Is there a strong interaction sector in the standard lattice Higgs model?

From the suspected ''triviality'' of the standard lattice Higgs model one expects that the physical Higgs self-coupling cannot exceed a certain maximal value, which depends on the ultra-violet cutoff Λ=1/a (a: lattice spacing). We have determined this upper bound for all values of the cutoff larger than twice the Higgs mass in the approximation proposed by Dashen and Neuberger, where the gauge coupling is treated as a small parameter. As a result we find that the Higgs self-coupling is always smaller than about 2/3 of the tree level unitarity bound, i.e. there is no strong coupling lattice Higgs model which could be regarded as an effective continuum theory at low energies. (orig.)