Lattice effective potential of massless $(\lambda\Phi^4)_4$: `triviality' and spontaneous symmetry breaking

TL;DR

This paper uses lattice computations to study the effective potential of massless $( abla ext{lambda} ext{Phi}^4)_4$ theory, confirming spontaneous symmetry breaking via dimensional transmutation and challenging the triviality hypothesis.

Contribution

It provides the first precise lattice evidence of spontaneous symmetry breaking in $( abla ext{lambda} ext{Phi}^4)_4$ without residual self-interactions, contradicting perturbative predictions.

Findings

Confirmation of a phase with spontaneous symmetry breaking on the lattice.

Effective potential shows no residual self-interaction effects.

Higgs mass is not a measure of observable interaction.

Abstract

We present a precise lattice computation of the slope of the effective potential for massless $(\lambda\Phi^4)_4$ theory in the region of bare parameters indicated by the Brahm's analysis of lattice data. Our results confirm the existence on the lattice of a remarkable phase of $(\lambda\Phi^4)_4$ where Spontaneous Symmetry Breaking is generated through ``dimensional transmutation''. The resulting effective potential shows no evidence for residual self-interaction effects of the shifted `Higgs' field $h(x)=\Phi(x)-\langle\Phi\rangle$, as predicted by ``triviality'', and cannot be reproduced in perturbation theory. Accordingly the mass of the Higgs particle, by itself, does not represent a measure of any observable interaction.