^{1,2}

^{1}

^{1}

^{2}

We discuss the triviality and spontaneous symmetry breaking scenario where the Higgs boson
without self-interaction coexists with spontaneous symmetry breaking. We argue that
nonperturbative lattice investigations support this scenario. Moreover, from lattice simulations, we predict that the Higgs boson is rather heavy. We estimate the Higgs boson mass

A cornerstone of the Standard Model is the mechanism of spontaneous symmetry breaking that, as is well known, is mediated by the Higgs boson. Then, the discovery of the Higgs boson is the highest priority of the Large Hadron Collider (LHC) [

Usually the spontaneous symmetry breaking in the Standard Model is implemented within the perturbation theory which leads to predict that the Higgs boson mass squared,

It is noteworthy to point out that (

The plan of the paper is as follows. In Section

In this section, we discuss the triviality and spontaneous symmetry breaking scenario within the simplest scalar field theory, namely, a massless real scalar field

Now, the problem is to see if it exists the continuum limit

Let us introduce the renormalized field

The lattice approach to quantum field theories offers us the unique opportunity to study a quantum field theory by means of nonperturbative methods. Starting from the classical Lagrangian (

It is known that there is a critical coupling [

As discussed in Section

On the lattice, the ultraviolet cutoff is

In [

We show the lattice data for

On the other hand, the prediction based on 2-loop renormalized perturbation theory is [

Additional numerical evidences would come from the direct detection of the condensate rescaling

The lattice data for

By adopting this alternative interpretation of triviality, there are important phenomenological implications. In fact, assuming to know the value of

The values of

One could object that our lattice estimate of the Higgs mass (

Recently, both the ATLAS and CMS collaborations [^{−1} and 2.3 fb^{−1}.

It is worthwhile to briefly discuss the main physical properties of our proposal for the trivial Higgs boson. For Higgs mass in the range

The main difficulty in the experimental identification of a very heavy Standard Model Higgs (

A thorough discussion of the experimental signatures of our trivial Higgs is presented in [^{−1} and 2.3 fb^{−1}. In fact, we argue that the available experimental data seem to be consistent with our scenario.

The Standard Model requires the existence of a scalar Higgs boson to break electroweak symmetry and provide mass terms to gauge bosons and fermion fields. Usually the spontaneous symmetry breaking in the Standard Model is implemented within the perturbation theory which leads to predict that the Higgs boson mass squared is proportional to the self-coupling. However, there exist several results which point to vanishing scalar self-coupling. Therefore, within the perturbative approach, scalar field theories represent just an effective description valid only up to some cutoff scale, for without a cutoff, there would be no scalar self-interactions and without them no symmetry breaking. In other words, spontaneous symmetry breaking is incompatible with strictly local scalar fields in the perturbative approach.

In this paper, we have shown that local scalar fields are compatible with spontaneous symmetry breaking. In this case, the continuum dynamics is governed by an ultraviolet Gaussian fixed point (triviality) and a nontrivial rescaling of the scalar condensate. We argued that nonperturbative lattice simulations are consistent with this scenario. Moreover, we find that the Higgs boson is rather heavy. Finally, the nontrivial rescaling of the Higgs condensate suggests that the whole issue of generation of fermion masses through the Yukawa couplings must be reconsidered.

^{4}model in the broken phase revisited