NLO QCD and electroweak corrections to $WW+\mathbf{\text{jet}}$ production with leptonic $W$-boson decays at LHC

We present the complete next-to-leading order (NLO) QCD and NLO electroweak (EW) corrections to the $W$-boson pair production associated with a hard jet at the LHC including the spin correlated $W$-boson leptonic decays. The dependence of the leading order (LO) and NLO corrected cross sections on the jet transverse momentum cut is investigated. In dealing with the subsequent resonant $W$-boson decays, we adopt the madspin method where the spin correlation effect is included. We also provide the LO and NLO corrected distributions of the transverse momenta and rapidities of final products. The results show that the NLO EW correction is significant in high transverse momentum region due to the EW Sudakov effect.

Figure 1

The LO Feynman diagrams for the partonic process $u\overline{u}\to W^{+}{W}^{-}g$.

Figure 2

Some representative box and pentagon diagrams for the partonic process $u\overline{u}\to W^{+}{W}^{-}g$.

Figure 3

The LO transverse momentum distributions of ${\mu }^{-}$ and the corresponding relative deviations by applying the naive NWA and madspin methods with (a) $p_{T,j}>50\mathrm{GeV}$, and (b) $p_{T,j}>50\mathrm{GeV}$ and the additional constraints in (3.9).

Figure 4

The LO transverse momentum distributions of $e^{+}$ and the corresponding relative deviations by applying the naive NWA and madspin methods with (a) $p_{T,j}>50\mathrm{GeV}$, and (b) $p_{T,j}>50\mathrm{GeV}$ and the additional constraints in (3.9).

Figure 5

The LO distributions of the azimuthal-angle difference ${\varphi }_{e^{+}{\mu }^{-}}$ between the final $e^{+}$ and ${\mu }^{-}$ and the corresponding relative deviations by applying the naive NWA and madspin methods with (a) $p_{T,j}>50\mathrm{GeV}$, and (b) $p_{T,j}>50\mathrm{GeV}$ and the additional constraints in (3.9).

Figure 6

The LO, NLO QCD and NLO EW corrected transverse momentum distributions of (a) $W^{+}$ and (b) $W^{-}$.

Figure 7

The LO, NLO QCD and NLO EW corrected rapidity distributions of (a) $W^{+}$ and (b) $W^{-}$.

Figure 8

The LO, NLO QCD and NLO EW corrected $W$-pair invariant mass distributions.

Figure 9

The LO, NLO QCD and NLO EW corrected transverse momentum distributions of (a) ${\mu }^{-}$ and (b) $e^{+}$.

Figure 10

The LO, NLO QCD and NLO EW corrected distributions of the missing transverse momentum.