The minimal composite Higgs model and electroweak precision tests

A complete analysis of the electroweak precision observables is performed within a recently proposed minimal composite Higgs model, realized as a 5-dimensional warped compactification. In particular, we compute Z→bb¯ and the one-loop correction to the ρ   parameter. We find that oblique data can be easily reproduced without a significant amount of tuning in the parameters of the model, while Z→bb¯ imposes a stronger constraint. As a consequence of the latter, some of the new fermionic resonances must have mass around 4 TeV, which corresponds to an electroweak fine tuning of a few percent. Other resonances, such as Z′Z′, can be lighter in sizeable portions of the parameter space. We discuss in detail the origin of the Z→bb¯ constraint and we suggest several possible avenues beyond the minimal model for weakening it.