Phenomenology of Compositeness at the LHC

The hierarchy problem of the weak scale calls for extensions of the Standard Model at the TeV, and thus within the reach of the CERN Large Hadron Collider (LHC). One of the best motivated proposals builds on the idea that the Higgs could be a composite pseudo-Nambu-Goldstone boson. In this thesis we discuss several topics in the phenomenology of composite Higgs models, concentrating mainly on LHC physics. In Chapter 1 we introduce the hierarchy problem and the essential features of viable theories of compositeness at the TeV scale. Chapter 2 is dedicated to a review of concrete constructions realizing the composite Higgs idea, focusing mostly on models with partial compositeness. In Chapter 3 we present the effective Lagrangians suited for describing the Higgs boson and the constraints placed by electroweak precision tests on their parameters. Motivated by hints in the experimental results, we also reconsider the possibility of custodial breaking in the couplings of the Higgs to the W and Z. Chapter 4 is devoted to two different aspects of Higgs physics at the LHC. First we discuss the loop-induced Higgs couplings to photons and gluons in the context of compositeness, focusing on the contribution of fermionic resonances, which are expected to be relatively light (< 1 - 1.5 TeV) by naturalness arguments. We point out the potentially important role of double Higgs production in providing indirect information on the resonances. Then we turn our attention to the coupling of the Higgs to the top quark, which is currently poorly constrained. We argue that single top and Higgs associated production can be used to probe the sign of this coupling. The phenomenology of fermionic resonances is discussed in Chapter 5. We analyze their impact on electroweak precision data and the constraints from LHC searches for heavy vector-like quarks. The latter give lower bounds in the range 700 - 800 GeV, implying that the exploration of the natural region has already started. Chapter 6 is devoted to the phenomenology of heavy vectors, which are generically subject to a strong constraint (m_rho > 2 - 2.5 TeV) from the S parameter. After a general introduction we study in detail an isospin-singlet W', which, as we will explain, is rather weakly constrained and could thus be lighter than the aforementioned bound. We point out that the subleading decay of the resonance into a W and a photon would constitute a signal of compositeness. Finally, Chapter 7 contains our conclusions.