QCD evolution equations: Numerical algorithms from the Laguerre expansion

Abstract A complete numerical implementation, in both singlet and nonsinglet sectors, of a very elegant method to solve the QCD Evolution equations, due to Furmanski and Petronzio, is presented. The algorithm is directly implemented in x-space by a Laguerre expansion of the parton distributions. All the leading-twist distributions are evolved: longitudinally polarized, transversely polarized and unpolarized, to NLO accuracy. The expansion is optimal at finite x, up to reasonably small x-values (x ≈ 10... Title of program: QCD EVOLUTION EQUATIONS Catalogue Id: ADJS_v1_0 Nature of problem The programs provided here solve the DGLAP evolution equations, with next-to-leading order alphas effects taken to account, for unpolarized, longitudinally polarized and transversely polarized parton distributions. Versions of this program held in the CPC repository in Mendeley Data ADJS_v1_0; QCD EVOLUTION EQUATIONS; 10.1016/S0010-4655(98)00158-1 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)摘要：本文提出了一种由Furmanski与Petronzio提出的求解量子色动力学（Quantum Chromodynamics, QCD）演化方程的优雅方法，并在单态区（singlet sector）与非单态区（nonsinglet sector）实现了完整的数值化方案。该算法通过对部分子分布函数（parton distributions）进行拉盖尔展开（Laguerre expansion），直接在x空间中实现。所有领头扭度（leading-twist）分布均被演化至次领头阶（Next-to-Leading Order, NLO）精度，涵盖纵向极化、横向极化与非极化三类分布。该展开方案在有限x区间内表现最优，适用x值下限可达合理小的范围（x≈10... 程序名称：QCD演化方程 目录编号：ADJS_v1_0 问题本质：本文提供的程序可求解Dokshitzer-Gribov-Lipatov-Altarelli-Parisi（DGLAP）演化方程，计入次领头阶强耦合常数修正效应，适用于非极化、纵向极化与横向极化的部分子分布函数演化。 孟德尔莱数据（Mendeley Data）中CPC库内的该程序版本：ADJS_v1_0；QCD EVOLUTION EQUATIONS；10.1016/S0010-4655(98)00158-1 本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2018年）。