On the avor structure of natural composite Higgs models & top avor violation

We explore the up avor structure of composite pseudo Nambu-Goldstone- boson Higgs models, where we focus on the avor anarchic minimal SO(5) case. We identify the dierent sources of avor violation in this framework and emphasise the dierences from the anarchic Randall-Sundrum scenario. In particular, the fact that the avor symmetry does not commute with the symmetries that stabilize the Higgs potential may constrain the avor structure of the theory. In addition, we consider the interplay between thene tuning of the model and avor violation. Wend that generically the tuning of this class of models is worsen in the anarchic case due to the contributions from the additional fermion resonances. We show that, even in the presence of custodial symmetry, large top avor violating rate are naturally expected. In particular, t ! cZ branching ratio of order of 10 5 is generic for this class of models. Thus, this framework can be tested in the next run of the LHC as well as in other future colliders. We alsond that the top avor violation is weakly correlated with the increase amount ofne tuning. Finally, other related avor violation eects, such as t ! ch and in the D system, are found to be too small to be observed by the current and near future colliders.