A 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 particle numbers the n-particle spectral densities are “self-similar” in being basically rescaled copies of a universal shape function. This can be viewed as a 2-dimensional, but non-perturbative analogue of the KNO scaling in QCD. Promoted to a working hypothesis, it allows one to compute the two point functions at all energy or length scales. In addition, the values of two non-perturbative constants (needed for a parameter-free matching of the perturbative and the nonperturbative regime) are determined exactly. ∗On leave of absence from the Research Institute for Particle and Nuclear Physics, Budapest, Hungary