have investigated the implications of top compositeness, computing the contributions to the Peskin-Takeuchi $T$-parameter [@Peskin:1990zt] and determining the allowed degree of top compositeness. They have also focus on the phenomenology calculating the four top production at the LHC.

The paper is organized as follows: in the next section we describe the model introducing an elementary sector, a composite sector and a Lagrangian mixing both sectors. In section \[Zbb\] we show the tree level corrections to $Zb\bar b$ in this kind of models. Sections \[sym\] and \[nosym\] contain the most important results, there we show different models with and without a symmetry protecting $Zb_L\bar b_L$, discuss the main issues of each approach and show our numerical results. In section \[phenomenology\] we discuss some important predictions for the phenomenology, like the spectrum of lightest excitations and the corrections to $Zt\bar t$. In section \[5d\] we briefly describe a five dimensional completion of the effective two sector model. We conclude in section \[conclusions\] and compare our results with other similar scenarios already present in the literature.

Effective Model {#effmodel}
===============

We consider an effective model with elementary fields describing the SM particle content and a composite sector with composite fields (we include the 