Preprint number: CP3-Origins-2014-3 DNRF90 and DIAS-2014-3
We provide a unified description, both at the effective and fundamental Lagrangian level, of models of composite Higgs dynamics where the Higgs itself can emerge, depending on the way the electroweak symmetry is embedded, either as a quasi Goldstone boson or as a massive excitation of the condensate. Our results will help clarify the main differences, similarities, benefits and shortcomings of the different ways one can realise naturally a composite nature of the electroweak sector of the Standard Model. We will analyse specific underlying realisations in terms of fundamental strongly coupled gauge theories. In particular we will consider as underlying gauge theory for the universal composite dynamics an SU(2) gauge theory with two Dirac fermions transforming according to the fundamental representation of the gauge group. This minimal choice enables us to use recent first principle lattice results to make the first predictions for the massive spectrum for models of composite (Goldstone) Higgs dynamics. These results are of the upmost relevance to guide searches of new physics at the Large Hadron Collider.