the fermionic lines. In this case the Higgs vev mixes the different composite fermions $\psi^{cp}$ with equal electric charge, inducing a shift in the $Z\psi\bar \psi$ coupling [@Agashe:2006at]: $$\label{deltagf}
\delta g^\psi \simeq \frac{g}{c_w} \sum_i |\alpha_{i}|^2[T^{3L}(\psi^{cp}_i)-T^{3L}(\psi^{el})] \ ,$$ where $\psi^{cp}_i$ are the composite fermions mixing with $\psi^{el}$ through Higgs vev and elementary/composite insertions, $\alpha_{i}$ is the mixing coefficient between $\psi^{el}$ and $\psi^ {cp}_{i}$. $\alpha_i$ can be obtained by diagonalizing the full mass matrix after EWSB, at perturbative level $\alpha_i\sim y_{cp}v\Delta_\psi/m_\psi m_{\psi_i}$.

The $A^b_{FB}$ anomaly and the spectrum of the third generation
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The experimental data on $A_{FB}^b$ and $R_b$ prefer a shift in the $Zb\bar b$ couplings of order $\delta g^{b_L}\sim-0.01 g^{b_L}_{SM}\sim0.003$ and $\delta g^{b_R}\sim0.25 g^{b_R}_{SM}\sim0.02$. To obtain such $\delta g^{b_R}$ we need a large mixing between $\tilde b^{el}_R$ and the composite states, this means a large $\sin\theta_b$, whereas to obtain $\delta g^{b_L}$ we require a smaller mixing between $b^{el}_L$ and the composite states, controlled by $\sin\theta_q$, as can be seen from Eqs. (\[deltagg\]) and (\[deltagf\]). In the simplest model where $q^{el}_L=(t^{el}_L,b^{el}_L)^t$ mixes with just one composite multiplet $q^{cp}$, there is just one parameter controlling the size of the interactions of $t_L$ and $b_L$ with the heavy resonances, $\sin\theta_q$. In particular 