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

TL;DR

This paper revisits the triviality bound on the Higgs mass, suggesting it could be as high as 750 GeV based on large N calculations and lattice data, implying a strongly coupled scalar sector.

Contribution

It introduces a simple criterion for selecting lattice actions likely to produce a heavy Higgs and revises the Higgs mass bound upward using large N expansion and numerical data.

Findings

Higgs mass bound could be around 750 GeV.

Replacing lattice actions increases the Higgs mass estimate.

The Higgs width at 750 GeV is approximately 290 GeV.

Abstract

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 $\sim 650~GeV$ previously obtained. Preliminary numerical work indicates that an increase of at least 19\% takes place at $N=4$ on the $F_4$ 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 $M_H / F ~ \sim 6$, a meaningful ``minimal elementary Higgs'' theory cannot have $M_H/ F~ \gtapprox 3$. Still, even at 750 $GeV$, the Higgs particle is so wide ($\sim 290~$GeV), that one cannot argue any more that the scalar sector is weakly coupled.