Nonstandard implementation of the standard Higgs boson

We discuss an alternative implementation of the Higgs boson within the Standard Model which is possible if the renormalizability condition is relaxed. Namely, at energy scale Λ the Higgs boson interacts at tree-level only with matter fermions, while the full gauge invariance is still maintained. The interactions with the electroweak gauge bosons are induced at low energies through the radiative corrections. In this scenario the Higgs boson can be arbitrarily heavy, interacting with the Standard Model fields arbitrarily weakly. No violation of unitarity in the scattering of longitudinal electroweak bosons occurs, since they become unphysical degrees of freedom at energies Λ ∼ TeV. The Higgs particle [1] is widely expected to be found in high energy experiments at LHC. A theoretical motivation for the existence of such a particle is related to a ”bad” high energy behaviour of the electroweak theory with purely massive vector bosons. Namely, scattering amplitudes of longitudinal modes (WL and ZL) of the massive electroweak vector bosons scale (at tree level) as √ s with the center-of-mass energy (ECoM = √ s), and thus quickly saturate the unitarity bound at about √ s ∼ 800 GeV. A relatively light (with a mass less than the unitarity bound) Higgs boson, which couples to the electroweak gauge bosons in gauge invariant way, automatically provides cancellation of the bad energy behaviour of the tree-level (and also higher order) amplitudes, regaining the unitarity of the theory. The converse statement is also true: any unitary and renormalizable theory of massive electroweak bosons must involve gauge invariant interactions with the Higgs particle [2]. If so, than the coupling of the Higgs particle to electroweak vector bosons is fixed by the gauge invariance. This fact is crucial in searching for the Higgs particle in actual experiments, e.g. in associate production of the Higgs and vector bosons. In this paper we would like to explore unortodox model of spontaneous electroweak symmetry breaking with nonstandard interactions of the Higgs particle and electroweak vector bosons, which, to the best of our knowledge, has not been discussed previously. The model we are going to present is based on the observation that, contrary to a widespread belief, gauge invariance per se does not uniquely fix the interactions of the Higgs boson. The standard interactions of the Higgs boson with electroweak vector fields implied in the Standard Model, follow only if, in addition to the gauge invariance, one demands the renormalizability of the theory. However, from a modern perspective, the Standard Model is widely viewed as an effective low-energy theory, and thus its renormalizability perhaps is not very well justified requirement. If one relaxes the renormalizability requirement, one can write down an alternative to the Standard Model theory which is also perfectly unitary and gauge invariant, but the interactions of the Higgs boson are entirely different. The key idea behind such a theory is the following. If the coupling of the Higgs boson to the electroweak gauge bosons is absent, then the longitudinal modes are non-propagating degrees of the freedom due to the gauge invariance in the classical theory at certain energy scale Λ 1. The interactions with the electroweak gauge bosons and their masses are induced at low energies through the radiative corrections involving fermionic loops. No violation of unitarity in the scattering of longitudinal electroweak bosons occurs, since they are unphysical degrees of freedom at energies Λ ∼ TeV. The remarkable thing then is that the unitarity bound is decoupled from the Higgs boson mass. That is to say, the Higgs boson can be arbitrarily heavy, providing it interacts arbitrarily weakly with the Standard Model fields. In this regime, the Higgs boson might not be observable at LHC. 1In [3] we have discussed the model with the explicit breaking of the electroweak symmetry where all the components of the electroweak doublet are not propagating degrees of freedom at the classical level.