Structure functions of 2d integrable asymptotically free models

Abstract We investigate structure functions in the 2-dimensional (asymptotically free) non-linear O( n ) σ -models using the non-perturbative S-matrix bootstrap program. In particular the exact small (Bjorken) x behavior is exhibited ; the structure is rather universal and is probably the same in a wide class of (integrable) asymptotically free models. Structurally similar universal formulae may also hold for the small x behavior of QCD in 4-dimensions. Structure functions in the special case of the n =3 model are accurately computed over the whole x range for − q 2 / M 2 5 , and some moments are compared with results from renormalized perturbation theory. Some remarks concerning the structure functions in the 1/ n approximation are also made.