Unitarity cutting rules for the nucleus excitation and topological cross sections in hard production off nuclei from nonlinear k_t-factorization

At the partonic level, a typical final state in small-x deep inelastic scattering off nuclei and hard proton-nucleus collisions can be characterized by the multiplicity of color-excited nucleons. Within reggeon field theory, each color-excited nucleon is associated with the unitarity cut of the pomeron exchanged between the projectile and nucleus. In this communication we derive the unitarity rules for the multiplicity of excited nucleons, alias cut pomerons, alias topological cross sections, for typical hard dijet production processes. We demonstrate how the coupled-channel non-Abelian intranuclear evolution of color dipoles, inherent to pQCD, gives rise to the reggeon field theory diagrams for final states in terms of the uncut, and two kinds of cut, pomerons. Upon the proper identification of the uncut and cut pomeron exchanges, the topological cross sections for dijet production follow in a straightforward way from the earlier derived nonlinear k_t - factorization quadratures for the inclusive dijet cross sections. The concept of a coherent (collective) nuclear glue proves extremely useful for the formulation of reggeon field theory vertices of multipomeron - cut and uncut - couplings to particles and between themselves. A departure of our unitarity cutting rules from the ones suggested by the pre-QCD Abramovsky-Kancheli-Gribov rules, stems from the coupled-channel features of intranuclear pQCD. We propose a multiplicity re-summation as a tool for the isolation of topological cross sections for single-jet production.Comment: 53 pages, 16 eps-figures, to appear in Phys. Rev.

The hard scale in the exclusive rho-meson production in diffractive DIS

We re-examine the issue of the pQCD factorization scale in the exclusive rho production in diffractive DIS from the k_t-factorization point of view. We find that this scale differs significantly from, and possesses much flatter Q^2 behavior than widely used value (Q^2 + m_\rho^2)/4. With these results in mind, we discuss the Q^2 shape of the rho meson production cross section. We introduce rescaled cross sections, which might provide further insight into the dynamics of rho production. We also comment on the recent ZEUS observation of energy-independent ratio sigma(gamma* p --> rho p) / sigma_{tot}(gamma*p).Comment: 14 pages, 7 eps figure

Quenching of Leading Jets and Particles: the p_t Dependent Landau-Pomeranchuk-Migdal effect from Nonlinear k_t Factorization

We report the first derivation of the Landau-Pomeranchuk-Migdal effect for leading jets at fixed values of the transverse momentum p_t in the beam fragmentation region of hadron-nucleus collisions from RHIC (Relativistic Heavy Ion Collider) to LHC (Large Hadron Collider). The major novelty of this work is a derivation of the missing virtual radiative pQCD correction to these processes - the real-emission radiative corrections are already available in the literature. We manifestly implement the unitarity relation, which in the simplest form requires that upon summing over the virtual and real-emission corrections the total number of scattered quarks must exactly equal unity. For the free-nucleon target, the leading jet spectrum is shown to satisfy the familiar linear Balitsky-Fadin-Kuraev-Lipatov leading log(1/x) (LL-1/x) evolution. For nuclear targets, the nonlinear k_t-factorization for the LL-1/x evolution of the leading jet sepctrum is shown to exactly match the equally nonlinear LL-1/x evolution of the collective nuclear glue - there emerges a unique linear k_t-factorization relation between the two nonlinear evolving nuclear observables. We argue that within the standard dilute uncorrelated nucleonic gas treatment of heavy nuclei, in the finite energy range from RHIC to LHC, the leading jet spectrum can be evolved in the LL-1/x Balitsky-Kovchegov approximation. We comment on the extension of these results to, and their possible reggeon field theory interpretation for, mid-rapidity jets at LHC.Comment: 36 pages, 8 eps figs, revised, discussion on reggeon interpretation and refs. adde

Breaking of k_\perp-factorization for Single Jet Production off Nuclei

The linear k_\perp-factorization is part and parcel of the pQCD 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 [2] of nonlinear nuclear k_\perp-factorization for forward dijet production in DIS 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.Comment: 55 pages, 9 eps figures, presentation shortened, a number of typos removed, to appear in Phys. Rev.

