& = & \frac{1}{m_{V_3}} (p', E_3 {\rm sin} \theta,
0,  E_3 {\rm cos} \theta)  \\
{\epsilon}^{\pm}_4 & = & \frac{1}{\sqrt{2}} (0, \mp {\rm cos} \theta,
 {\rm i}, \pm {\rm sin} \theta)  \\
{\epsilon}^0_4 & = & \frac{1}{m_{V_4}} (p', -E_4 {\rm sin} \theta,
0, -E_4 {\rm cos} \theta)\end{aligned}$$

The number of independent helicity amplitudes in fusion processes of massive gauge bosons, such as $Z^0Z^0 \rightarrow
Z^0Z^0$, $W^+W^- \rightarrow Z^0Z^0$, $W^+Z^0 \rightarrow
W^+Z^0$ or $W^-Z^0 \rightarrow W^-Z^0$, is $3^4=81$. The photon has only two polarized transverse states and therefore, in the processes $W^+\gamma
\rightarrow W^+Z^0$ or $W^-\gamma \rightarrow W^-Z^0$ the number of helicity amplitudes is $2 \times 3^3 = 54$. As our chiral Lagrangian affecting the boson scattering is invariant under $C$, $P$ and $T$ transformations, we can derive many relations between different helicity amplitudes. However we have not used those relations to save computations. Instead we have calculated all the helicity amplitudes in each process and the relations between them have been only used to check our results.

$Z^0Z^0$ final state
--------------------

Now we concentrate in the different processes that contribute to the final state $Z^0Z^0$ [@si]:

$$\begin{aligned}
gg           &   \rightarrow   &   Z^0Z^0  \\
q\bar{q}     &   \rightarrow   &   Z^0Z^0  \\
Z^0_TZ^0_T   