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QCD evolution equations: Numerical algorithms from the Laguerre expansion. (English) Zbl 0998.81111
Summary: 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 (\(x\approx 10^{-3}\)), below which the convergence of the expansion slows down. The polarized evolution is smoother, due to the less singular structure of the polarized DGLAP kernels 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.

MSC:
81V05 Strong interaction, including quantum chromodynamics
81-08 Computational methods for problems pertaining to quantum theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
Software:
ffevol1.0; LAG2NS
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