Numerical solution of $Q^2$ evolution equations in a brute-force method

Abstract

We investigate numerical solution of $Q^2$ evolution equations for structure functions in the nucleon and in nuclei. (Dokshitzer-Gribov-Lipatov-)Altarelli-Parisi and Mueller-Qiu evolution equations are solved in a brute-force method. Spin-independent flavor-nonsinglet and singlet equations with next-to-leading-order ${\alpha }_s$ corrections are studied. Dividing the variables $x$ and $Q^2$ into small steps, we simply solve the integrodifferential equations. Numerical results indicate that accuracy is better than 2\% in the region $10^{-4}<x<0.8$ if more than two-hundred $Q^2$ steps and more than one-thousand $x$ steps are taken. The numerical solution is discussed in detail, and evolution results are compared with $Q^2$ dependent data in CDHSW, SLAC, BCDMS, EMC, NMC, Fermilab-E665, ZEUS, and H1 experiments. We provide a FORTRAN program for Q${}^2$ evolution (and ``devolution'') of nonsinglet-quark, singlet-quark, $q_i+{\bar{q}}_i$, and gluon distributions (and corresponding structure functions) in the nucleon and in nuclei. This is a very useful program for studying spin-independent structure functions.

48 pages, LATEX, figs. 1-6. Complete postscript file including the figure is available at ftp://ftp.cc.saga-u.ac.jp/pub/paper/riko/quantum1/saga-he-81.ps.gz or at http://www.cc.saga-u.ac.jp/saga-u/riko/physics/quantum1/structure.html (We had a problem in taking a file in WWW, but the problem was fixed recently.) Email: 94sm10 or [email protected]

References in corpus (9)

• Global QCD Analysis and the CTEQ Parton Distributions
• Pinning down the Glue in the Proton
• A Re-Evaluation of the nuclear Structure Function Ratios for D, He, Li, C and Ca
• A Measurement of the Proton Structure Function $F_2(x,Q^2)$
• The Jacobi Polinomials QCD Analysis of the CCFR Data for xF_3 and the Q^2-Dependence of the Gross-Llewllyn Smith Sum Rule
• FORTRAN program for a numerical solution of the nonsinglet Altarelli-Parisi equation
• Nuclear Shadowing in a Parton Recombination Model: Q${}^2$ Variation
• Nuclear Shadowing in the Structure Function $F_3(x)$
• SU(2)-Flavor-Symmetry Breaking in Nuclear Antiquark Distributions

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