embedding leading to the correct phenomenology. We describe first the contributions arising from the mixings between vector bosons after EWSB. We perform a perturbative expansion in insertions of the Higgs vacuum expectation value (vev) and in insertions of the elementary/composite mixing. In Fig. \[deltag-gauge\] we show the leading contribution arising from Higgs vev insertions in the bosonic sector.

(300,110) (-5,50)(44,50)[3]{}[4]{} (50,50)(6,0,360) (56,50)(105,50)[3]{}[4]{} (105,50)[3]{} (105,50)(89,94)[4]{} (88,100)(6.2,0,360) (93,95)(83,104) (93,104)(83,95) (105,50)(121,94)[4]{} (122,100)(6.2,0,360) (117,95)(127,104) (117,104)(127,95) (105,50)(155,50)[3]{}[4]{} (155,50)[3]{} (155,50)(185,95) (185,5)(155,50) (191,95)(6,0,360) (191,5)(6,0,360) (197,95)(247,95) (247,5)(197,5) (20,30)\[\][$Z^{el}$]{} (75,30)\[\][$Z^{cp}$]{} (130,30)\[\][$L_3^{cp},R_3^{cp}$]{} (180,60)\[\][$\psi^{cp}$]{} (220,75)\[\][$\psi^{el}$]{}

The elementary/composite insertion in the bosonic leg mixes $Z^{el}$ with $Z^{cp}$, where $Z^{el}$ is the usual combination between $B^{el}$ and $W_3^{el}$, and $Z^{cp}$ is the corresponding combination of composite vector fields (note that defining $B^{cp}$ as the field associated with $T^{3R}+T^X$, $B^{cp}$ can be written as a combination of $R_3^{cp}$ and $X^{cp}$). The Higgs vev adds a new mixing with $L_3^{cp}$ and $R_3^{cp}$. The composite bosons couple with a pair of composite fermions $\psi^{cp}$ that mix with the elementary fermions $\psi^{el}$. We obtain [@Agashe:2006at] $$\label{deltagg}
\delta g^\psi \simeq \frac{g}{c_w} \Delta g_\psi[T^{3R}({\cal P}_\psi\psi^{cp})-T^{3L}({\cal P}_\psi\psi^{cp})]$$ with $\Delta g_\psi$ defined by: $$\Delta g_\psi=\frac{g_{cp}^2}{4}\frac{v^2}{m_A^2}\frac{\Delta_\psi^2}{m_\psi^2} \ .$$ There is also a contribution to $\delta g^\psi$ arising from Higgs vev insertions in 