Numerical solution of Q2Q^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 quark-hadron matters in heavy-ion collisions, for finding the origin of nucleon spin in polarized lepton-nucleon and nucleon-nucleon 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 $\alpha_s$. Its $Q^2$ dependence is described by the standard DGLAP (Dokshitzer-Gribov-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 order (LO) and next-to-leading order (NLO) of $\alpha_s$. The renormalization scheme is $\overline{MS}$ in the NLO evolution. Our evolution code is explained for using it in one's studies on the fragmentation functions.Comment: 16 pages, 6 figures, To be published in Computer Physics Communication

The Physics of the B Factories

“The Physics of the B Factories” describes a decade long effort of physicists in the quest for the precise determination of asymmetry — broken symmetry — between particles and anti-particles. We now recognize that the matter we see around us is the residue — one part in a billion — of the matter and antimatter that existed in the early universe, most of which annihilated into the cosmic background radiation that bathes us. But the question remains: how did the baryonic matter-antimatter asymmetry arise? This book describes the work done by some 1000 physicists and engineers from around the globe on two experimental facilities built to test our understanding of this phenomenon, one at the SLAC National Accelerator Laboratory in California, USA, and a second at the KEK Laboratory, Tsukuba, Japan, and what we have learned from them in broadening our understanding of nature