The variety of ideas put forward in the context of a "composite" picture for the Higgs boson calls for a simple and effective description of the related phenomenology. Such a description is given here by means of a "minimal" model and is explicitly applied to the example of a Higgs-top sector from an SO(5) symmetry. We discuss the spectrum, the ElectroWeak Precision Tests, B-physics and naturalness. We show the difficulty to comply with the different constraints. The extended gauge sector relative to the standard SU (2) × U (1), if there is any, has little or no impact on these considerations. We also discuss the relation of the "minimal" model with its "little Higgs" or "holographic" extensions based on the same symmetry.

We investigate grand unified theories (GUTs) in scenarios where electroweak (EW) symmetry breaking is triggered by a light composite Higgs, arising as a NambuGoldstone boson from a strongly interacting sector. The evolution of the standard model (SM) gauge couplings can be predicted at leading order, if the global symmetry of the composite sector is a simple group G that contains the SM gauge group. It was noticed that, if the right-handed top quark is also composite, precision gauge unification can be achieved. We build minimal consistent models for a composite sector with these properties, thus demonstrating how composite GUTs may represent an alternative to supersymmetric GUTs. Taking into account the new contributions to the EW precision parameters, we compute the Higgs effective potential and prove that it realizes consistently EW symmetry breaking with little fine-tuning. The G group structure and the requirement of proton stability determine the nature of the light composite states accompanying the Higgs and the top quark: a coloured triplet scalar and several vector-like fermions with exotic quantum numbers. We analyse the signatures of these composite partners at hadron colliders: distinctive final states contain multiple top and bottom quarks, either alone or accompanied by a heavy stable charged particle, or by missing transverse energy.

We provide detailed estimates of the proton lifetime in the context of simple supersymmetric SU(5) grand unified models with an extra compact spatial dimension, described by the orbifold S 1 /(Z 2 × Z 2 ) and by a large compactification scale M c ≈ 10 14 ÷ 10 16 GeV. We focus on a class of models where the grand unified symmetry is broken by the compactification mechanism and where baryon violation proceeds mainly through gauge vector boson exchange so that the proton lifetime scales as M 4 c . We carefully compute M c from a next-to-leading analysis of gauge coupling unification and we find that M c can only be predicted up to an overall factor 10 ±1 . The simplest model, where the dominant decay mode is π 0 e + and has no flavour suppression, is strongly constrained by existing data, but not totally ruled out. We also analyze models where some of the matter fields are localized in the extra space and proton decay is flavour suppressed. In models associated to anarchy in the neutrino sector the preferred decay channel is K +ν and the lifetime can be within the reach of the next generation of experiments.