= q_\nu K^{\mu \nu} = 0$. This property enables the simplification of the target-related tensor, via the introduction of its effective form $$(P_{\mu \nu})_{\rm eff} = 8 \left( 2 p_\mu p_\nu + \frac{q^2}{2} g_{\mu\nu} - i \epsilon_{\mu \nu c d} p^c q^d \right) \, \, \, .$$

The contraction of the tensors $K^{\mu \nu}$ and $(P_{\mu \nu})_{\rm eff}$ finally yields the value of $64 s^2$. Necessary in the extraction of this result are the relations: $s \coloneqq (k+p)^2 = 2 k \cdot p$, $u \coloneqq (k-p^\prime)^2 = -2 k \cdot p^\prime$, and $t \coloneqq (k-k^\prime)^2 = -2k \cdot k^\prime$, which are the expressions of the Mandelstam variables for massless initial and final states. One additional relation is needed, namely $$\epsilon_{\mu \nu c d} \epsilon^{\mu \nu a b} = - 2 \left( \delta^a_c \delta^b_d - \delta^b_c \delta^a_d \right) \, \, \, ,$$ where $\delta$ denotes the standard Kronecker delta, equal to $1$ for identical indices and $0$ for different ones. Evidently, $$\label{eq:EQ120}
\lvert \mathscr{T} \rvert^2 = 8 G_F^2 s^2 \, \, \, .$$

Using this result, one obtains the DCS $$\label{eq:EQ130}
\frac{d\sigma}{d\Omega} = \frac{G^2_F s}{8 \pi^2} = \frac{\sigma_0}{8 \pi}$$ and, integrating over the solid angle, the TCS $$\sigma_{\rm tot} = \frac{\sigma_0}{2} 