Tests of quantum chromodynamics in two-photon collisions and high-pTphoton production

We use the diagrammatic approach to scale breaking to rederive the results of the renormalization-group approach to two-photon, ${\gamma }^{*}\gamma$, collisions, where one of the photons is highly virtual and the other nearly real. In an axial gauge only ladder diagrams contribute to leading-logarithmic accuracy. When interpreted in terms of the quark distribution of the real photon we obtain the result $G_{\frac{q}{\gamma }}(q^2,x)=\left[\frac{\alpha }{{\alpha }_s\left(q^2\right)}\right]{\tilde{f}}_q\mathrm{}\left(x\right)+O\left(1\right)\mathrm{}$, where ${\tilde{f}}_q\mathrm{}\left(x\right)\mathrm{}$ is an exactly calculable scaling function. By virtue of the fact that only ladder diagrams contribute in leading-logarithmic accuracy for this and other short-distance photon-target probes, we find that this form for $G_{\frac{q}{\gamma }}$ can be employed (to leading-logarithmic accuracy) in any short-distance application involving a photon target. We give a summary of these additional applications with emphasis on high-transverse-momentum phenomena. We present also estimates of the vector-dominance background to the pointlike component of the photon distribution function. In addition we present a convenient summary of leading-logarithmic quantum-chromodynamic corrections including dominant $x\to 1$ behaviors.