Structure functions of the 2d O(n) non-linear sigma models

TL;DR

This paper uses the non-perturbative S-matrix bootstrap to analyze structure functions in 2D O(n) sigma models, deriving exact small-x behavior and computing structure functions for n=3 across a wide range, comparing with perturbation theory.

Contribution

It provides the first non-perturbative derivation of structure functions and their small-x behavior in 2D O(n) sigma models, including precise computations for n=3.

Findings

Exact small-x behavior derived

Structure functions computed for n=3 over full x range

Comparison with perturbation theory results

Abstract

We investigate structure functions in the 2-dimensional (asymptotically free) non-linear O(n) sigma-models using the non-perturbative S-matrix bootstrap program. In particular the exact small (Bjorken) x behavior is derived. Structure functions in the special case of the n=3 model are accurately computed over the whole x range for $-q^2/M^2<10^5$, and some moments are compared with results from renormalized perturbation theory. Some results concerning the structure functions in the 1/n approximation are also presented.