The apparent finding of a 125 GeV light Higgs boson would close 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.
Any such new physics would induce departures from the SM in the low-energy dynamics for the minimal electroweak symmetry-breaking sector (EWSBS), with three Goldstone bosons (related to longitudinal W and Z bosons) and one light Higgs-like scalar.
With no new particle content, for most of the parameter space, the scattering is actually strongly interacting (with the SM a remarkable exception). We therefore explore various unitarization methods, that have already be applied to the tree-level WL WL amplitude; we find and study a natural second sigma-like scalar pole there. Of note is its appearance due to either elastic or coupled-channel dynamics, especially since the later is largely unconstrained by current LHC data and could be large.