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

: We obtain the operator product expansion of the self-energy in the O(N) non-linear oe-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 oe-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. 1. Short-distance observables in QCD, characterized by a large scale Q AE QCD , can be predicted perturbatively in ff s (Q) ø 1. In some cases non-perturbative power corrections in QCD=Q can be incorporated as well, using the operator product expansion (OPE) [1, 2]. Alternatively, one can deduce the structure of non-perturbative effects ..