Nonlinear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>k</mml:mi><mml:mo>⊥</mml:mo></mml:msub></mml:math>factorization for quark-gluon dijet production off nuclei

The breaking of conventional linear ${k}_{\ensuremath{\perp}}$ factorization for hard processes in a nuclear environment is by now well established. Here we report a detailed derivation of the nonlinear ${k}_{\ensuremath{\perp}}$-factorization relations for the production of quark-gluon dijets. This process is the dominant source of 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. 97, 441 (2003)], we reduce the description of the intranuclear evolution of the $qgg\overline{q}$ state to the $3\ifmmode\times\else\texttimes\fi{}3$ system of coupled equations in the space of color-singlet 4-parton states $|3\overline{3}⟩$, $|6\overline{6}⟩$, and $|15\overline{15}⟩$ (and their large-${N}_{c}$ generalizations). At large number of colors ${N}_{c}$, the eigenstate $(|6\overline{6}⟩\ensuremath{-}|15\overline{15}⟩)/\sqrt{2}$ decouples from the initial state $|3\overline{3}⟩$. The resulting nuclear distortions of the dijet spectrum exhibit much similarity to those found earlier for forward dijets in deep inelastic scattering. 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 ${k}_{\ensuremath{\perp}}$ factorization for hard dijet production.

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