Study of the 4-component Φ4 model

The O(4) Φ4 scalar theory in four dimensions is investigated in the broken phase for various values of the quartic coupling λ and the bare mass, without and, in part, also with external source. The effect of the finite lattice size and of the Goldstone states is studied. The field expectation value, the wave-function renormalization constant, fG (the Goldstone equivalent of the pion decay constant) and the mass mσ of the massive scalar particle are determined. We obtain an upper bound on the ratio Rφ=mσ/fG, implying an upper bound of the renormalized quartic coupling λR=1/2Rφ2. It corresponds to an upper bound 8.2(5) on the ratio of Higgs mass over W-mass at values of the cut-off 1/mσ≅2.5. (orig.)