Using the approximate conformal invariance of QCD at high energies we consider a simple anti–de Sitter black disk model to describe saturation in deep inelastic scattering. Deep inside saturation the structure functions have the same power law scaling, $F_T\sim F_L\sim x^{-\omega }$, where $\omega$ is related to the expansion rate of the black disk with energy. Furthermore, the ratio $F_L/F_T$ is given by the universal value $\frac{1+\omega }{3+\omega }$, independently of the target. For ${\gamma }^{*}-{\gamma }^{*}$ scattering at high energies we obtain explicit expressions and ratios for the total cross sections of transverse and longitudinal photons in terms of the single parameter $\omega$.

• Received 11 January 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.072003