Combining QED and QCD transverse-momentum resummation for W and Z boson production at hadron colliders

In this article, we consider the transverse momentum ( q T ) distribution of W and Z bosons produced in hadronic collisions. We combine the q T resummation for QED and QCD radiation including the QED soft emissions from the W boson in the final state. In particular, we perform the resummation of enhanced logarithmic contributions due to soft and collinear emissions at next-to-leading accuracy in QED, leading-order accuracy for mixed QED-QCD and next-to-next-to-leading accuracy in QCD. In the small- q T region we consistently include in our results the next-to-next-to-leading order (i.e. two loops) QCD corrections and the next-to-leading order (i.e. one loop) electroweak corrections. The matching with the fixed-order calculation at large q T has been performed at next-to-leading order in QCD (i.e. at 𝒪(α_S^2) ) and at leading order in QED. We show numerical results for W and Z production at the Tevatron and the LHC. Finally, we consider the effect of combined QCD and QED resummation for the ratio of W and Z q T distributions, and we study the impact of the QED corrections providing an estimate of the corresponding perturbative uncertainties.