A simulation of the search for the Standard Model Higgs boson at the LHC, in the channel gg -> H -> WW -> lnu lnu, is described. Higher-order QCD corrections are taken into account by using a reweighting procedure, which allows us to combine event rates obtained with the PYTHIA Monte Carlo program with the most up-to-date theoretical predictions for the transverse-momentum spectra of the Higgs signal and its corresponding WW background. With this method the discovery potential for Higgs masses between 140 and 180 GeV is recalculated and the potential statistical significance of this channel is found to increase considerably. For a Higgs mass of 165 GeV a signal-to-background ratio of almost 2:1 can be obtained. A statistical significance of five standard deviations might already be achieved with an integrated luminosity close to 0.4 fb^{-1}. Using this approach, an experimental effective K-factor of about 2.04 is obtained for the considered Higgs signature, which is only about 15 % smaller than the theoretical inclusive K-factor.
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