First lattice evidence for a non-trivial renormalization of the Higgs condensate

General arguments related to ``triviality’’ predict that, in the broken phase of $(\lambda {\mathrm{\Phi }}^4{)}_4$ theory, the condensate $<\mathrm{\Phi }>$ re-scales by a factor $Z_{\varphi }$ different from the conventional wavefunction-renormalization factor, $Z_{prop}$. Using a lattice simulation in the Ising limit we measure $Z_{\varphi }=m^2\chi$ from the physical mass and susceptibility and $Z_{prop}$ from the residue of the shifted-field propagator. We find that the two $Z$’s differ, with the difference increasing rapidly as the continuum limit is approached. Since $Z_{\varphi }$ affects the relation of $<\mathrm{\Phi }>$ to the Fermi constant it can sizeably affect the present bounds on the Higgs mass.