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 M_H/ F~
\gtapprox 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.Comment: 8 pages. Latex file with 4 ps figures included. Preprint RU-92-22,
SCRI-92-11