Soft gluon effects on lepton pairs at hadron colliders

We consider the Collins-Soper-Sterman resummation formalism, which describes the vector boson transverse momentum ${(Q}_T)$ distribution at hadron colliders, and extend it for the distributions of the decay leptons by correctly including the effects of the polarization and the width of the vector boson. Numerous aspects of the formalism are reviewed at the $O\left({\alpha }_S^2\right)$ level, including the matching of the $Q_T$ distribution and the value of the total cross section. Detailed comparisons of several $O\left({\alpha }_S\right)$ fixed order (NLO) and resummed lepton distributions are presented. The total rates and the distributions of the lepton charge asymmetry predicted by the resummed and the NLO calculations are shown to differ when kinematic cuts are applied. We also show how to test the rich dynamics of the QCD multiple soft gluon radiation, among others by measuring the ratio $R_{\mathrm{CSS}}\equiv \sigma {(Q}_T>Q_T^{\min })/{\sigma }_{\mathrm{total}}.$