Next-to-leading-order Q(sup 2) evolution program for spin-dependent structure functions

Abstract

Spin-dependent structure functions which are measured in the polarized lepton-nucleon scattering depend on the two kinematical variables, x and Q(sup 2). The Q(sup 2) dependence is described within the perturbative QCD (Quantum Chromodynamics) by integro-differential equations. Using the next-to-leading-order splitting functions evaluated recently, numerical solutions of the spin-dependent evolution equations were studied. A brute-force method was used for the polarized structure functions, though the Laguerre-polynomial method was used for the unpolarized ones. Variables were divided into small steps, and derivatives were replaced by differences. The integro-differential equations were solved numerically. Results of numerical calculations for the nonsinglet, singlet and gluon distributions indicated that several hundred of x steps were necessary for obtaining good accuracy, but 50 steps for the momentum transfer was found to be large enough.

スピン依存構造関数は偏極レプトンと偏極核子の散乱で測定されるが、非弾性度xと運動量移行に依存する。運動量移行依存性は摂動論的QCD(量子色力学)の枠内で積分微分方程式によって記述できる。最近求められた高次補正を含む分岐関数を用いて、スピン依存の発展方程式の数値解を調べた。非偏極構造関数に対してはラゲーレ多項式法を使用したが、偏極構造関数の場合は力まかせ法を用いた。変数を小さなステップに分割し、微分を差分に置き換えて積分微分方程式を数値演算で解いた。非1重項、1重項およびグルーオンの分布について数値計算した結果、充分な精度を得るには、非弾性度xは数百個に分割する必要があるが、運動量移行の分割数は50で充分であることが分った。