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 pseudo-Goldstone
boson or as a massive excitation of the condensate. We show that, in general, these states mix with repercussions on the electroweak physics and phenomenology. Our results will help clarify the main differences, similarities, benefits and shortcomings of the different ways one can naturally realize a composite nature of the electroweak sector of the Standard Model. We will analyze the minimal underlying realization in terms of fundamental strongly coupled gauge theories supporting the flavor symmetry breaking pattern SU(4)/Sp(4) $sim$ SO(6)/SO(5). The most minimal fundamental description consists of 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.
Little Higgs models with T-parity can easily satisfy electroweak precision tests and at the same time give a stable particle which is a candidate for cold dark matter. In addition to little Higgs heavy gauge bosons, this type of models predicts a set
of new T-odd fermions, which may show quite interesting signatures at colliders. We study purely leptonic signatures of T-odd leptons at the Large Hadron Collider (LHC).
Little Higgs models are often endowed with a T-parity in order to satisfy electroweak precision tests and give at the same time a stable particle which is a candidate for cold dark matter. This type of models predicts a set of new T-odd fermions in a
ddition to the heavy gauge bosons of the Little Higgs models, which may show interesting signatures at colliders. In this paper, we study the signatures of strong and electroweak pair production of the first two generations of T-odd quarks at the LHC. We focus on the dileptonic signatures (p p to l l j j MET) with (a) opposite-sign dileptons and (b) same-sign dileptons.
