Quantum-hydrodynamical picture of the massive Higgs boson

The phenomenon of spontaneous symmetry breaking admits a physical interpretation in terms of the Bose-condensation process of elementary spinless quanta. In this picture, the broken-symmetry phase emerges as a real physical medium, endowed with a hierarchical pattern of scales, supporting two types of elementary excitations for k \to 0: a massive energy branch E_a(k) \to M_H, corresponding to the usual Higgs boson field, and a collective gap-less branch E_b(k) \to 0. This is similar to the coexistence of phonons and rotons in superfluid He-4 that, in fact, is usually considered the condensed-matter analog of the Higgs condensate. After previous work dedicated to the properties of the gap-less, phonon branch, in this paper we use quantum hydrodynamics to propose a physical interpretation of the massive branch. On the base of our results, M_H coincides with the energy-gap for vortex formation and a massive Higgs boson is like a roton in superfluid He-4. Within this interpretation of the Higgs particle, there is no "naturalness" problem since M_H remains a naturally intermediate, fixed energy scale, even for an ultimate ultraviolet cutoff Lambda \to \infty.Comment: Latex file, 20 pages, no figure

A weak, attractive, long-range force in Higgs condensates

Due to the peculiar nature of the underlying medium, density fluctuations in a `Higgs condensate' are predicted to propagate for infinitely long wavelengths with a group velocity $c_s\to \infty$. On the other hand, for any large but finite $c_s$ there is a weak, attractive $1/r$ potential of strength ${{1}\over{c^2_s}}$ and the energy spectrum deviates from the purely massive form \sqrt{p}^2 + M^2_h} at momenta smaller than $\delta\sim {{M_h}\over{c_s}}$. Physically, the length scale $\delta^{-1}$ corresponds to the mean free-path for the elementary constituents in the condensate and would naturally be placed in the millimeter range.Comment: 12 pages, LaTe

Long-wavelength excitations of Higgs condensates

Quite independently of the Goldstone phenomenon, recent lattice data suggest the existence of gap-less modes in the spontaneously broken phase of a $\lambda \Phi^4$ theory. This result is a direct consequence of the quantum nature of the `Higgs condensate' that cannot be treated as a purely classical c-number field.Comment: 6 page

Large rescaling of the Higgs condensate: theoretical motivations and lattice results

In the Standard Model the Fermi constant is associated with the vacuum expectation value of the Higgs field, `the condensate', usually believed to be a cutoff-independent quantity. General arguments related to the `triviality' of $\Phi^4$ theory in 4 space-time dimensions suggest, however, a dramatic renormalization effect in the continuum limit that is clearly visible on the relatively large lattices available today. The result can be crucial for the Higgs phenomenology and in any context where spontaneous symmetry breaking is induced through scalar fields.Comment: LATTICE99(Higgs) 3 pages, 3 figure

Indications on the Higgs boson mass from lattice simulations

The `triviality' of $\Phi^4_4$ has been traditionally interpreted within perturbation theory where the prediction for the Higgs boson mass depends on the magnitude of the ultraviolet cutoff $\Lambda$. This approach crucially assumes that the vacuum field and its quantum fluctuations rescale in the same way. The results of the present lattice simulation, confirming previous numerical indications, show that this assumption is not true. As a consequence, large values of the Higgs mass $m_H$ can coexist with the limit $\Lambda\to \infty$. As an example, by extrapolating to the Standard Model our results obtained in the Ising limit of the one-component theory, one can obtain a value as large as $m_H=760 \pm 21$ GeV, independently of $\Lambda$.Comment: 3 pages, 2 figures, Lattice2003(higgs