On composite two Higgs doublet models

We investigate the issue of anomalous contribution to the T parameter and to Flavor Changing Neutral Currents in models with two Higgs doublets arising as composite pseudo Nambu-Coldstone modes. The non linear Lagrangians of several models are explicitly derived and the anomalous contributions to T are identified. The breaking patterns SU(5) -> SU(4) x U(1) and SU(5) -> SU(4), are analyzed first and we show how anomalous contributions to T arise in both models. Apart front that, the embedding of the Standard Model fermions in a 10 of SU(5) avoids at the same time large corrections to the Zb (b) over bar coupling and Flavor Changing Neutral Current transitions. Finally, we propose a model based on the breaking SO(9)/SO(8) that is free from anomalous contributions to T and in which the problems of the Zb (b) over bar coupling and of Flavor Changing Neutral Currents can be simultaneously solved.