Normalization of the Drell-Yan cross section in QCD

We analyze the Drell-Yan cross section in perturbative QCD, resummed to include large corrections associated with threshold behavior in the partonic hard scattering. Resummed threshold corrections are known to exponentiate in the space of moments. Here, we derive an explicit expression for the hard scattering function directly in momentum space, as it appears in the factorized form of the cross section. We show that leading logarithms exponentiate, while non-leading contributions appear as calculable multiplicative corrections. We also discuss the range of validity of perturbation theory in the calculation of the hard scattering corrections. We conclude that our new resummed formula in momentum space organizes all large and order unity threshold corrections in the entire region where perturbation theory gives the dominant contribution. To evaluate the resummed form at this level of accuracy as an asymptotic series, it is only necessary to use existing one- and two-loop calculations.