&   \rightarrow   &   Z^0Z^0  \\
Z^0_TZ^0_L   &   \rightarrow   &   Z^0Z^0  \\
Z^0_LZ^0_T   &   \rightarrow   &   Z^0Z^0  \\
Z^0_LZ^0_L   &   \rightarrow   &   Z^0Z^0  \\
W^+_TW^-_T   &   \rightarrow   &   Z^0Z^0  \\
W^+_TW^-_L   &   \rightarrow   &   Z^0Z^0  \\
W^+_LW^-_T   &   \rightarrow   &   Z^0Z^0  \\
W^+_LW^-_L   &   \rightarrow   &   Z^0Z^0\end{aligned}$$

Note that we separate the contribution of the different polarizations channels in the initial state, since different polarizations will have different luminosities in $pp$ collisions. In particular we use the Weizsaker-Williams [@fegamm] and the effective $W$ approximation [@Daw] to compute the $V_1V_2$ pair luminosity in the $LHC$ beams. Therefore, we have to divide these cross-sections into the contributions coming from the different gauge boson initial polarizations.

On the other hand, it is well known that at supercollider energies the one-loop process $gg \rightarrow ZZ$ is not negligible. The gluon-gluon fusion cross section was calculated in the Minimal Standard Model, $MSM$ (with just one Higgs doublet) via one-loop of quarks by Glover and Van deer Bij [@Glo]. The corresponding diagrams are shown in Figure \[fig:gg\]. As we are using a chiral Lagrangian description of the ESB sector we do not include the contribution coming from diagrams with the Higgs boson in our computations.

The quark-antiquark 