Perturbative versus non-perturbative QFT lessons from the O(3) NLS model

The two-point functions of the energy-momentum tensor and the Noether current are used to probe the O(3) nonlinear sigma model in an energy range below 104 in units of the mass gap m. We argue that the form factor approach, with the form factor series truncated at the 6-particle level, provides an almost exact solution of the model in this energy range. The onset of the (2-loop) perturbative regime is found to occur only at energies around 100m.