The BFKL Pomeron with running coupling constant: how much of its hard nature survives?

We discuss the BFKL equation with a running gauge coupling and identify in its solutions the contributions originating from different transverse momentum scales. We show that for a running coupling constant the distribution of the gluons making up the BFKL Pomeron shifts to smaller transverse momenta so that the dominant part of Pomeron can have a nonperturbative origin. It is demonstrated how this soft physics enters into the BFKL solution through the boundary condition. We consider two kinematical regimes leading to different behaviour of the rapidity and transverse momentum dependence of the gluon distribution. In the diffusion approximation to the BFKL kernel with running $\alpha_s$, we find a sequence of poles which replaces the cut for fixed $\alpha_s$. The second regime corresponds to the singular part of the kernel, which gives the dominant contribution in the limit of very large transverse momenta. Finally, a simple more general picture is obtained for the QCD Pomeron in hard processes: it is of soft, nonperturbative nature, but has hard ends of DGLAP-type.Comment: 23 pages REVTEX and 4 figures include

Anisotropic flows from initial state of a fast nucleus

We analyze azimuthal anisotropy in heavy ion collisions related to the reaction plane in terms of standard reggeon approach and find that it is nonzero even when the final state interaction is switched off. This effect can be interpreted in terms of partonic structure of colliding nuclei. We use Feynman diagram analysis to describe details of this mechanism. Main qualitative features of the appropriate azimuthal correlations are discussed.Comment: 16 pages, 11 figures. This paper is an extended version of a talk given at Session of Nuclear Physics Division of Russian Academy of Sciences in November 200

Measuring the saturation scale in nuclei

The saturation momentum seeing in the nuclear infinite momentum frame is directly related to transverse momentum broadening of partons propagating through the medium in the nuclear rest frame. Calculation of broadening within the color dipole approach including the effects of saturation in the nucleus, gives rise to an equation which describes well data on broadening in Drell-Yan reaction and heavy quarkonium production.Comment: 11 pages, 5 figures, based on the talk presented by B.K. at the INT workshop "Physics at a High Energy Electron Ion Collider", Seattle, October 200

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.

Gluon Shadowing in DIS off Nuclei

Within a light-cone quantum-chromodynamics dipole formalism based on the Green function technique, we study nuclear shadowing in deep-inelastic scattering at small Bjorken xB < 0.01. Such a formalism incorporates naturally color transparency and coherence length effects. Calculations of the nuclear shadowing for the \bar{q}q Fock component of the photon are based on an exact numerical solution of the evolution equation for the Green function, using a realistic form of the dipole cross section and nuclear density function. Such an exact numerical solution is unavoidable for xB > 0.0001, when a variation of the transverse size of the \bar{q}q Fock component must be taken into account. The eikonal approximation, used so far in most other models, can be applied only at high energies, when xB < 0.0001 and the transverse size of the \bar{q}q Fock component is "frozen" during propagation through the nuclear matter. At xB < 0.01 we find quite a large contribution of gluon suppression to nuclear shadowing, as a shadowing correction for the higher Fock states containing gluons. Numerical results for nuclear shadowing are compared with the available data from the E665 and NMC collaborations. Nuclear shadowing is also predicted at very small xB corresponding to LHC kinematical range. Finally the model predictions are compared and discussed with the results obtained from other models.Comment: 29 pages including 7 figures; Fig.7 modified, some references and corresponding discussion adde

Diffractive neutrino-production of pions on nuclei: Adler relation within the color-dipole description

Effects of coherence in neutrino-production of pions off nuclei are studied employing the color dipole representation and path integral technique. If the nucleus remains intact, the process is controlled by the interplay of two length scales. One is related to the pion mass and is quite long (at low Q^2), while the other, associated with heavy axial-vector states, is much shorter. The Adler relation is found to be broken at all energies, but especially strongly at \nu > 10 GeV, where the cross section is suppressed by a factor ~A^{-1/3}. On the contrary, in a process where the recoil nucleus breaks up into fragments, the Adler relation turns out to be strongly broken at low energies, where the cross section is enhanced by a factor ~A^{1/3}, but has a reasonable accuracy at higher energies, where all the coherence length scales become long.Comment: 9 pages, 5 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

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

Nuclear suppression at RHIC and LHC in Glauber-Gribov approach

The approach to problem of nuclear shadowing based on Gribov Reggeon calculus is presented. Here the total cross section of $h A$ interaction is found in a parameter-free description, employing the new data on the gluon density of the Pomeron, measured with high precision at HERA, as input. The model is then applied for calculation of $J/\psi$ production in $d Au$ collisions at top RHIC energy. It is shown that the theoretical estimates are in a very good agreement with the PHENIX data, and further predictions for the $J/\psi$ suppression in $p Pb$ collisions at coming soon LHC are made.Comment: SQM2007 proceedings, 6 page

Mini Black Holes in the first year of the LHC

The experimental signatures of TeV-mass black hole (BH) formation in heavy ion collisions at the LHC is examined. We find that the black hole production results in a complete disappearance of all very high $p_T$ ({$> 500$} GeV) back-to-back correlated di-jets of total mass {$M > M_f \sim 1$}TeV. We show that the subsequent Hawking-decay produces multiple hard mono-jets and discuss their detection. We study the possibility of cold black hole remnant (BHR) formation of mass $\sim M_f$ and the experimental distinguishability of scenarios with BHRs and those with complete black hole decay. Due to the rather moderate luminosity in the first year of LHC running the least chance for the observation of BHs or BHRs at this early stage will be by ionizing tracks in the ALICE TPC. Finally we point out that stable BHRs would be interesting candidates for energy production by conversion of mass to Hawking radiation.Comment: 10 pages, 2 figure