The asymptotic states in weak interactions need to be gauge-invariant with respect to the weak gauge symmetry. This is required by a number of formal reasons, but also to ensure a smooth transition e.g. across the electroweak crossover at finite temperature.
Such states are necessarily composite. However, for the standard model, the Fröhlich-Morchio-Strocchi mechanism yields a map, which, depending on the process, alters predictions only at either NLO or NNLO. It also shows that th spectrum has identical properties to the elementary one.
We discuss an augmentation of perturbation theory to take this into account, and dicuss a few examples of consequences in a reduced standard model setups on the lattice. This includes impacts on spectral functions, cross sections as well as electroweak PDFs.