Numerical solution of Q2 Q 2 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 quarkhadron matters in heavy-ion collisions, for finding the origin of nucleon spin in polarized leptonnucleon and nucleonnucleon reactions, and possibly for finding exotic hadrons. In describing the hadron-production cross sections in high-energy reactions, fragmentation functions are essential quantities. A fragmentation function indicates the probability of producing a hadron from a parton in the leading order of the running coupling constant ?s ? s . Its Q2 Q 2 dependence is described by the standard DGLAP (DokshitzerGribovLipatovAltarelliParisi) 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 GaussLegendre quadrature for evaluating integrals, and a useful code is provided for calculating the Q2 Q 2 evolution of the fragmentation functions in the leading order (LO) and next-to-leading order (NLO) of ?s ? s . The renormalization scheme is MS  in the NLO evolution. Our evolution code is explained for using it in one?s studies on the fragmentation functions. Program title: ffevol1.0 Catalogue identifier: AELJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELJ_v1_0.html Program obtainable from: CPC Program Library, Queen?s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1535 No. of bytes in distributed program, including test data, etc.: 10?191 Distribution format: tar.gz Programming language: Fortran77 Computer: Tested on an HP DL360G5-DC-X5160 Operating system: Linux 2.6.9-42.ELsmp RAM: 130 M bytes Classification: 11.5 Nature of problem:  This program solves time-like DGLAP Q2 Q 2 evolution equations with or without next-to-leading order ?s ? s effects for fragmentation functions. The evolved functions can be calculated for D g h , D u h , D u  h , D d h , D d  h , D s h , D s  h , D c h , D c  h , D b h and D b  h of a hadron h. Solution method:  The DGLAP integro-differential equations are solved by the Euler method for the differentiation of ln Q 2 and the GaussLegendre method for the x integral as explained in Section 4 of the manuscript. Restrictions:  This program is used for calculating Q2 Q 2 evolution of fragmentation functions in the leading order or in the next-to-leading order of ?s ? s . Q2 Q 2 evolution equations are the time-like DGLAP equations. The double precision arithmetic is used. The renormalization scheme is the modified minimal subtraction scheme ( MS  ). A user provides initial fragmentation functions as the subroutines FF_INI and HQFF in the end of the distributed code FF_DGLAP.f. In FF_DGLAP.f, the subroutines are given by taking the HKNS07 (2) functions as an example of the initial functions. Then, the user inputs kinematical parameters in the file setup.ini as explained in Section 5.2 of the manuscript. Running time: A few seconds on HP DL360G5-DC-X5160.
fragmentation function q2 q 2 evolution q2 q 2 q2 q 2 q 2 quark gluon qcd