Top-antitop production from $W_L^{+}{W}_L^{-}$ and $Z_L{Z}_L$ scattering under a strongly-interacting symmetry-breaking sector

By using a Non-linear Electroweak Chiral Lagrangian, including the Higgs, coupled to heavy quarks, and the Equivalence Theorem, we compute (in the regime $M_t^2\mathrm{/}{v}^2\ll \sqrt{s}{M}_t\mathrm{/}{v}^2\ll s\mathrm{/}{v}^2$) the one-loop amplitudes $W^+W^-\to t\bar t$,$ZZ\to t\bar t$and$hh\to t\bar t$ (to NLO in the effective theory). We calculate the scalar partial-wave helicity amplitudes which allow us to check unitarity at the perturbative level in both $M_t\mathrm{/}v$ and $s\mathrm{/}v$. As with growing energy perturbative unitarity deteriorates, we also introduce a new unitarization method with the right analytical behavior on the complex $s$-plane and that can support poles on the second Riemann sheet to describe resonances in terms of the Lagrangian couplings. Thus we have achieved a consistent phenomenological description of any resonant $t\bar{t}$ production that may be enhanced by a possible strongly interacting Electroweak Symmetry Breaking Sector.