Nonlinear k_\perp-factorization for Quark-Gluon Dijet Production off Nuclei

The breaking of conventional linear k_\perp-factorization for hard processes in a nuclear environment is by now well established. Here we report a detailed derivation of the nonlinear k_\perp-factorization relations for the production of quark-gluon dijets. This process is of direct relevance to dijets in the proton hemisphere of proton-nucleus collisions at energies of the Relativistic Heavy Ion Collider (RHIC). The major technical problem is a consistent description of the non-Abelian intranuclear evolution of multiparton systems of color dipoles. Following the technique developed in our early work [ N.N. Nikolaev, W. Sch\"afer, B.G. Zakharov and V.R. Zoller, J. Exp. Theor. Phys.\ {\bf 97} (2003) 441], we reduce the description of the intranuclear evolution of the $qgg\bar{q}$ state to the system of three coupled-channel equations in the space of color singlet 4-parton states $\ket{3\bar{3}}, \ket{6\bar{6}}$ and $\ket{15\bar{15}}$ (and their large-N_c generalizations). At large number of colors N_c, the eigenstate $(\ket{6\bar{6}}-\ket{15\bar{15}})/\sqrt{2}$ decouples from the initial state $\ket{3\bar{3}}$. The resulting nuclear distortions of the dijet spectrum exhibit much similarity to those found earlier for forward dijets in Deep Inelastic Scattering (DIS). Still there are certain distinctions regarding the contribution from color-triplet $qg$ final states and from coherent diffraction excitation of dijets. To the large-N_c approximation, we identify four universality classes of nonlinear k_\perp-factorization for hard dijet production.