QCD corrections to $W^+W^-$ production through gluon fusion

We compute the next-to-leading order (NLO) QCD corrections to the $gg \to W^+ W^- \to l^+_1 \nu_1 l^-_2 \bar \nu_2$ process, mediated by a massless quark loop, at the LHC. This process first contributes to the hadroproduction of $W^+W^-$ at $\mathcal{O}(\alpha_s^2)$, but, nevertheless, has a sizable impact on the total production rate. We find that the NLO QCD corrections to the $gg \to W^+W^-$ process amount to ${\cal O}(50)$%, and increase the NNLO QCD cross sections of $pp \to W^+W^-$ by approximately two percent, at both the 8 TeV and 13 TeV LHC. We also compute the NLO corrections to gluonic $W^+W^-$ production within a fiducial volume used by the ATLAS collaboration in their 8 TeV measurement of the $W^+W^-$ production rate and find that the QCD corrections are significantly smaller than in the inclusive case. While the current experimental uncertainties are still too large to make these differences relevant, the observed strong dependence of perturbative corrections on kinematic cuts underscores that extrapolation from a fiducial measurement to the total cross section is an extremely delicate matter, and calls for the direct comparison of fiducial volume measurements with corresponding theoretical computations.