Solving the AFBb 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 A(FB)(b), 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 A(FB)(b) puzzle. We study a class of natural composite Higgs models that can solve the A(FB)(b) 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 Zb(L)(b) over bar (L) 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 Zb (b) over bar 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 Ztt in this scenario.