Direct photon production by polarized beam and target: Complete next-to-leading-order corrections

For large-$p_T$ direct photon production by a longitudinally polarized beam and target complete next-to-leading-order corrections [higher-order corrections (HOC's)] are determined. For these, one loop corrections to the basic subprocesses $\overrightarrow{g}\overrightarrow{q}\to \gamma q$ and $\overrightarrow{q}\overrightarrow{\overline{q}}\to \gamma g$, as well as the contributions of $\overrightarrow{g}\overrightarrow{g}\to \gamma q\overline{q}$ and $\overrightarrow{q}\overrightarrow{q}\to \gamma \mathrm{qq}$, are calculated. For $\overrightarrow{p}\overrightarrow{p}\to \gamma +X$, $K$ factors greater than unity and polarized cross sections and asymmetries well measurable are obtained. Certain differences in the regularization procedures and the question of dominance of HOC's by soft, collinear, and virtual gluons are also discussed.