Gluon fusion contribution to W+W- + jet production

TL;DR

This work computes the gluon-gluon fusion contribution to W+W− production in association with a jet (gg→W+W−g), a finite and gauge-invariant piece of the NNLO QCD corrections to pp→W+W−+jet. Using generalized unitarity and OPP reduction, it includes leptonic W decays and Z/γ exchange, with careful treatment to avoid double-counting in cyclic insertions, and validates against independent codes. The results show that, under standard cuts, the gluon-fusion contribution modestly enhances the background by about 3–5% relative to NLO, but under ATLAS Higgs-search cuts this enhancement rises to roughly 6–12% and can noticeably distort key distributions used in signal extraction. The analysis highlights a strong dependence on experimental cuts and provides a public MCFM add-on for NLO QCD treatment of pp→W+W−+jet, informing background modeling for Higgs studies at the LHC.

Abstract

We describe the computation of the $gg \to W^+W^-g$ process that contributes to the production of two $W$-bosons and a jet at the CERN Large Hadron Collider (LHC). While formally of next-to-next-to-leading order (NNLO) in QCD, this process can be evaluated separately from the bulk of NNLO QCD corrections because it is finite and gauge-invariant. It is also enhanced by the large gluon flux and by selection cuts employed in the Higgs boson searches in the decay channel $ H \to W^+W^-$, as was first pointed out by Binoth {\it et al.} in the context of $gg \to W^+W^-$ production. For cuts employed by the ATLAS collaboration, we find that the gluon fusion contribution to $pp \to W^+W^-j$ enhances the background by about ten percent and can lead to moderate distortions of kinematic distributions which are instrumental for the ongoing Higgs boson searches at the LHC. We also release a public code to compute the NLO QCD corrections to this process, in the form of an add-on to the package {\tt MCFM}.

Figures (4)

• Figure 1: Sample Feynman diagrams for $gg \to W^+W^-g$ through a fermion loop.
• Figure 2: Primitive amplitudes $A_f(g_1,g_2,g_3)$ and $A_f(g_1,g_3,g_2)$. One ordering of the $W$-bosons is shown. However, we need to consider every insertion of the electroweak bosons relative to the ordered gluons.
• Figure 3: Two double cuts on a primitive amplitude with different orderings of the $W$-bosons, leading to a potential source of double counting.
• Figure 4: Distributions of the mass of the charged lepton system $m_{ll}$, transverse mass of the $W$-pair $m_{T,WW}$, the azimuthal angle between the leptons $\Delta \phi_{ll}$ and the transverse momentum of the positron $p_{T, e^+}$, shown at NLO accuracy with and without the fermion loop NNLO contribution. We use the Higgs search cuts as described in the text, and we display results for the $8$ TeV LHC. The upper and lower bands show the maximum and minimum deviations from the central scale value $2m_W$. The ratio $K_{\rm NLO}$ as defined in Eq.(3.3) is also displayed.