We reexamine the unitarity constraints on the high-energy scattering of longitudinally polarized

W' s

and

Z' s

and Higgs bosons in the standard model including one-loop corrections. Using an Argand diagram analysis, we find that the

j = 0

scattering amplitudes are approximately unitary and weakly interacting at order

λ^{2}

for Higgs-boson couplings

λ (s, M_{H}^{2}) ≲ 2

, but that corrections of order

λ^{3}

or higher must be included to restore perturbative unitarity for larger values of

λ

. We show also that two-loop

[O (λ^{3})]

corrections cannot extend the range of validity of perturbation theory beyond

λ \approx 2.2

. An analysis of inelastic 2 → 4 scattering in the

W_{L}^{\pm}

Z_{L}

H

system gives an independent but weaker limit

λ (s, M_{H}^{2}) ≲ 5

. The limit

λ (s, M_{H}^{2}) < 2

translates to a physical-Higgsboson mass

M_{H} ≲ 400

GeV if the bound is to hold up to energies of a few TeV, or

M_{H} ≲ 160

GeV in perturbatively unified theories with a mass scale of order

10^{15}

GeV. For masses much larger than these bounds, low-order perturbation theory fails and the Higgs sector of the standard model becomes effectively strongly interacting.

Publications with shared reference:

0 publications found