  The apparent finding of a 125-GeV light Higgs boson closes unitarity of the
minimal Standard Model (SM), that is weakly interacting: this is an exceptional
feature not generally true if new physics exists beyond the mass gap found at
the LHC up to 700 GeV. Such new physics induces departures of the low-energy
dynamics for the minimal electroweak symmetry-breaking sector, with three
Goldstone bosons (related to longitudinal W bosons) and one light scalar, from
the SM couplings. We calculate the scattering amplitudes among these four
particles and their partial-wave projections in effective theory. For this we
employ the Electroweak Chiral Lagrangian extended by one light scalar and carry
out the complete one-loop computation at high energy including the counterterms
needed for perturbative renormalization, of dimension eight. For most of
parameter space, the scattering is strongly interacting (with the SM a
remarkable exception). We therefore explore various unitarization methods, that
can already be applied to the tree-level $W_L W_L$ amplitude; we find and study
a natural second sigma-like scalar pole there.
