Abstract
We consider the production of Wγ and Zγ pairs at hadron colliders. We report on the complete fully differential computation of radiative corrections at next-to-next-to-leading order (NNLO) in QCD perturbation theory. The calculation includes the leptonic decay of the vector boson with the corresponding spin correlations, off shell effects and final-state photon radiation. We present numerical results for pp collisions at 7 and 8 TeV and we compare them with available LHC data. In the case of Zγ production, the impact of NNLO corrections is generally moderate, ranging from 8% to 18%, depending on the applied cuts. In the case of Wγ production, the NNLO effects are more important, and range from 19% to 26%, thereby improving the agreement of the theoretical predictions with the data. As expected, the impact of QCD radiative corrections is significantly reduced when a jet veto is applied.
Highlights
When considering the V γ final state, besides the direct production in the hard subprocess, the photon can be produced through the fragmentation of a QCD parton, and the evaluation of the ensuing contribution to the cross section requires the knowledge of a non-perturbative photon fragmentation function, which typically has large uncertainties
The V γ cross section is known in next-lo-leading-order (NLO) QCD [16, 17], and the leptonic decay of the vector boson has been included in ref
We extend this calculation to the complete class of V γ production with leptonic decays, namely to both Zγ production with visible (Z → l+l−) and invisible (Z → νν) Z-boson decays, and to W γ production with the respective decays W + → νl+ and W − → l−ν
Summary
We discuss the details of our calculation. We first point out that the notation “V γ” suggests the production of an on-shell vector boson plus a photon, followed by a factorized decay of the vector boson. The NNLO computation requires the evaluation of tree-level scattering amplitudes with up to two additional (unresolved) partons, of one-loop amplitudes with up to one additional (unresolved) parton [30, 31], and of one-loop squared and two-loop corrections to the Born subprocess (qq → l+l−γ and qq → νlνlγ for Zγ, qq′ → lνlγ for W γ). Processes with charge-neutral final states receive loop-induced contributions from the gluon fusion channel (gg → l+l−γ and gg → νlνlγ).
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