Lattice Computation of the Effective Potential in O(2)-Invariant $\lambda\Phi^4$ Theory

TL;DR

This paper uses lattice computations to analyze the effective potential of an O(2)-invariant $rac{}{}^4$ theory, confirming predictions about a weakly interacting 2.2 TeV Higgs particle.

Contribution

It provides non-perturbative lattice results for the effective potential in an O(2)-invariant $rac{}{}^4$ theory, validating the relation between Higgs mass and vacuum expectation value.

Findings

Good agreement with one-loop predictions.

Perturbative leading-log approximation fails.

Confirms Higgs mass relation $m_h^2=8\u03C0^2 v_R^2$.

Abstract

We present a lattice computation of the effective potential for O(2)-invariant $(\lambda\Phi^4)_4$ theory in the region of bare parameters corresponding to a classically scale-invariant theory. As expected from ``triviality'' and as in the one-component theory, we find very good agreement with the one-loop prediction, while a perturbative leading-log improvement of the effective potential fails to reproduce the Monte Carlo data. The mass $m_h$ of the free shifted radial field is related to the renormalized vacuum expectation value $v_R$ through the same relation $m^2_h=8\pi^2 v^2_R$ as in the one-component case. This confirms the prediction of a weakly interacting 2.2 TeV Higgs particle in the standard model.