ar X iv : h ep - p h / 05 01 14 9 v 1 1 7 Ja n 20 05 1 High energy scattering in QCD as a statistical process

The scattering of two hadronic objects at high energy is similar to a reaction-diffusion process described by the stochastic Fisher-Kolmogorov equation. This basic observation enables us to derive universal properties of the scattering amplitudes in a straightforward way, by borrowing some general results from statistical physics. 1. An event-by-event picture of high energy scattering We consider the scattering of a dipole of size r off a target |q ¯ q-dipole of size r 0 as a toy model for high energy scattering. In the QCD parton model and in the rest frame of the target, the projectile interacts through one of its quantum fluctuations |q ¯ qgggg · · · which are produced by QCD radiation. At high energy, these fluctuations are dominated by dense gluonic states, generically called " color glass condensate " [ 1]. It proves useful to view the partonic configurations as collections of color dipoles [ 2] characterized by their transverse sizes r 1 , ..., r n. Each of these dipoles may interact with the target according to the elementary amplitude T el