Non-perturbative aspects in a weakly interacting Higgs sector

Just like the weakly interacting QED can support non-perturbative phenomena, like atoms, so can the weak and Higgs interactions. Especially, there are strong field-theoretical arguments that only bound states can be the (quasi-)asymptotic physical degrees of freedom of this sector. After a brief review of these arguments, the 2-point, 3-point and 4-point correlation functions of the Higgs-W system are determined using lattice gauge theory. The results support a conjectured duality between elementary states and bound states for weak Higgs self-interactions. This leads to relations between the bound states and the experimentally observed particles. Interestingly, these may yield pseudo-scalar admixtures at the Higgs energy, and possibly a faint standard-model signal in the channel where a Kaluza-Klein graviton would be expected.