ar X iv : h ep - p h / 98 12 42 4 v 1 1 8 D ec 1 99 8 Nontriviality of the Linear Sigma Model

We consider techniques (based on an ultraviolet cutoff) used to prove that the pure boson (φ 4) 4 field theory is trivial and apply them instead to the dynamically generated quark-level linear sigma model. This cutoff approach leads to the conclusion that the latter field theory is in fact nontrivial. Owing to the recent observational identification [1] of a nonstrange scalar σ meson below 1 GeV, formal field theories discarding such a scalar σ due to " triviality " theorems (meaning the meson-meson coupling λ → 0 when cutoff Λ → ∞) should be reanalyzed as well. In the present paper we show that the quark-level Linear Sigma Model (LσM) is a non-trivial field theory in contrast with the possibly trivial pure boson (λφ 4) 4 theory. Prior studies of λφ 4 field theory using perturbative and partially nonperturbative methods [2-4] extracted physical constraints on a scalar meson mass via renormalization group bounds and scaling laws [2]. In a somewhat different manner, there 1