Signal-background interference effects for $gg \to H \to W^+ W^-$ beyond leading order

We study the effect of QCD corrections to the $gg\to H\to W^+ W^-$ signal-background interference at the LHC for a heavy Higgs boson. We construct a soft-collinear approximation to the NLO and NNLO corrections for the background process, which is exactly known only at LO. We estimate its accuracy by constructing and comparing the same approximation to the exact result for the signal process, which is known up to NNLO, and we conclude that we can describe the signal-background interference to better than ten percent accuracy. We show that our result implies that, in practice, a fairly good approximation to higher-order QCD corrections to the interference may also be obtained by rescaling the known LO result by a K-factor computed using the signal process.