We analyze deep inelastic scattering at small Bjorken $x$, using the approximate conformal invariance of QCD at high energies. Hard Pomeron exchanges are resummed eikonally, restoring unitarity at large values of the phase shift in the dual anti-de Sitter (AdS) geometry. At weak coupling this phase is imaginary, corresponding to a black disk in AdS space. In this saturated regime, cross sections exhibit geometric scaling and have a simple universal form, which we test against available experimental data for the proton structure function $F_2(x,Q^2)$. We predict, in particular, the dependence of the cross section on the scaling variable $(Q/Q_{\mathrm{s}}{)}^2$ in the deeply saturated region, where $Q_{\mathrm{s}}$ is the usual saturation scale. We find agreement with current data on $F_2$ in the kinematical region $0.5<Q^2<10{\mathrm{GeV}}^2$, $x<{10}^{-2}$, with an average 6% accuracy. We conclude by discussing the relation of our approach with the commonly used dipole formalism.

• Received 9 June 2008

DOI:https://doi.org/10.1103/PhysRevD.78.096010