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

Abstract

General arguments related to ``triviality'' predict that, in the broken phase of $(λΦ^4)_4$ theory, the condensate $<Φ>$ re-scales by a factor $Z_ϕ$ different from the conventional wavefunction-renormalization factor, $Z_{prop}$. Using a lattice simulation in the Ising limit we measure $Z_ϕ=m^2 χ$ 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 $Z_ϕ$ affects the relation of $<Φ>$ to the Fermi constant it can sizeably affect the present bounds on the Higgs mass.