result, $g/M_W=g_N/M_Z$. The Fermi coupling constant, the sole regulator of the strength of the weak-interaction processes in Fermi’s current-current framework (pointlike approximation), is related to the aforementioned quantities via the expression $$\frac{G_F}{\sqrt{2}} = \frac{g^2}{8 M_W^2} = \frac{g_N^2}{8 M_Z^2} \, \, \, .$$

The last ingredient, which is necessary in order to advance to the derivation of the various weak-interaction scattering amplitudes, is the propagator associated with the virtual state; it is of the form $$\Pi^{\mu \nu} (q) = i \frac{-g^{\mu \nu} + q^\mu q^\nu / M^2}{q^2 - M^2} \, \, \, ,$$ where $M$ stands for the mass of the exchanged IVB.

Let me now combine these elements and obtain the weak-interaction scattering amplitude of one simple process, e.g., of the one involving the scattering of two neutrini of different flavour: $\nu_a \nu_b \to \nu_a \nu_b$. Such a process, featuring an electron neutrino as projectile, is schematically shown in Fig. \[fig:NuNu\](c). The current-propagator-current form of the scattering amplitude reads as $$\begin{aligned}
\mathscr{T} & \coloneqq - i \bra{u(\nu_a)} J_\mu \ket{u(\nu_a)} \Pi^{\mu \nu} \bra{u(\nu_b)} J_\nu \ket{u(\nu_b)}\\
&= -i \frac{g_N}{2} \bar{u}(\nu_a) \gamma_\mu \frac{1 - \gamma_5}{2} u(\nu_a) i \frac{-g^{\mu \nu} + q^\mu q^\nu / M_Z^2}{q^2 - M_Z^2} \frac{g_N}{2} \bar{u}(\nu_b) \gamma_\nu \frac{1 - \gamma_5}{2} u(\nu_b)\\
