On Flavour and Naturalness of Composite Higgs Models

We analyse the interplay of the constraints imposed on flavour-symmetric Composite Higgs models by Naturalness considerations and the constraints derived from Flavour Physics and Electroweak Precision Tests. Our analysis is based on the Effective Field Theory which describes the Higgs as a pseudo-Nambu-Goldstone boson and also includes the composite fermionic resonances. Within this approach one is able to identify the directions in the parameter space where the $U(3)$-symmetric flavour models can pass the current experimental constraints, without conflicting with the light Higgs mass. We also derive the general features of the $U(2)$-symmetric models required by the experimental bounds, in case of elementary and totally composite $t_R$. An effect in the $Z \bar b b$ coupling, which can potentially allow for sizable deviations in $Z \to \bar b b$ decay parameters without modifying flavour physics observables, is identified. We also present an analysis of the mixed scenario, where the top quark mass is generated due to Partial Compositeness while the light quark masses are Technicolor-like.