\sum_{i=1}^{3}
[{\partial}^{\mu}(W_{i\mu})]^2 - \frac{1}{2 {\xi}}
[{\partial}^{\mu}(B_{\mu})]^2  \nonumber   \\
{\cal L}_{FPG} & = & {\partial}_{\mu} {c_i}^{\dag} {\partial}^{\mu} c^i
- g{\epsilon}_{ijk} {c^i}^{\dag} c^j {\partial}^{\mu} {W_{\mu}}^k +
{\partial}_{\mu} c_0^{\dag} {\partial}^{\mu} c^0
\label{eq:quant}\end{aligned}$$

In the Appendix we show the Feynman rules derived from the Lagrangian ${\cal L}_{NLSM}$ eq.(\[eq:MENL\]) that we use for our calculations. They correspond to Figures \[fig:GF2\], \[fig:GF3\] and \[fig:GF4\]. As usual it has been useful to redefine the gauge fields as:

$$\begin{aligned}
W^{\pm}_{\mu} & = & \frac{{W_{\mu}}^1 \mp i{W_{\mu}}^2}{\sqrt{2}}  \\
Z_{\mu} & = & {\rm cos}{\theta}_W {W_{\mu}}^3 -{\rm sin}{\theta}_W
B_{\mu}
\\ A_{\mu} & = & {\rm sin}{\theta}_W {W_{\mu}}^3 + {\rm cos}{\theta}_W
B_{\mu}\end{aligned}$$

where the weak angle is defined by

$${\rm tg}{\theta}_W = \frac{g'}{g}$$

and the $GB$ as:

$$\begin{aligned}
{\pi}^{\pm} & = & \frac{{\pi}^1 \mp i{\pi}^2}{\sqrt{2}}  \\
{\pi}^0 & = & {\pi}^3\end{aligned}$$

The subprocesses cross-sections
===============================

In this work we are interested in studying of the different cross sections that contribute to the final states $Z^0Z^0$ and $W^{\pm}Z^0$ at $pp$ colliders such as $LHC$ since they are the most promising from the experimental point of view. In both cases we focus our attention on the so-called gold-plated events, where the produced bosons decay to the leptonic final states $l=e,\mu,
\nu$. In spite 