematic expansion in higher powers of transverse momentum is developed and applied to the Drell-Yan process, refining the understanding of its factorization structure. Finally, a new semi-analytical ansatz for the evolution of parton distributions is explored. Together, these methods improve analytic control over radiative corrections, kinematic dependence, and scale evolution in processes relevant to the Electron-Ion Collider and other collider experiments.
CommentsPhD thesis, University of Tübingen, 2025. 509 pages; includes 10 reprints of publications. Based on material from 2102.08943, 2211.14110, 2302.01956, 2403.09773, 2403.18741, 2404.18667, 2405.13120, 2410.18177, 2505.18109, and 2508.00693
DOI：10.15496/publikation-124834
