The Cutoff $λφ^4$ O(N) Model in the Large N Limit

Details The Cutoff $λφ^4$ O(N) Model in the Large N Limit The Cutoff $λφ^4$ O(N) Model in the Large N Limit

1993-11-19

arxiv.org/abs/hep-ph/9311319v2

Int.J.Mod.Phys. A10 (1995) 719-738

Physics

High Energy Physics

High Energy Physics - Phenomenology

17 pages, BRX--TH--351-rev, Additional references; a note added, additional section on double scaling limit, and enlarged disc

Scientific paper

10.1142/S0217751X95000334

A cutoff version of the $\lambda \phi^4$ O(N) model is considered to leading order in 1/N with particular attention to the effective potential, which is surprisingly rich in structure. With suitable restriction on a background classical field, one finds a phenomenologically viable model with spontaneously broken symmetry, a potential bounded below, and amplitudes free of tachyons. The model has an O(N-1) singlet resonance in both weak and strong coupling, which can be interpreted as the Higgs meson in applications. Further, an unphysical resonance, which can be used to define a triviality scale for the model, appears at a mass above the cutoff mass $\L$. The phenomelogical aspects of our discussion are consistent with previous studies of closely related models by Heller, {\it et al.} The question of the double-scaling limit for the cutoff model is considered as an application of the effective potential. It is shown that the double-scaling limit is not possible.

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