Diffractive Hard Dijets and Nuclear Parton Distributions

Diffraction plays an exceptional role in DIS off heavy nuclei. First, diffraction into hard dijets is an unique probe of the unintegrated glue in the target. Second, because diffraction makes 50 per cent of total DIS off a heavy target, understanding diffraction in a saturation regime is crucial for a definition of saturated nuclear parton densities. After brief comments on the Nikolaev-Zakharov (NZ) pomeron-splitting mechanism for diffractive hard dijet production, I review an extension of the Nikolaev-Schafer-Schwiete (NSS) analysis of diffractive dijet production off nuclei to the definition of nuclear partons in the saturation regime. I emphasize the importance of intranuclear final state interactions for the parton momentum distributions.Comment: 9 pages, 2 figures, to be published in Proceedings of the Workshop on Exclusive Processes at High Momentum Transfer, Jefferson Lab, May 15-18, 2002. Typos corrected, discussion of the results extende

Nonlinear kT factorization for Forward Dijets in DIS off Nuclei in the Saturation Regime

We develop the QCD description of the breakup of photons into forward dijets in small-x deep inelastic scattering off nuclei in the saturation regime. Based on the color dipole approach, we derive a multiple scattering expansion for intranuclear distortions of the jet-jet transverse momentum spectrum. A special attention is paid to the non-Abelian aspects of the propagation of color dipoles in a nuclear medium. We report a nonlinear $k_{\perp}$-factorization formula for the breakup of photons into dijets in terms of the collective Weizs\"acker-Williams (WW) glue of nuclei as defined in ref. \cite{Saturation,NSSdijet}. For hard dijets with the transverse momenta above the saturation scale the azimuthal decorrelation (acoplanarity) momentum is of the order of the nuclear saturation momentum QA. For minijets with the transverse momentum below the saturation scale the nonlinear kT-factorization predicts a complete disappearance of the jet-jet correlation. We comment on a possible relevance of the nuclear decorrelation of jets to the experimental data from the STAR-RHIC Collaboration.Comment: 40 pages, 7 figure

High Density QCD, Saturation and Diffractive DIS

We review a consistent description of the fusion and saturation of partons in the Lorentz-contracted ultrarelativistic nuclei in terms of a nuclear attenuation of color dipole states of the photon and collective Weizs\"acker-Williams (WW) gluon structure function of a nucleus. Diffractive DIS provides a basis for the definition of the WW nuclear glue. The point that all observables for DIS off nuclei are uniquely calculable in terms of the nuclear WW glue amounts to a new form of factorization in the saturation regime.Comment: 13 pages, 4 figures, Invited talk at NATO Advanced Research Workshop On Diffraction 2002, 31 Aug - 6 Sep 2002, Alushta, Ukrain

Nonlinear k_\perp-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. 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.Comment: 53 pages, 9 figures, a few typos fixe

Non-linear BFKL dynamics: color screening vs. gluon fusion

A feasible mechanism of unitarization of amplitudes of deep inelastic scattering at small values of Bjorken $x$ is the gluon fusion. However, its efficiency depends crucially on the vacuum color screening effect which accompanies the multiplication and the diffusion of BFKL gluons from small to large distances. From the fits to lattice data on field strength correlators the propagation length of perturbative gluons is $R_c\simeq 0.2-0.3$ fermi. The probability to find a perturbative gluon with short propagation length at large distances is suppressed exponentially. It changes the pattern of (dif)fusion dramatically. The magnitude of the fusion effect appears to be controlled by the new dimensionless parameter $\sim R_c^2/8B$, with the diffraction cone slope $B$ standing for the characteristic size of the interaction region. It should slowly $\propto 1/\ln Q^2$ decrease at large $Q^2$. Smallness of the ratio $R_c^2/8B$ makes the non-linear effects rather weak even at lowest Bjorken $x$ available at HERA. We report the results of our studies of the non-linear BFKL equation which has been generalized to incorporate the running coupling and the screening radius $R_c$ as the infrared regulator.Comment: 16 pages, 2 figures, version accepted for publication, references adde