Unitarity constraints on multiparticle weak production

We discuss the scenario where the weak interaction cross section grows rapidly with energy. Naively, the unitarity bound is reached at energies of order mwα-1, where mw is the W-boson mass and α is the fine structure constant, while the multiplicity is of order α-1 at these energies. We argue that because of strong dominance of inelastic channels, the actual bound on the total cross section is more stringent than the geometrical value. We speculate also on the possible existence of resonance-like structures in the total cross section with masses of order mwα-1 and widths or order mw. The resonances would signify the onset of the unitarity constraints on the cross section, which grows infinite in the tree approximation. (orig.)