Consider the scattering $$e^-e^-\rightarrow e^-e^-$$ in QED. The cross-section is a Lorentz invariant quantity and therefore, given by $$\sigma=\sigma(m_e,e,s,\theta)$$ where electron mass $m_e$, electron charge $e$ etc are running mass and running charge. They change with the centre-of-mass energy. $\theta$ is the scattering angle and $s$ stands for the Mandelstam variable.
QED gives a finite formula for the RHS. LHS is measured directly from experiments by measuring the scattered flux of particles in a given direction $(\theta,\phi)$. In order to check the consistency i.e., whether LHS=RHS, we have to put values of $m_e$, $e$ on the RHS by independently measuring $m_e$ and $e$ (at the colliding energy).
$m_e$ can be measured by measuring four-momenta of the scattered electrons and using dispersion relation, and by similarly measuring $e$. Is that correct?
However, if a scattering was mediated by Z/W boson as the virtual particle, the expression for $\sigma$ would contain the mass of W boson at that energy. But I believe, Z/W boson mass cannot be recovered here by measuring the four-momenta of the scattered particles. This is because, being a virtual particle, it doesn't obey energy-momentum relation.
How does one verify then the consistency of the corresponding scattering cross-section formula?