  Higgs Effective Field Theory can be used to study vector-boson elastic
scattering at the high energies relevant for the LHC. For most of the parameter
space, the scattering is strongly interacting, with the minimal Standard Model
being a remarkable exception. From its one-loop treatment complemented with
dispersion relations and the Equivalence Theorem, we derive 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 a function of the starting HEFT
parameters. We compare the different unitarizations and we find that they are
qualitatively, and in many cases quantitatively, very similar. However, for
different reason it is more interesting to use one of the two methods depending
on the particular channel for WW, ZZ, WZ, Zh, Wh or hh scattering. In this note
we briefly describe the possible I and J channels for these reactions and give
the unitarization method of choice in each case. 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.
