N ov 2 00 3 Lattice measurement of the rescaling of the scalar condensate

We have determined the rescaling of the scalar condensate Z ≡ Z ϕ near the critical line of a 4D Ising model. Our lattice data, supporting previous numerical indications, confirm the behaviour Z ϕ ∼ ln(cutoff). This result is predicted in an alternative description of symmetry breaking where there are no upper bounds on the Higgs boson mass from 'triviality'. There are many computational and analytical evidences pointing towards the 'triviality' of Φ 4 theories in 3 + 1 dimensions [1,2], though a rigorous proof is still lacking. Nevertheless these theories continue to be useful and play an important role for unified model of electroweak interactions. The conventional view, when used in the Standard Model, leads to predict a proportionality relationship between the squared Higgs boson mass m 2 H and the known weak scale v R (246 GeV) through the renormalized scalar self-coupling g R ∼ 1/ln Λ. In this picture, where m 2 H ∼ g R v 2 R , the ratio m 2 H /v 2 R is a cutoff dependent quantity that becomes smaller and smaller when Λ is made larger and larger. This usual interpretation of triviality has important phenomenological implications. For instance, a precise measurement of m H , say m H = 760 ± 21 GeV, would constrain the cutoff Λ to be smaller than 2 TeV leading to predict the existence of 'new physics' at that energy scale.