amplitude in this process receives contributions from the $t$ and $u$ channels, by exchanging a $W$ or a $\pi$, and directly from the vertex $W^+W^-Z^0Z^0$ (Figure \[fig:WW\]). Therefore we can write:

$$M_{{{\lambda}_1}{{\lambda}_2}{{\lambda}_3}{{\lambda}_4}} = [M_{t_1} +
M_{t_2} + M_{u_1} + M_{u_2} + M_4 ]_{{{\lambda}_1}{{\lambda}_2}
{{\lambda}_3}{{\lambda}_4}}$$

where the subscript $1$($2$) is referred to the exchange of a gauge boson (Goldstone boson) through the corresponding channel. There are $81$ helicity amplitudes, but the number of independent $M_{{{\lambda}_1}
{{\lambda}_2} {{\lambda}_3} {{\lambda}_4}}$ is reduced to $25$ by means of symmetry relations derived from $P$ and $C$ invariance.

As we expected, the amplitudes that we have obtained satisfy these equalities. On the other hand, all the chiral parameters, ${\alpha}_k$ (but ${\alpha}_{10}$), affect this process as we can deduce from the Feynman rules eqs.(\[eq:GF3\] and \[eq:GF4\]) and from the different diagrams that contribute to the collision $W^+W^- \rightarrow Z^0Z^0$.

$W^{\pm}Z^0$ final state
------------------------

As it was previously said, we have also studied the $W^{\pm}Z^0$ final state. The different sources for $W^{\pm}Z^0$ pairs in $pp$ colliders at tree level order are the following:

$$\begin{aligned}
q\bar{q'}  &  \rightarrow  &  W^+Z^0    \\
q'\bar{q}  &  \rightarrow  &  W^-Z^0    \\
W^+_T Z^0_T &  \rightarrow  &  W^+ Z^0  \\
W^+_T Z^0_L &  \rightarrow  