Soft gluon effects on lepton pairs at hadron colliders

With a large integrated luminosity expected at the Tevatron, a next-to-leading order (NLO) calculation is no longer sufficient to describe the data which yield the precision measurement of $M_W$, etc. Thus, we extend the Collins-Soper-Sterman resummation formalism, for on-shell vector boson production, to correctly include the effects of the polarization and the width of the vector boson to the distributions of the decay leptons. We show how to test the rich dynamics of the QCD multiple soft gluon radiation, for example, by measuring the ratio $R_{CSS} \equiv \frac{\sigma (Q_T>Q_T^{\min})}{\sigma _{Total}}$. ($Q_T$ is the transverse momentum of the vector boson.) We conclude that both the total rates and the distributions of the lepton charge asymmetry predicted by the resummed and the NLO calculations are different when kinematic cuts are applied.