Understanding Geometric Scaling at Small x

Abstract

Geometric scaling is a novel scaling phenomenon observed in deep inelastic scattering at small x: the total virtual photon-proton cross section depends upon the two kinematical variables Q^2 and x only via their combination Q^2 R_0^2(x), with R_0^2(x) \propto x^{\lambda}. At sufficiently low Q^2, below the saturation scale Q_s^2(x) (a few GeV^2), this phenomenon finds a natural explanation as a property of the Color Glass Condensate, the high-density matter made of saturated gluons. To explain the experimental observation of geometric scaling up to much higher values of Q^2, of the order of 100 GeV^2, we study the solution to the BFKL equation subjected to a saturation boundary condition at Q^2\sim Q_s^2(x). We find that the scaling extends indeed above the saturation scale, within a window 1 < \ln(Q^2/Q_s^2) << \ln(Q_s^2/\Lambda^2_{\rm QCD}), which is consistent with phenomenology.