A variational study of bound states in the Higgs model

The possible existence of Higgs-Higgs bound states in the Higgs sector of the Standard Model is explored using the |hh>+|hhh> variational ansatz of Di Leo and Darewych. The resulting integral equations can be decoupled exactly, yielding a one-dimensional integral equation, solved numerically. We thereby avoid the extra approximations employed by Di Leo and Darewych, and we find a qualitatively different mass renormalization. Within the conventional scenario, where a not-too-large cutoff is invoked to avoid "triviality", we find, as usual, an upperbound on the Higgs mass. Bound-state solutions are only found in the very strong coupling regime, but at the same time a relatively small physical mass is required as a consequence of renormalization.