Structure Functions for small DIS $x$

Abstract

Structure Functions for small DIS (deep inelastic scattering) $x$ for integrable models are investigated, in particular, for the $O(N)$~$\ddot{I}ƒ$-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 $x^{-\hat{I}»}$. The special behavior of the structure function for the Sine-Gordon model is probably crucial for future investigation in 4D QCD.

31 pages, 5 figures