Coarse-grained binning in Drell-Yan transverse momentum spectra

We report a study of the determination of the intrinsic transverse momentum of partons, the intrinsic $k_T$, from the dilepton transverse momentum $p_T$ in Drell-Yan (DY) production at hadron colliders. The result shows that a good sensitivity to the intrinsic $k_T$ distribution is achieved by measuring relative ratios between the cross sections of suitably defined low-$p_T$ and high-$p_T$ regions. The study is performed through both a pseudo-data test and an extraction from measurements of the DY process by the CMS collaboration. Since the methodology does not rely on any dedicated partition of bins, this $p_T$-ratio observable requires less special treatment in very low $p_T$ regions, and propagates lower systematic uncertainties induced from unfolding or momentum migration, in contrast with previous proposals of using a fine-binning measurement of the differential cross section.