Two real parton contributions to non-singlet kernels for exclusive QCD DGLAP evolution

Results for the two real parton differential distributions needed for implementing a next-to-leading order (NLO) parton shower Monte Carlo are presented. They are also integratedoverthephasespaceinordertoprovidesolidnumericalcontroloftheMCcodes and for the discussion of the differences between the standard \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \overline {MS} $\end{document} factorization and Monte Carlo implementation at the level of inclusive NLO evolution kernels. Presented results cover the class of non-singlet diagrams entering into NLO kernels. The classic work of Curci-Furmanski-Pertonzio was used as a guide in the calculations.