Deviations of the top electroweak couplings from their Standard Model values
imply that certain amplitudes for the scattering of third generation fermions
and longitudinally polarized vector bosons or Higgses diverge quadratically
with momenta. This high-energy growth is a genuine signal of models where the
top quark is strongly coupled to the sector responsible for electroweak
symmetry breaking. We propose to profit from the high energies accessible at
the LHC to enhance the sensitivity to non-standard top-Z couplings, which are
currently very weakly constrained. To demonstrate the effectiveness of the
approach, we perform a detailed analysis of tW→tW scattering, which can
be probed at the LHC via pp→ttˉWj. By recasting a CMS analysis at 8
TeV, we derive the strongest direct bounds to date on the Ztt couplings. We
also design a dedicated search at 13 TeV that exploits the distinctive features
of the ttˉWj signal. Finally, we present other scattering processes in
the same class that could provide further tests of the top-Higgs sector.Comment: 37 pages, 10 figures; v2: minor improvements in the discussion,
references added. Matches version published in JHE