A Scaling Hypothesis for the Spectral Densities in the O(3) Nonlinear Sigma-Model

TL;DR

The paper proposes a universal scaling hypothesis for spectral densities in the O(3) nonlinear sigma-model, enabling the calculation of two-point functions across all scales and determining key non-perturbative constants exactly.

Contribution

It introduces a self-similarity scaling hypothesis for spectral densities, extending the understanding of non-perturbative effects in the O(3) sigma-model.

Findings

Spectral densities exhibit self-similarity at large particle numbers.

Two non-perturbative constants are determined exactly.

The hypothesis allows computation of two-point functions at all scales.

Abstract

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 non-perturbative regime) are determined exactly.