ar X iv : h ep - p h / 02 05 19 8 v 1 1 8 M ay 2 00 2 UNDERSTANDING GEOMETRIC SCALING AT SMALL X

Geometric scaling is a novel scaling phenomenon observed in deep inelastic scattering at small x: the total γ * p cross section depends upon the two kinematical variables Q 2 and x only via their combination ξ ≡ Q 2 R 2 0 (x), with R 2 0 (x) ∝ x λ. At sufficiently low Q 2 , below the saturation scale Q 2 s (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 ∼ Q 2 s (x). We find that the scaling extends indeed above the saturation scale, within a window 1 < ∼ ln(Q 2 /Q 2 s) ≪ ln(Q 2 s /Λ 2 QCD), which is consistent with phenomenology. Recently, Sta´sto, Golec-Biernat and Kwieci´nski have shown 1 that the HERA data on deep inelastic scattering at low x, which are a priori functions of two independent variables — the photon virtuality Q 2 and the Bjorken variable x —, are consistent with scaling in terms of the variable ξ = Q 2 R 2 0 (x) (1) where R 2 0 (x) = (x/x 0) λ /Q 2 0 with the parameters λ = 0.3 ÷ 0.4, Q 0 = 1 GeV, and x 0 ∼ 3 × 10 −4 determined to fit the data. In particular, the data for the virtual photon total cross section at x < 0.01 and 0.045 < Q 2 < 450 GeV 2 are consistent with being only a function of ξ. This is the phenomenon called the " geometric scaling ". In this talk, we argue that this is a manifestation of gluon saturation and explain why it holds even outside the saturation regime. For more details, see Ref. 2.