English

Triviality" and the Perturbative Expansion in $\lambda\Phi^4$ Theory

High Energy Physics - Phenomenology 2007-05-23 v1

Abstract

The "triviality" of (λΦ4)4(\lambda\Phi^4)_4 quantum field theory means that the renormalized coupling λR\lambda_R vanishes for infinite cutoff. That result inherently conflicts with the usual perturbative approach, which begins by postulating a non-zero, cutoff-independent λR\lambda_R. We show how a "trivial" solution λR=0\lambda_R=0 can be compatible with the known structure of perturbation theory to arbitrarily high orders, by a simple re-arrangement of the expansion. The "trivial" solution reproduces the result obtained by non-perturbative renormalization of the effective potential. The physical mass is finite, while the renormalized coupling strength vanishes: the two are NOT proportional. The classically scale-invariant λΦ4\lambda \Phi^4 theory coupled to the Standard Model predicts a 2.2 TeV Higgs, but does NOT imply strong interactions in the scalar sector.

Keywords

Cite

@article{arxiv.hep-ph/9403299,
  title  = {Triviality" and the Perturbative Expansion in $\lambda\Phi^4$ Theory},
  author = {M. Consoli and P. M. Stevenson},
  journal= {arXiv preprint arXiv:hep-ph/9403299},
  year   = {2007}
}

Comments

10 pages, LaTeX, no figures, DE-FG05-92ER40717-13, MAD/TH/94-4

R2 v1 2026-07-22T14:20:21.037Z