Padé approximants and unitarity in ${\mathit{W}}^{+}$${\mathit{W}}^{\mathrm{-}}$ and ${\mathit{Z}}^0$${\mathit{Z}}^0$ scattering

The effect of unitarization on the s-wave amplitudes for the coupled ${\mathit{W}}_{\mathit{L}}^{+}$ ${\mathit{W}}_{\mathit{L}}^{\mathrm{-}}$-${\mathit{Z}}_{\mathit{L}}^0$ ${\mathit{Z}}_{\mathit{L}}^0$ system is studied using the Padé-approximant method and the complete one-loop expressions for the perturbative amplitudes. For values of the Higgs-boson-mass parameter ${\mathit{m}}_{\mathit{H}}$ less than 1.0 TeV, the Padé amplitudes and those unitarized using the one-loop K-matrix method are essentially identical. When ${\mathit{m}}_{\mathit{H}}$, which also determines the strength of the Higgs-boson self-coupling in the standard model, exceeds 2.6 TeV, the Padé amplitudes begin to develop a resonant feature below the value of ${\mathit{m}}_{\mathit{H}}$. The K-matrix amplitudes do not develop a low-mass resonance. At ${\mathit{m}}_{\mathit{H}}$=10 TeV, this peak occurs at about 1.4 TeV, while at ${\mathit{m}}_{\mathit{H}}$=50 TeV, it occurs at 950 GeV with a width of about 325 GeV. The Argand diagrams exhibit resonant behavior at these energies. By examining the Argand diagrams for a large range of values of ${\mathit{m}}_{\mathit{H}}$, it appears that this Higgs-boson-like resonance has a mass that does not exceed 2.6 TeV. It is also evident that both the mass and width of the resonance decrease as ${\mathit{m}}_{\mathit{H}}$ increases beyond 10 TeV. The couplings of the resonance to ${\mathit{W}}_{\mathit{L}}^{+}$ ${\mathit{W}}_{\mathit{L}}^{\mathrm{-}}$ and ${\mathit{Z}}_{\mathit{L}}^0$ ${\mathit{Z}}_{\mathit{L}}^0$ are similar to the standard-model couplings of a low-mass elementary Higgs boson. We compare our conclusions with those reached by Dobado, Herrero, and Truong for ${\mathit{W}}_{\mathit{L}}^{+}$ ${\mathit{W}}_{\mathit{L}}^{\mathrm{-}}$ scattering.