QCD Evolution Equations: Numerical Algorithms from the Laguerre Expansion

Abstract

A complete numerical implementation, in both singlet and non-singlet 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 ($x\approx 10^{-3}$), below which the convergence of the expansion slows down. The polarized evolution is smoother, due to the less singular structure of the anomalous dimensions at small-x. In the region of fast convergence, which covers most of the usual perturbative applications, high numerical accuracy is achieved by expanding over a set of approximately 30 polynomials, with a very modest running time.

30 pages, 13 figures

References in corpus (5)

• Nonforward Parton Distributions
• Numerical solution of Q^2 evolution equations for polarized structure functions
• Two-loop anomalous dimensions for the structure function h1
• Probing Nucleon Spin Structure
• Proton Spin in Chiral Quark Models

Cited by in corpus (11)

• The high energy cosmic ray spectrum from relic particle decay
• A C++ Code to Solve the DGLAP Equations Applied to Ultra High Energy Cosmic Rays
• Evolution of singlet structure functions from DGLAP equation at next-to-next-to-leading order at small-x
• Nucleon and nuclear structure functions with non-perturbative and higher order perturbative QCD effects
• A Matrix Approach to Numerical Solution of the DGLAP Evolution Equations
• Direct Solution of Renormalization Group Equations of QCD in $x-$space: NLO Implementations at Leading Twist
• Markovian Monte Carlo program EvolFMC v.2 for solving QCD evolution equations
• Evolution program for parton densities with perturbative heavy flavor boundary conditions
• Laguerre polynomials method in the valon model
• Supersymmetric Scaling Violations (I). Solving the Supersymmetric DGLAP Evolution
• Truncated first moment of the parton distribution - a modified approach