M. Consoli

Lattice (Φ4)4 effective potential giving spontaneous symmetry breaking and the role of the Higgs mass

We present a critical reappraisal of the available results on the broken phase ofλ(Φ4)4 theory, as obtained from rigorous formal analyses and from lattice calculations. All the existing evidence is compatible with Spontaneous Symmetry Breaking but dictates a trivially free shifted field that becomes controlled by a quadratic hamiltonian in the continuum limit. As recently pointed out, this implies that the simple one-loop effective potential should become effectively exact. Moreover, the usual naive assumption that the Higgs mass-squaredmh2 is proportional to its “renormalized” self-couplingλR is not valid outside perturbation theory: the appropriate continuum limit hasmh finite and vanishingλR. A Monte Carlo lattice computation of theλ(Φ4)4 effective potential, both in the single-component and in theO(2)-symmetric cases, is shown to agree very well with the one-loop prediction. Moreover, its perturbative leading-log improvement (based on the concept ofλR) fails to reproduce the Monte Carlo data. These results, while supporting in a new fashion the peculiar “triviality” of theλ(Φ4)4 theory, also imply that, outside perturbation theory, the magnitude of the Higgs mass does not give a measure of the observable interactions in the scalar sector of the standard model.

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

Abstract 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 /gf4 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.

Indications on the Higgs boson mass from lattice simulations

Abstract The ‘triviality’ of Φ 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 π. 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 π → ∞. 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 mH = 760 ± 21 GeV, independently of π.

Quantum-hydrodynamical picture of the massive Higgs boson

Abstract.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

Dynamics of the scalar condensate in thermal 4D self-interacting scalar field theory on the lattice

{\vec{k}} \to 0

(λΦ4)4 theory on the lattice: evidence for a non-trivial rescaling of the scalar condensate.

: a massive energy branch

The (λθ4)4 theory on the lattice: effective potential and triviality

E_a({\vec{k}}) \to M_H

Large logarithmic rescaling of the scalar condensate: a subtlety with substantial phenomenological implications

, corresponding to the usual Higgs boson field, and a collective gapless branch

Large logarithmic rescaling of the scalar condensate: new lattice evidences

E_b({\vec{k}}) \to 0

The Real Test of ``Triviality'' on the Lattice

. This is similar to the coexistence of phonons and rotons in superfluid 4He that, in fact, is usually considered the condensed-matter analog of the Higgs condensate. After previous work dedicated to the properties of the gapless phonon branch, in this paper we use quantum hydrodynamics to propose a physical interpretation of the massive branch. On the base of our results, MH coincides with the energy gap for vortex formation and a massive Higgs boson is like a roton in superfluid 4He. Within this interpretation of the Higgs particle, there is no naturalness problem since MH remains a naturally intermediate, fixed energy scale, even for an ultimate ultraviolet cutoff