Can one really observe signatures of the weak interaction with multi-TeV colliding hadron rings?

We discuss two possible signatures of weak interactions in multi-TeV hadron-hadron collisions: (i) production of the weak boson $W^{\pm }$ and its neutral partner $Z$; (ii) observation of secondaries with transverse momentum so large that they cannot be electromagnetic or strong in origin. After summarizing theoretical prejudices on the properties of weak bosons and their production mechanism, we calculate their actual experimental signature, i.e., the momentum distributions of their decay lepton, as well as the competing backgrounds. Contrary to popular belief, we conclude that the weak-boson signature is not expected to be pronounced and backgrounds could be severe (especially the production of direct photons). Our calculation reinforces the case for antiproton-proton storage rings.