Scaling hypothesis for the spectral densities in the O(3) nonlinear sigma model

A scaling hypothesis for the n-particle spectral densities of the O(3) nonlinear sigma model is described. It states that for large n the n-particle spectral densities are ''self-similar'' in being rescaled copies of a universal shape function. Promoted to a working hypothesis, it allows one to compute the two-paint functions at all energy scales and yields exact values for two nonperturbative constants. Applied to nonintegrable perturbations of the model, the hypothesis implies scaling laws for multiparticle production processes analogous to Koba-Nielsen-Olesen scaling in QCD.