Kfactors for processes involving real photons

First, corrections to order ${\alpha }_s$ ${\mathrm{}}^2$ (K factors) for photoproduction of large-$p_T$ hadrons are determined in an approximate approach; and preliminary data for this process and for the inclusive deep-inelastic QED Compton effect are found to be in good agreement with theoretical calculations. The study of approximate K factors for large-$p_T$ direct photon production is also extended. Furthermore, a general assessment of our approximate approach of determining next-to-leading logarithm corrections is presented: A formulation of the rules, which have consistently been applied, is given; and the results of all available complete calculations for large-transverse-momentum processes are compared to those of our approach. In most of the cases agreement is at least satisfactory. Finally, an unnatural large variable $Q^2$, introduced in certain recent complete calculations, is discussed.