Structure Functions for small DIS $x$

TL;DR

This paper investigates the behavior of structure functions in small-x deep inelastic scattering for various integrable models, revealing universal and model-specific asymptotic behaviors, and confirming a conjecture in the field.

Contribution

It provides the first detailed analysis of structure functions in integrable models at small x, confirming a universal behavior and identifying model-specific power laws.

Findings

Universal behavior $x^{-1} ln^{-2}x$ at small x for certain models

Power law $x^{- ext{lambda}}$ for Sine-Gordon and related models

Confirmation of the Balog Weisz conjecture

Abstract

Structure Functions for small DIS (deep inelastic scattering) $x$ for integrable models are investigated, in particular, for the $O(N)$~$\sigma $-model and $SU(N)$ chiral Gross-Neveu model, which are asymptotically free. We get the universal behavior $x^{-1}\ln^{-2}x$ at small Bjorken variable $x$ and confirm a Balog Weisz conjecture. For a the second group of models, the Sine-Gordon, sinh-Gordon and $Z(N)$, we find power behavior $x^{-\lambda}$. The special behavior of the structure function for the Sine-Gordon model is probably crucial for future investigation in 4D QCD.