Large perturbative corrections from gluon bremsstrahlung

A new source of large corrections in perturbative QCD, arising from gluon bremsstrahlung, is identified and studied. These corrections are different from the so-called ${\pi }^2$ terms arising from loop graphs in the soft-gluon limit. In one case (the total cross section for $e^{+}{e}^{-}\to \mathrm{hadrons}$ large terms to $O\left({\alpha }_s\right)$ from these two sources are shown to cancel each other, finally leaving a small correction. However, regarding the transverse-momentum ($q_T$) distribution of ${\pi }^{-}N\to l^{+}{l}^{-}+X$ [subprocess $q\overline{q}\to {\gamma }^{*}g$, corrections to $O\left({{\alpha }_s}^2\right)$], the new source leads to a sizable $K$ factor (∼2) that significantly improves agreement with experiment; also, our result gives a simple explanation of the fact that this $K$ factor is weakly dependent on $q_T$. In large-$p_T$ hadron production (subprocess $\mathrm{qq}\to \mathrm{qq}$) the new source leads to a large $O\left({{\alpha }_s}^3\right)$ correction as well. For the deep Compton effect (subprocess $q\gamma \to q\gamma$) no large corrections arise to $O\left({\alpha }_s\right)$. Complete higher-order QCD calculations, whenever available, are compared with our simple results and discussed.