$W^{+}{W}^{-}$ Production at Hadron Colliders in Next to Next to Leading Order QCD

Charged gauge boson pair production at the Large Hadron Collider allows detailed probes of the fundamental structure of electroweak interactions. We present precise theoretical predictions for on-shell $W^{+}{W}^{-}$ production that include, for the first time, QCD effects up to next to next to leading order in perturbation theory. As compared to next to leading order, the inclusive $W^{+}{W}^{-}$ cross section is enhanced by 9% at 7 TeV and 12% at 14 TeV. The residual perturbative uncertainty is at the 3% level. The severe contamination of the $W^{+}{W}^{-}$ cross section due to top-quark resonances is discussed in detail. Comparing different definitions of top-free $W^{+}{W}^{-}$ production in the four and five flavor number schemes, we demonstrate that top-quark resonances can be separated from the inclusive $W^{+}{W}^{-}$ cross section without a significant loss of theoretical precision.

Figure 1

The on-shell $W^{+}{W}^{-}$ cross section in the 4FNS at LO (dotted line), NLO (dashed line), $\mathrm{NLO}+gg$ (dot-dashed line), and NNLO (solid line) combined with $gg\to H\to W{W}^{*}$ is compared to recent ATLAS and CMS measurements [5, 6, 7, 8]. In the lower panel, NNLO and $\mathrm{NLO}+gg$ results are normalized to NLO predictions. The bands describe scale variations.

Figure 2

The $pp\to W^{+}{W}^{-}$ cross section in the 5FNS at $\sqrt{s}=8\mathrm{TeV}$ is plotted versus a $b$-jet veto, $p_{T,\text{bjet}}<p_{T,\text{bjet}}^{\text{veto}}$, and compared to results in the 4FNS (which are $p_{T,\text{bjet}}^{\text{veto}}$ independent). Full 5FNS results (left panel) are contrasted with top-subtracted 5FNS predictions (right panel). The relative agreement between 5FNS and 4FNS results is displayed in the lower frames. Jets are defined using the anti-$k_T$ algorithm [72] with $R=0.4$, and in order to guarantee the cancellations of final-state collinear singularities, $b\overline{b}$ pairs that are recombined by the jet algorithm are not vetoed.