  Higgs Effective Field Theory (HEFT) is deployed to study elastic vector-boson
scattering at the high LHC energies. The interaction is strong over most of the
parameter space, with the minimal Standard Model being a remarkable exception.
One-loop HEFT complemented with dispersion relations and the Equivalence
Theorem leads to two different unitarization methods which produce analytical
amplitudes corresponding to different approximate solutions to the dispersion
relations: the Inverse Amplitude method (IAM) and the N/D method. The partial
waves obtained can show poles in the second Riemann sheet whose natural
interpretation is that of dynamical resonances with masses and widths depending
on the starting HEFT parameters. Different unitarizations yield qualitatively,
and in many cases quantitatively, very similar results. The amplitudes obtained
provide realistic resonant and nonresonant cross sections to be compared with
and to be used for a proper interpretation of the LHC data.
