Low x Scattering as a Critical Phenomenon

Abstract

We discuss deep inelastic scattering at low $x$ as a critical phenomenon in 2+1 space-time dimensions. QCD (SU2) near the light cone becomes a critical theory in the limit of $\lim x \to 0$ with a correlation mass $m(x) \propto x^{ν/2}$. We conjecture that the perturbative dipole wave function of the virtual photon in the region $1/Q<x_{\bot}<1/m$ obeys correlation scaling $Ψ\propto (x_{\bot})^{-(1+n)}$ before exponentially decaying for distances larger than the inverse correlation mass. This behavior combined with an $x$ -independent dipole proton cross section gives a longitudinal structure function which shows the dominant features of the experimental data. For SU3 QCD a similar second order phase transition is possible in the presence of quark zero modes on the light cone.