Use and misuse of the Drell-Yan formalism

Politzer's approach to the analysis of the Drell-Yan process is reviewed, extended, and explained. The naive Drell-Yan picture of quark-antiquark annihilation is found to be inadequate to describe the process $p+p\to {\mu }^{+}{\mu }^{-}+\mathrm{anything}$. Quark-gluon and quark-quark scattering are equally important in two ways: They implement the renormalization-group logarithmic $Q^2$ dependence of the parton distribution functions and they contribute new nonlogarithmic pieces to the cross section. Antiquark distributions obtained by ignoring these interaction corrections are worthless.