Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model

TL;DR

This paper constructs form factors in the 2D O(3) sigma model, computes their contribution to the spin-spin correlation function, and confirms the scaling hypothesis aligns with asymptotic freedom predictions.

Contribution

It provides explicit 7-particle form factors and compares their impact on correlation functions with theoretical predictions, supporting the scaling hypothesis in the model.

Findings

Good agreement with perturbation theory in the expected energy range

Simple bounds for form factor sums are identified

Supports the scaling hypothesis in the 2D O(3) sigma model

Abstract

The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $\sigma$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the spectral density scaling hypothesis. The resulting approximation to the spin--spin correlation function agrees well with that computed in renormalized (asymptotically free) perturbation theory in the expected energy range. Further we observe simple lower and upper bounds for the sum of the absolute square of the form factors which may be of use for analytic estimates.