Abstract
The Drell-Yan process offers a unique insight into Quantum chromodynamics (QCD). Higher order effects in QCD directly affect the dilepton transverse momentum, distribution. It is interesting to verify that perturbative calculations are able to accurately describe the shape of this distribution. In addition, the very low region is sensitive to non-perturbative effects that cannot be calculated from first principles. The dependence of these non-perturbative effects on the dilepton rapidity is rather poorly constrained by existing data. The Tevatron has collected huge samples of dilepton events with an invariant mass around the boson mass. Despite the available statistics, the distribution can only be measured with limited precision due to the large corrections that are needed for experimental resolution and efficiency. Measurements with only one tenth of the final dataset were already limited by systematic uncertainties.