Basics of the Color Glass Condensate ∗

The physics of the color glass condensate [1–3] covers and unifies under the same banner topics which have originally appeared and developed under various names — “small–x physics”, “BFKL evolution”, “unitarity corrections”, “parton saturation”, “multiple pomeron exchanges”, “higher twist effects”, etc. —, but which are modernly understood as manifestations or consequences of the same basic physical mechanism: a change in the form of gluonic matter in the hadron wavefunction at small–x. This change can be visualized as a “critical line” which divides the kinematical plane for deep inelastic scattering into two regions (see Fig. 1): a low density region at high Q (for a given value of x, or τ ≡ ln(1/x)), in which parton densities evolve according to linear evolution equations (DGLAP or BFKL) and grow rapidly with 1/x, and a high density regime at relatively low Q, where the parton densities saturate because of the large non–linear effects, and the gluons form a condensate. This is a high–density state characterized by an intrinsic scale, the saturation momentum Qs(x), and by large occupation numbers, of order 1/αs, for the gluonic modes with momentum less than or equal to Qs. The saturation momentum is the typical momentum of the saturated gluons, and grows rapidly with the energy, as a power of 1/x . The saturation line Q = Q s (x) is the separating line in Fig. 1. Note that the transition across this line is rather smooth, and should not be thought of as a phase transition in the sense of thermodynamics: to my knowledge, no quantity becomes discontinuous at this line. The smooth character of the transition is best demonstrated by the fact that a qualitative