Hunting composite vector resonances at the LHC: naturalness facing data

We introduce a simplified low-energy effective Lagrangian description of the phenomenology of heavy vector resonances in the minimal composite Higgs model, based on the coset SO(5)/SO(4), analysing in detail their interaction with lighter top partners. Our construction is based on robust assumptions on the symmetry structure of the theory and on plausible natural assumptions on its dynamics. We apply our simplified approach to triplets in the representations (3, 1) and (1, 3) and to singlets in the representation (1, 1) of SO(4). Our model captures the basic features of their phenomenology in terms of a minimal set of free parameters and can be efficiently used as a benchmark in the search for heavy spin-1 states at the LHC and at future colliders. We devise an efficient semi-analytic method to convert experimental limits on {\sigma} {\times} BR into bounds on the free parameters of the theory and we recast the presently available 8 TeV LHC data on experimental searches of spin-1 resonances as exclusion regions in the parameter space of the models. These latter are conveniently interpreted as a test of the notion of naturalness.