Geometrical Scaling due to Critical Behavior Near the Light Cone

Abstract

At low $x$ a transition from a dilute parton gas to a dense parton liquid takes place. We derive geometrical scaling for the structure function in deep inelastic scattering at low $x$ from a diverging correlation length $ξ(x)$ of Wilson lines near the light cone. QCD (SU(3)) in 2+1 space - time dimensions near the light cone becomes a critical theory in the limit of $x \to 0$ with a diverging correlation length $ξ(x) \propto x^{-\frac{1}{2 λ_2}}$ where the exponent $λ_2=2.52$ is obtained from the center group Z(3) of SU(3).