Nonlineark⊥factorization for gluon-gluon dijets produced off nuclear targets

The origin of the breaking of conventional linear $k_{\perp }$ factorization for hard processes in a nuclear environment is by now well established. The realization of the nonlinear nuclear $k_{\perp }$ factorization which emerges instead was found to change from one jet observable to another. A basic ingredient of the master formula for the dijet spectrum is the $\mathsf{S}$ matrix for color-singlet multiparton states, and here we report on an important technical progress, the evaluation of the four-gluon color-dipole cross section operator. It describes the coupled seven-channel non-Abelian intranuclear evolution of the four-gluon color-singlet states. An exact diagonalization of this seven-channel problem is possible for large number of colors $N_c$ and allows a formulation of nonlinear $k_{\perp }$ factorization for production of gluon-gluon dijets. The momentum spectra for dijets in all possible color representations are reported in the form of explicit quadratures in terms of the collective nuclear unintegrated glue. Our results fully corroborate the concept of universality classes.