Large $N$ analysis of the Higgs mass triviality bound

TL;DR

This paper investigates the theoretical limits on the Higgs boson mass using large N analysis of scalar field models, suggesting that a Higgs mass up to 0.75 TeV is consistent with triviality bounds and no large cutoff effects.

Contribution

It extends triviality bound analysis to large N scalar models and estimates Higgs mass bounds for N=4, highlighting universality and implications for the standard model.

Findings

Higgs mass up to 0.75 TeV is feasible without large cutoff effects.

Triviality bounds show universality across models.

Strong scalar self interactions remain compatible with current bounds.

Abstract

We calculate the triviality bound on the Higgs mass in scalar field theory models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial} \approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity. Limits on observable cutoff effects at four percent in several regularized models with tunable couplings in the bare action yield triviality bounds displaying a large degree of universality. Extrapolating from $N=\infty$ to $N=4$ we conservatively estimate that a Higgs particle with mass up to $0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff effects, indicating that strong scalar self interactions in the standard model are not ruled out. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called lrg_n_hig.ps (to get it type: get lrg_n_hig.ps)