On the lattice approach to the maximum Higgs boson mass

If the triviality upper bound on the Higgs boson mass mH occurs for strong self-coupling, inferring properties of the Higgs from the euclidean propagator is in principle theoretically difficult whether in coordinate or momentum space. In that case, common methods of identifying mH in lattice field theory simulations may produce a value for which is at best distantly related to the true upper limit. We discuss some shortcomings and ambiguities of recent results suggesting that the maximum occurs for weak coupling and emphasize potential complications due to finite-size and non-Lorentz-invariant effects of the lattice. The situation is illustrated by reference to the behavior in analytically soluble approximation based on a 1/N expansion. (orig.)