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arXiv · hep-ph/9809287

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

M. Beneke·V. M. Braun·N. Kivel
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Abstract

We obtain the operator product expansion of the self-energy in the O(N) non-linear $σ$-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 $σ$-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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M. Beneke, V. M. Braun, N. Kivel. 1998-09-07. The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $σ$-Model. https://doi.org/10.1016/s0370-2693(98)01339-2

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