Combining QED and QCD transverse-momentum resummation for W and Z boson production at hadron colliders
Andrea Autieri, Leandro Cieri, Giancarlo Ferrera, Germán F. R. Sborlini
Abstract
A bstract 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 $$ \mathcal{O}\left({\alpha}_S^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>S</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> ) 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.