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Solving the [FORMULA] anomaly in natural composite models

The Standard Model with a light Higgs provides a very accurate description of the electroweak precision observables. The largest deviation between the Standard Model predictions and the experimental measurements, the forward-backward asymmetry of the bottom quark [FORMULA], can be interpreted as an indication of new physics at the TeV scale. The strong agreement between theory and experiment in the branching fraction of the Z into b-quarks puts strong constraints for new physics aiming to solve the [FORMULA] puzzle. We study a class of natural composite Higgs models that can solve the [FORMULA] anomaly reproducing the observed R b as well as the top and bottom masses. We find that the subgroup of the custodial symmetry able to protect [FORMULA] from large corrections generated by the top sector play an important role if we want to maintain naturalness in the composite sector. We make a thorough study of the composite operators mixing with the b-quark, determine their embedding under the global composite symmetry and the parameter space that lead to the correct [FORMULA] couplings while keeping the top and bottom masses to their physical values. We study the predictions for the spectrum of light fermionic resonances and the corrections to [FORMULA] in this scenario.