Analytic continuation of Mellin transforms up to two-loop order

Abstract The analytic continuation of the Mellin transforms to complex values of N for the basic functions g_i (x) of the momentum fraction x emerging in the quantities of massless QED and QCD up to two-loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space- and time-like momentum transfer are evaluated. These Mellin transforms provide the analytic continuations of all finite harmonic sums up to the level of the threefold s... Title of program: ANCONT v1.0 Catalogue Id: ADMU_v1_0 Nature of problem Calculation of the analytic continuation of the Mellin transforms to complex values of N for the basic functions gi(x) emerging in the splitting and coefficient functions of massless QED and QCD up to two-loop order. Versions of this program held in the CPC repository in Mendeley Data ADMU_v1_0; ANCONT v1.0; 10.1016/S0010-4655(00)00156-9 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要 针对无质量量子电动力学（Quantum Electrodynamics, QED）与量子色动力学（Quantum Chromodynamics, QCD）两圈阶精度下各类物理量中出现的、依赖动量份额$x$的基函数$g_i(x)$，本研究完成了其梅林变换（Mellin transform）关于复变量$N$的解析延拓（analytic continuation）计算，涵盖未极化与极化劈裂函数、系数函数，以及类空、类时动量传递下的硬散射截面。上述梅林变换可实现所有有限调和和直至三重阶（原文此处截断为"threefold s..."）的解析延拓。 程序名称：ANCONT v1.0 目录编号：ADMU_v1_0 问题本质 计算无质量QED与QCD两圈阶精度下，劈裂函数及系数函数中出现的基函数$g_i(x)$的梅林变换关于复变量$N$的解析延拓。 存放于Mendeley数据集的CPC仓库中的该程序版本：ADMU_v1_0；ANCONT v1.0；10.1016/S0010-4655(00)00156-9 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019）。