Breaking ofk⊥factorization for single jet production off nuclei

The linear $k_{\perp }$ factorization is part and parcel of the perturbative QCD description of high-energy hard processes off free nucleons. In the case of heavy nuclear targets the very concept of nuclear parton density becomes ill-defined as exemplified by the recent derivation [N. N. Nikolaev, W. Schäfer, B. G. Zakharov, and V. R. Zoller, J. Exp. Theor. Phys. 97, 441 (2003).] of nonlinear nuclear $k_{\perp }$ factorization for forward dijet production in deep inelastic scattering off nuclei. Here we report a derivation of the related breaking of $k_{\perp }$ factorization for single-jet processes. We present a general formalism and apply it to several cases of practical interest: open-charm and quark and gluon-jet production in the central to beam fragmentation region of ${\gamma }^{*}p$, ${\gamma }^{*}A$, $pp$, and $pA$ collisions. We show how the pattern of $k_{\perp }$ factorization breaking and the nature and number of exchanged nuclear pomerons do change within the phase space of produced quark and gluon jets. As an application of the nonlinear $k_{\perp }$ factorization we discuss the Cronin effect. Our results are also applicable to the $p_{\perp }$ dependence of the Landau-Pomeranchuk-Migdal effect for, and nuclear quenching of, jets produced in the proton hemisphere of $pA$ collisions.