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Phenomenology of heavy fermion and vector resonances in composite Higgs models

In this project we study the phenomenology of models where the Higgs is a bound state of a strongly interacting dynamics at the TeV scale and we assess the LHC potential to discover new heavy colored states. In the first part of the thesis we analyze the bounds on the spectrum of Composite Higgs Models (CHM) that come from flavor observables. In the second part we propose a novel strategy to discover a heavy gluon ($G^*$) and heavy fermions at the LHC. We do so by means of simple two-site effective Lagrangians, which could also be used in further phenomenological studies on CHM. From the analysis of the bounds on the CHM spectrum, we derive an important constraint on the masses of the heavy fermions which does not depend on the flavor structure of the sector beyond the SM. This bound is obtained from the infrared contribution to $b \to sγ$ induced by the flavor-conserving effective vertex $Wt_Rb_R$. We find that the presence of a custodial symmetry can play a role in protecting this effective coupling. Studying the heavy colored vectors phenomenology, we find that heavy composite fermions have a great impact on the phenomenology of heavy composite gluon at the LHC. If the composite gluon is heavier than the composite fermions, as flavor observables seem to suggest, the search in the channels where $G^*$ decays into one heavy fermion plus its Standard Model partner is very promising, with the possibility for both the $G^*$ and heavy fermions to be discovered at the early stage of the LHC. These channels offer also the possibility to extract important information on model's parameters, such as the top degree of compositeness.