&  W^+ Z^0  \\
W^+_L Z^0_T &  \rightarrow  &  W^+ Z^0  \\
W^+_L Z^0_L &  \rightarrow  &  W^+ Z^0  \\
W^-_T Z^0_T &  \rightarrow  &  W^- Z^0  \\
W^-_T Z^0_L &  \rightarrow  &  W^- Z^0  \\
W^-_L Z^0_T &  \rightarrow  &  W^- Z^0  \\
W^-_L Z^0_L &  \rightarrow  &  W^- Z^0  \\
W^+_T \gamma & \rightarrow  &  W^+ Z^0  \\
W^+_L \gamma & \rightarrow  &  W^+ Z^0  \\
W^-_T \gamma & \rightarrow  &  W^- Z^0  \\
W^-_L \gamma & \rightarrow  &  W^- Z^0\end{aligned}$$

where we call $q=u,c$ and $q'=d,s,b$.

Most of the boson pairs $W^{\pm}Z^0$ are obtained in $pp$ colliders via quark-antiquark annihilations. Using the chiral Lagrangian framework we calculate the corresponding cross section at tree level order. As we can see in Figure \[fig:qq’\], three standard $s$, $t$ and $u$ diagrams contribute, but the new physics coming from the non-linear lagrangian is isolated in the three boson vertex, which in this process affects only the $s$ channel.

$$M = M_s + M_t + M_u$$

If we look at the Feynman rules (Figure \[fig:GF3\]) we can deduce that the set of ${\alpha}_k$ parameters contributing to this process are ${\alpha}_1$, ${\alpha}_2$, ${\alpha}_3$, ${\alpha}_8$, ${\alpha}_9$, ${\alpha}_{11}$, ${\alpha}_{12}$ and ${\alpha}_{13}$ eq.(\[eq:GF3\]). In the 