Structure functions for small DIS x

A bstract Structure Functions for small DIS (deep inelastic scattering) x for integrable models are investigated, in particular, for the O ( N ) σ -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 the second group of models, the Sine-Gordon, sinh-Gordon and Z ( N ), we find power behavior x − λ . The special behavior of the structure function for the Sine-Gordon model is probably crucial for future investigation in 4D QCD.