Numerical solution of Q2 evolution equations for fragmentation functions

Semi-inclusive hadron-production processes are becoming important in high-energy hadron reactions. They are used for investigating properties of quark- hadron matters in heavy-ion collisions, for finding the origin of nucleon spin in polarized lepton-nu cleon and nucleon-nucleon reactions, and possibly for finding exotic hadrons. In describing the ha dron-production cross sections in high-energy reactions, fragmentation functions are essen tial quantities. A fragmentation function indicates the probability of producing a hadron from a parto n in the leading order of the running coupling constantαs. Its Q 2 dependence is described by the standard DGLAP (DokshitzerGribov-Lipatov-Altarelli-Parisi) evolution equations, which are often used in theoretical and experimental analyses of the fragmentation functions and in calculating semi-inclusive cross sections. The DGLAP equations are complicated integro-differential equations, which cannot be solved in an analytical method. In this work, a simple method is employed for solving the evolution equations by using Gauss-Legendre quadrature for evaluating integrals, and a useful code is provided for calculating the Q 2 evolution of the fragmentation functions in the leading ord er (LO) and next-to-leading order (NLO) ofαs. The renormalization scheme is MS in the NLO evolution. Our evolution code is explained for using it in on e’s studies on the fragmentation functions.

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