{
  "id": "hep-ph/9712410",
  "version": "v1",
  "published": "1997-12-17T09:16:08.000Z",
  "updated": "1997-12-17T09:16:08.000Z",
  "title": "Numerical solution of Q^2 evolution equation for the transversity distribution Delta_T q",
  "authors": [
    "M. Hirai",
    "S. Kumano",
    "M. Miyama"
  ],
  "comment": "1+29 pages, LaTeX2e, epsfig.sty, amsmath.sty, 6 eps figures. Submitted for publication. Complete postscript file is available at ftp://ftp.cc.saga-u.ac.jp/pub/paper/riko/quantum1 or at http://www.cc.saga-u.ac.jp/saga-u/riko/physics/quantum1/structure.html Our evolution program may be obtained upon email request. (See the WWW home page for the details.) Email: 96sm18@edu.cc.saga-u.ac.jp, kumanos@cc.saga-u.ac.jp, 96td25@edu.cc.saga-u.ac.jp",
  "journal": "Comput.Phys.Commun. 111 (1998) 150-166",
  "doi": "10.1016/S0010-4655(98)00028-9",
  "categories": [
    "hep-ph",
    "hep-ex",
    "nucl-th"
  ],
  "abstract": "We investigate numerical solution of the Dokshitzer-Gribov-Lipatov-Altarelli- Parisi (DGLAP) Q^2 evolution equation for the transversity distribution Delta_T q or the structure function h_1. The leading-order (LO) and next-to- leading-order (NLO) evolution equations are studied. The renormalization scheme is MS or overline{MS} in the NLO case. Dividing the variables x and Q^2 into small steps, we solve the integrodifferential equations by the Euler method in the variable Q^2 and by the Simpson method in the variable x. Numerical results indicate that accuracy is better than 1% in the region 10^{-5}<x<0.8 if more than fifty Q^2 steps and more than five hundred x steps are taken. We provide a FORTRAN program for the Q^2 evolution and devolution of the transversity distribution Delta_T q or h_1. Using the program, we show the LO and NLO evolution results of the valence-quark distribution Delta_T u_v + Delta_T d_v, the singlet distribution sum_i (Delta_T q_i + Delta_T qbar_i), and the flavor asymmetric distribution Delta_T ubar - Delta_T dbar.They are also compared with the longitudinal evolution results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-12-17T09:16:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "evolution equation",
      "transversity distribution",
      "numerical solution",
      "longitudinal evolution results",
      "nlo evolution results"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Comput. Phys. Commun."
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 452520
    }
  }
}