Corrections to certain hadronic reactions involving photons are studied at $O\left({{\alpha }_s}^2\right)$ in the soft-gluon limit; in this limit we carefully preserve the analytic structure of amplitudes in the small-momenta integration regions. For the production of real or virtual photons at large $p_T$ via the quark-gluon channel the result is a rather large correction to the Born term. The phenomenological status of $p+p\to \gamma +X$ at large $p_T$ is discussed, and the large correction is shown to significantly improve agreement with data. The same technique is applied to study $O\left({{\alpha }_s}^2\right)$ corrections to $e^{+}{e}^{-}\to 3$ jets; here it reproduces the ${\pi }^2$ terms that are the dominant part of the known correction to this process. Some remarks on other reactions, including hadronic lepton-pair and single-lepton production, are made and the nature of the problem of nonleading large corrections is discussed.

• Received 22 September 1981

DOI:https://doi.org/10.1103/PhysRevD.25.1280