Variational study of bound states in the Higgs model

Abstract

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.

Light Higgs bosons from a strongly interacting Higgs sector

“…We have shown that a further increase of the coupling strength yields a decrease of the mass [12], and this has also been confirmed by recent Bethe-Salpeter calculations [13]. The physical reason is very simple: at tree level m is proportional to λ; however the interaction renormalizes the mass, since the attractive self-coupling reduces the energy of a free boson.…”

“…An exact decoupling can be easily achieved by the method of Ref. [12], thus avoiding any further approximation. The full details will be published elsewhere.…”

“…In the framework of a study on bound states we have recently shown [12] that the variational equations can be decoupled exactly, giving important consequences on mass renormalization. In this letter we show that the same method can be used for decoupling the variational equations arising from a more complete trial state, describing a Higgs field h which interacts with a neutral gauge vector field Z µ :…”

“…[12] for a decrease of the numerical coefficient of the first (repulsive) term inside the brackets. In Eq.…”

Study of virtual annihilation and retardation effects in relativistic two-, four-, and six-body wave equations in scalar QFT

“…Hence, it would be also of interest to investigate the existence of bound states and related relativistic effects of the few-body Higgs bosons such as fourbody Higgs systems or even larger structures. For example, the existence of two-Higgs-boson bound states has been studied in references [33,34].…”