Structure functions of 2d integrable asymptotically free models

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 {\it 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 $-q^2/M^2<10^5$, 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.

16 pages, 6 figures

References in corpus (3)

• Deep-Inelastic Inclusive ep Scattering at Low x and a Determination of alpha_s
• Small x Phenomenology: Summary and Status
• Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model

Cited by in corpus (4)

• Construction and clustering properties of the 2-d non-linear sigma-model form factors: O(3), O(4), large n examples
• Structure functions of the 2d O(n) non-linear sigma models
• Bjorken and threshold asymptotics of a space-like structure function in the 2D $U(N)$ Gross-Neveu model
• Asymptotic factorization of n-particle SU(N) form factors