NLO QCD and electroweak corrections to WWW production at the LHC
In this paper we calculate the next to leading order (NLO) QCD \cal O}\alpha_s \alpha^3) and electroweak (EW) \cal O}\alpha^4) corrections to the $WWW$ production at the LHC and deal with the subsequent leptonic decays from $W$ bosons by adopting an improved narrow width approximation which takes into account the spin correlation and finite width effects. The NLO QCD correction from the real jet radiation is discussed, which significantly enhances the production rate, particularly in the high energy region. We also provide the integrated cross section for the $WWW$ production and various kinematic distributions of final products at the QCD+EW NLO. We find that the convergence of the perturbative QCD description can be improved by applying a hard jet veto in the event selection, but this jet veto would introduce a new source of theoretical uncertainty. The pure NLO QCD relative correction to the integrated cross section for the $W^+W^ W^ production at the $14~\rm TeV} LHC is on the order of $30\ in the jet veto event selection scheme with $p^ \rm cut}}_{T, \rm jet} 50~\rm GeV} while the genuine NLO EW relative correction can reach about $15\ in the inclusive event selection scheme. Our numerical results show that both the NLO QCD and NLO EW corrections should be taken into consideration in precision predictions.