标题： $Q^2$演化方程的数值解在暴力方法中的应用 显示英文标题

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

摘要： 我们研究核子和原子核中结构函数的$Q^2$演化方程的数值解。 (Dokshitzer-Gribov-Lipatov-)Altarelli-Parisi和Mueller-Qiu演化方程是用暴力方法求解的。 研究了具有次领头阶$\alpha_s$修正的自旋无关味非奇异和奇异方程。 将变量$x$和$Q^2$分成小步，我们简单地求解积分微分方程。 数值结果表明，在区域$10^{-4}<x<0.8$内，如果采用超过二百个$Q^2$步和超过一千个$x$步，精度优于2%。 数值解被详细讨论，演化结果与CDHSW、SLAC、BCDMS、EMC、NMC、Fermilab-E665、ZEUS和H1实验中的$Q^2$相关数据进行了比较。 我们提供了一个FORTRAN程序，用于核子和原子核中非奇异夸克、奇异夸克、$q_i+\bar q_i$和胶子分布（以及相应的结构函数）的Q$^2$演化（以及“反演化”）。 这是一个研究自旋无关结构函数的非常有用的程序。 显示英文摘要

摘要： 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.