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 (equivalent 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, find and study a natural second sigma-like scalar pole of the W_L W_L amplitude, and also map out how additional new resonances in these scattering amplitudes correlate with the parameters of the low-energy Lagrangian density. Based on arXiv:1308.1629 (JPG, in press) and arXiv:1311.5993 in collaboration with Rafael L. Delgado and Antonio Dobado.