Hadrons at very high energies are composed mainly of gluons. The non-linear evolution of these gluons is described by an infinite hierarchy of equations connecting the various k-body gluon densities to each other. This system of equations is greatly simplified if one neglects the correlations among the gluons, so that the many-body densities factorize. In this case one obtains a single, closed non-linear equation, and this equation has been intensely studied during the past years. In this work we examine both analytically and numerically the validity of the factorization assumption. We demonstrate that if one uses a dilute object, such as a proton, the correlation induced by the leading order evolution is generally strong, resulting in the violation of the factorization assumption by a factor ranging from 1.5 to order of 10. This suggests that, within the experimentally accessible energy interval, the correlations can significantly affect the non-linear evolution of the system under study.

IPhT Saclay