Gluon corrections to the Drell-Yan model

We calculate the $O\left({\alpha }_s\right)$ corrections to the Drell-Yan model for $\mathrm{pp}\to {\mu }^{+}{\mu }^{-}X$ in quantum chromodynamics. We find in agreement with previous work that the infrared and mass singularities can be consistently absorbed into the quark structure functions. The remaining finite terms are negative and rather small for the initial-gluon graphs but positive and about equal to Drell-Yan term for the final- and virtual-gluon graphs.