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

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 $m_h^2=8{\pi }^2{v}_R^2$ as in the one-component case. This confirms the prediction of a weakly interacting 2.2 TeV Higgs particle in the standard model.

13 pages, RevTeX