The Running BFKL: Resolution of Caldwell's Puzzle

The HERA data on the proton structure function, $F_2(x,Q^2)$, at very small $x$ and $Q^2$ show the dramatic departure of the logarithmic slope, $\partial F_2/\partial\log Q^2$, from theoretical predictions based on the DGLAP evolution. We show that the running BFKL approach provides the quantitative explanation for the observed $x$ and/or $Q^2$ -dependence of $\partial F_2/\partial\log Q^2$.Comment: 7 pages, Latex, 4 Figures, P

Evolution of high-mass diffraction from the light quark valence component of the pomeron

We analyze the contribution from excitation of the $(q\bar q)(f\bar f),(q\bar q)g_1...g_n(f\bar f)$ Fock states of the photon to high mass diffraction in DIS. We show that the large $Q^2$ behavior of this contribution can be described by the DLLA evolution from the non-perturbative $f\bar f$ valence state of the pomeron. Although of higher order in pQCD, the new contribution to high-mass diffraction is comparable to that from the excitation of the $q\bar q g$ Fock state of the photon.Comment: 12 pages, 2 figures, the oublished version. The slight numerical errors corrected, all conclusions are retaine

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.

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.

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

3D Jet Tomography of Twisted Strongly Coupled Quark Gluon Plasmas

The triangular enhancement of the rapidity distribution of hadrons produced in p+A reactions relative to p+p is a leading order in A^{1/3}/log(s) violation of longitudinal boost invariance at high energies. In A+A reactions this leads to a trapezoidal enhancement of the local rapidity density of produced gluons. The local rapidity gradient is proportional to the local participant number asymmetry, and leads to an effective rotation in the reaction plane. We propose that three dimensional jet tomography, correlating the long range rapidity and azimuthal dependences of the nuclear modification factor, R_{AA}(\eta,\phi,p_\perp; b>0), can be used to look for this intrinsic longitudinal boost violating structure of $A+A$ collisions to image the produced twisted strongly coupled quark gluon plasma (sQGP). In addition to dipole and elliptic azimuthal moments of R_{AA}, a significant high p_\perp octupole moment is predicted away from midrapidity. The azimuthal angles of maximal opacity and hence minima of R_{AA} are rotated away from the normal to the reaction plane by an `Octupole Twist' angle, \theta_3(\eta), at forward rapidities.Comment: 10 Pages, 16 Figures, RevTex, Replaced with Peer reviewed verion for PR

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

Production of two ccˉc \bar c pairs in gluon-gluon scattering in high energy proton-proton collisions

We calculate cross sections for $g g \to Q \bar Q Q \bar Q$ in the high-energy approximation in the mixed (longitudinal momentum fraction, impact parameter) and momentum space representations. Besides the total cross section as a function of subsystem energy also differential distributions (in quark rapidity, transverse momentum, $Q Q$, $Q \bar Q$ invariant mass) are presented. The elementary cross section is used to calculate production of $(c \bar c) (c \bar c)$ in single-parton scattering (SPS) in proton-proton collisions. We present integrated cross section as a function of proton-proton center of mass energy as well as differential distribution in $M_{(c \bar c)(c \bar c)}$. The results are compared with corresponding results for double-parton scattering (DPS) discussed recently in the literature. We find that the considered SPS contribution to $(c \bar c)(c \bar c)$ production is at high energy ($\sqrt{s} >$ 5 TeV) much smaller than that for DPS contribution.Comment: 17 pages, 11 figure

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