The triviality bound on the Higgs mass; its value and what it means

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Older lattice work exploring the Higgs mass triviality bound is briefly reviewed. It indicates that a strongly interacting scalar sector in the minimal standard model cannot exist; on the other hand low energy QCD phenomenology might be interpreted as an indication that it could. We attack this puzzle using the 1/N expansion and discover a simple criterion for selecting a lattice action that is more likely to produce a heavy Higgs particle. Depending on the precise form of the limitation put on the cutoff effects, our large N calculations, when combined with old numerical data, suggest that the Higgs mass bound might be around 750 GeV, which is higher than the 650 GeV previously obtained. Preliminary numerical work indicates that an increase of at least 19% takes place at N=4 on the F₄ lattice when the old simple action is replaced with a new action (still containing only nearest neighbor interactions) if one uses the lattice spacing as the physical cutoff for both actions. It appears that, while a QCD like theory could produce Mₕ / F 6, a meaningful ``minimal elementary Higgs'' theory cannot have Mₕ/ F 3. Still, even at 750 GeV, the Higgs particle is so wide (290 GeV), that one cannot argue any more that the scalar sector is weakly coupled.