Replacing elementary Higgs exchange in vector-boson scattering by an angular-momentum-zero unitarity-saturating partial wave amplitude described by a dispersion relation which incorporates low-energy gauge theory and high-energy partial-wave unitarity constraints, we find an upper bound of Λ≲Λmax≅0.8 TeV for the scale, Λ, at which saturation of partial wave unitarity is to occur. Upon inserting the partial wave amplitude into a novel integral representation for the bosonic vacuum polarization contribution to the electroweak ρ parameter, Δρb, we establish an upper bound on −Δρb(≲0.033), while for the case of the elementary Higgs scalar, the integral representation reproduces the well known ln mH/mW formula for Δρb. The upper bound on −Δρb implies that the value of the mass of the top quark extracted from LEP1 measurements becomes justified even in the case when the Higgs scalar is replaced by a strong-interaction-like J=0 partial wave.
On the partial wave amplitude of Coulomb scattering in three dimensions