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Manuscript Title: A Fortran program for numerical solution of Altarelli-Parisi equations by the Laguerre method.
Authors: S. Kumano, J.T. Londergan
Program title: LAG1
Catalogue identifier: ACGR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 69(1992)373
Programming language: Fortran.
Computer: VAX-8650.
Operating system: VAX-VMS-5.3.1.
Word size: 32
Keywords: Particle physics, Elementary, Numerical integration Of altarelli-parisi Evolution equation, Qcd evolution, Integrodifferential Equation, Laguerre method, Mellin transforms.
Classification: 11.5.

Nature of problem:
This program solves the QCD evolution integrodifferential equation (the Altarelli-Parisi equation) satisfied by quark or gluon distribution functions such as are measured in deep inelastic scattering.

Solution method:
The Altarelli-Parisi equations are transformed into a form suitable for orthogonal polynomial methods. The relevant orthonormal polynomials are the Laguerre polynomials. We make use of the convolution theorems for the Mellin transforms to produce analytic structures for part of the calculation. Numerical evaluation is facilitated by introducing an evolution operator, whose integrodifferential equation is set up and solved by the method advocated.

The present program is set up to utilize the lowest-order QCD form of the splitting functions, for both spin-independent and spin-dependent structure functions. This can be customized to replace input structure functions, as described in Section 3.2.

Running time:
Around 10 CPU seconds on VAX 8650 to evolve spin-independent or spin- dependent structure functions; see Section 5 for details.