Lattice measurement of the energy-gap in a spontaneously broken phase

TL;DR

This study uses lattice simulations to measure the energy spectrum in a broken phase of a scalar field theory, revealing that the energy gap differs from the Higgs mass and depends on lattice size, potentially vanishing in the infinite-volume limit.

Contribution

It provides the first lattice measurement showing the energy gap in a broken phase is not equal to the Higgs mass and varies with lattice size.

Findings

The energy gap decreases as lattice size increases.

The energy gap may vanish in the infinite-volume limit.

The measured energy gap differs from the Higgs mass.

Abstract

Using lattice simulations of a one-component $(\lambda \Phi^4)_4$ theory, we have measured the energy spectrum $\omega({\mathbf{k}})$ in the broken phase at various lattice sizes. Our data show that the energy-gap $\omega(0)$ is {\it not} the `Higgs mass' $M_h$ but an infrared-sensitive quantity that becomes smaller and smaller by increasing the lattice size and may even vanish in the infinite-volume limit.