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Based on an approach to non-Abelian propagation of color dipoles in a nuclear medium, we formulate a nonlinear k(perpendicular to) factorization for the breakup of photons and pions into forward hard dijets in terms of the collective Weizsacker-Williams glue of nuclei. We find quite distinct practical consequences of nonlinear nuclear k(perpendicular to) factorization for interactions of pointlike photons and nonpointlike pions. In the former case, the large transverse momentum p(perpendicular to) of jets comes from the intrinsic momentum of quarks and antiquarks in the photon, and nuclear effects manifest themselves as an azimuthal decorrelation with an acoplanarity momentum of the order of the nuclear saturation momentum Q(A). In the breakup of pions off free nucleons to the leading order in pQCD, the spectator parton has a small transverse momentum and the hard dijet cross section is suppressed. In the breakup of pions off heavy nuclei, the forward hard jets are predicted to be entirely decorrelated. We comment on the sensitivity of the pionic dijet cross section to the pion distribution amplitude. The predicted distinction between the breakup of photons and pions can be tested by the sphericity and thrust analysis of the forward hadronic system in the COMPASS experiment at CERN. (c) 2005 Pleiades Publishing, Inc.