Like-sign W-boson production has been proposed as a probe of possible strong scattering in the electroweak-symmetry-breaking sector that would enhance the production of longitudinally polarized gauge bosons. We evaluate the expected signals in the channel pp\ensuremath{\rightarrow}${\mathit{W}}^{+}$${\mathit{W}}^{+}$X, ${\mathit{W}}^{+}$\ensuremath{\rightarrow}${\mathit{l}}^{+}$\ensuremath{\nu} at pp supercolliders, for several different theoretical models in which strong scattering occurs, using realistic acceptance cuts and comparing with standard-model background contributions. We find that backgrounds are potentially a serious problem, especially those from electroweak production of transversely polarized W bosons. However, vetoing events with high-${\mathit{p}}_{\mathit{T}}$ jets in the central region makes it possible to suppress all backgrounds at little cost to the signal. With an integrated luminosity of 10 ${\mathrm{fb}}^{\mathrm{\ensuremath{-}}1}$ at the Superconducting Super Collider (SSC) or 100 ${\mathrm{fb}}^{\mathrm{\ensuremath{-}}1}$ at the CERN Large Hadron Collider (LHC) and a dilepton detection efficiency of 50%, there could be 3--8 signal events, depending on the model, with about 3.5 (1.7) background events at the SSC and 8.5 (2.5) background events at the LHC for ${\mathit{m}}_{\mathit{t}}$=100 (200) GeV.
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