Comparison of numerical solutions for Q^2 evolution equations

Details Comparison of numerical solutions for Q^2 evolution equations Comparison of numerical solutions for Q^2 evolution equations

2004-05-18

arxiv.org/abs/hep-ph/0405160v1

J.Comput.Phys. 201 (2004) 651-664

Physics

High Energy Physics

High Energy Physics - Phenomenology

12 pages, LaTeX, 13 eps files, Journal of Computational Physics in press, http://hs.phys.saga-u.ac.jp

Scientific paper

10.1016/j.jcp.2004.05.021

Q^2 evolution equations are important not only for describing hadron reactions in accelerator experiments but also for investigating ultrahigh-energy cosmic rays. The standard ones are called DGLAP evolution equations, which are integrodifferential equations. There are methods for solving the Q^2 evolution equations for parton-distribution and fragmentation functions. Because the equations cannot be solved analytically, various methods have been developed for the numerical solution. We compare brute-force, Laguerre-polynomial, and Mellin-transformation methods particularly by focusing on the numerical accuracy and computational efficiency. An efficient solution could be used, for example, in the studies of a top-down scenario for the ultrahigh-energy cosmic rays.

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