The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $σ$-Model

Details The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $σ$-Model The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $σ$-Model

1998-09-07

arxiv.org/abs/hep-ph/9809287v1

Phys.Lett.B443:308-316,1998

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, 3 figures

Scientific paper

10.1016/S0370-2693(98)01339-2

We obtain the operator product expansion of the self-energy in the O(N) non-linear $\sigma$-model to all orders in the coupling and the large momentum, and to next-to-leading order in 1/N. In the light of this result we discuss recent suggestions that there may be additional power corrections from short distances, associated with defining the coupling constant non-perturbatively. The non-linear $\sigma$-model provides no evidence for such `non-standard' power corrections. We also find that the OPE converges for sufficiently large external momentum, presumably because there are no multi-particle thresholds at arbitrarily high energies in the 1/N expansion.

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