Is the standard singlet Higgs a true massive field ?

TL;DR

This paper investigates whether the standard singlet Higgs boson is truly a massive particle or exhibits gapless behavior, using lattice simulations of the 4D Ising model to reveal deviations from the expected massive spectrum.

Contribution

It provides evidence that the conventional singlet Higgs may have a gapless branch, challenging the standard massive field interpretation through detailed lattice simulation results.

Findings

The single-particle energy spectrum deviates from the standard massive form in the broken phase.

The mass gap decreases with increasing lattice size, indicating volume dependence.

The results suggest the Higgs may not be a purely massive field in the infrared region.

Abstract

The phenomenon of spontaneous symmetry breaking admits a physical interpretation in terms of the Bose-condensation process of elementary spinless quanta. In a cutoff theory, this leads to a picture of the vacuum as a condensed medium whose excitations might deviate from exact Lorentz covariance in both the ultraviolet and infrared regions. For this reason, the conventional singlet Higgs boson, the shifted field of spontaneous symmetry breaking, rather than being a purely massive field, might possess a gapless branch describing the long-wavelength fluctuations of the scalar condensate. To test this idea, that might have substantial phenomenological implications, I compare with a detailed lattice simulation of the broken phase in the 4D Ising limit of the theory. The results are the following: i) differently from the symmetric phase, the single-particle energy spectrum is not reproduced by the standard massive form ii) for the value of the hopping parameter \kappa=0.076, increasing the lattice size from 20^4 to 32^4, the mass gap is found to decrease from the value 0.392(1) reported by Balog et al. (see Nucl. Phys. B714 (2005) 256) to the value 0.366(5). Both results confirm that, in the infrared region, the standard singlet Higgs cannot be considered as a simple massive field. Several arguments indicate that, approaching the continuum limit of the lattice theory, the observed volume dependence of the mass gap might require larger and larger lattice sizes before to show up.