Numerical solution of Q^2 evolution equations for polarized structure functions

Abstract

We investigate numerical solution of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) Q^2 evolution equations for longitudinally polarized structure functions. Flavor nonsinglet and singlet equations with next-to-leading-order ${\alpha }_s$ corrections are studied. A brute-force method is employed. Dividing the variables x and Q^2 into small steps, we simply solve the integrodifferential equations. Numerical results indicate that accuracy is better than 1% in the region 10^{-5}<x<0.8 if more than two-hundred Q^2 steps and more than one-thousand x steps are taken. Our evolution results are compared with polarized experimental data of the spin asymmetry A_1 by the SLAC-E130, SLAC-E143, EMC, and SMC collaborations. The comparison indicates that we cannot assume A_1 is independent of Q^2. We provide a FORTRAN program for the Q^2 evolution and devolution of polarized nonsinglet-quark, singlet-quark, Delta q_i+ Delta q-bar_i, and gluon distributions (and corresponding structure functions).

1+33 pages, LaTeX2e, epsfig.sty, amsmath.sty, 9 eps figures. Complete postscript file is available 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: [email protected], [email protected], [email protected]

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