Photon impact factor and kTk_T-factorization for DIS in the next-to-leading order

The photon impact factor for the BFKL pomeron is calculated in the next-to-leading order (NLO) approximation using the operator expansion in Wilson lines. The result is represented as a NLO $k_T$-factorization formula for the structure functions of small-$x$ deep inelastic scattering.Comment: 13 pages, 4 figures, typos corrected. arXiv admin note: substantial text overlap with arXiv:1009.472

Scattering of shock waves in QCD

The cross section of heavy-ion collisions is represented as a double functional integral with the saddle point being the classical solution of the Yang-Mills equations with boundary conditions/sources in the form of two shock waves corresponding to the two colliding ions. I develop the expansion of this classical solution in powers of the commutator of the Wilson lines describing the colliding particles and calculate the first two terms of the expansion.Comment: 23 pages, 13 figure

The Pomeranchuk Singularity and Vector Boson Reggeization in Electroweak Theory

We investigate the high energy behaviour of vector boson scattering in the electroweak sector of the standard model. In analogy with the BFKL analysis in QCD we compute production amplitudes in the multi-Regge limit and derive, for the vacuum exchange channel, the integral equation for vector particle scattering. We also derive and solve the bootstrap equations for the isospin-1 exchange channel, both for the reggeizing charged and non-reggeizing neutral vector bosons.Comment: 31 pages, 12 figures, 1 tabl

Properties of inclusive hadron production in Deep Inelastic Scattering on heavy nuclei at low x

In this paper we present a comprehensive study of inclusive hadron production in DIS at low $x$. Properties of the hadron spectrum are different in different kinematic regions formed by three relevant momentum scales: photon virtuality $Q^2$, hadron transverse momentum $k_T$ and the saturation momentum $Q_s(x)$. We investigate each kinematic region and derive the corresponding asymptotic formulas for the cross section at the leading logarithmic order. We also analyze the next-leading-order (NLO) corrections to the BFKL kernel that are responsible for the momentum conservation. In particular, we establish the asymptotic behavior of the forward elastic dipole--nucleus scattering amplitude at high energies deeply in the saturation regime and a modification of the pomeron intercept. We study the nuclear effect on the inclusive cross section using the nuclear modification factor and its logarithmic derivative. We argue that the later is proportional to the difference between the anomalous dimension of the gluon distribution in nucleus and in proton and thus is a direct measure of the coherence effects. To augment our arguments and present quantitative results we performed numerical calculations in the kinematic region that may be accessible by the future DIS experiments.Comment: 29 pages, 8 figure

A momentum Space Analysis of the Triple Pomeron Vertex in pQCD

We study properties of the momentum space Triple Pomeron Vertex in perturbative QCD. Particular attention is given to the collinear limit where transverse momenta on one side of the vertex are much larger than on the other side. We also comment on the kernels in nonlinear evolution equations.Comment: Minor misprints corrected. To be published in EPJ

High-energy hadron-hadron (dipole-dipole) scattering from lattice QCD

In this paper the problem of high-energy hadron-hadron (dipole-dipole) scattering is approached (for the first time) from the point of view of lattice QCD, by means of Monte Carlo numerical simulations. In the first part, we give a brief review of how high-energy scattering amplitudes can be reconstructed, using a functional-integral approach, in terms of certain correlation functions of two Wilson loops and we also briefly recall some relevant analyticity and crossing-symmetry properties of these loop-loop correlation functions, when going from Euclidean to Minkowskian theory. In the second part, we shall see how these (Euclidean) loop-loop correlation functions can be evaluated in lattice QCD and we shall compare our numerical results with some nonperturbative analytical estimates that appeared in the literature, discussing in particular the question of the analytic continuation from Euclidean to Minkowskian theory and its relation to the still unsolved problem of the asymptotic s-dependence of the hadron-hadron total cross sections.Comment: Revised version (to be published in Phys. Rev. D) with new comments in section 4, a new figure [Fig. 6], two new references in Refs. [3] and [34], and some other minor changes; 27 pages, 17 figure

Duality and Pomeron effective theory for QCD at high energy and large N_c

We propose an effective theory which governs Pomeron dynamics in QCD at high energy, in the leading logarithmic approximation, and in the limit where N_c, the number of colors, is large. In spite of its remarkably simple structure, this effective theory generates precisely the evolution equations for scattering amplitudes that have been recently deduced from a more complete microscopic analysis. It accounts for the BFKL evolution of the Pomerons together with their interactions: dissociation (one Pomeron splitting into two) and recombination (two Pomerons merging into one). It is constructed by exploiting a duality principle relating the evolutions in the target and the projectile, more precisely, splitting and merging processes, or fluctuations in the dilute regime and saturation effects in the dense regime. The simplest Pomeron loop calculated with the effective theory is free of both ultraviolet or infrared singularities.Comment: 13 pages, 1 figur

Dense-Dilute Duality at work: dipoles of the target

We explore the properties of the QCD high energy evolution in the limit of a dilute target. Using the recently established property of selfduality of the evolution operator (hep-ph/0502119), we show how to properly define the target gluon and dipole creation operators in terms of dual Wilson lines (dual eikonal factors). We explain how to expand these operators in terms of the functional derivatives of the color charge density, in the situation when they act on the eikonal factors of the projectile partons. We explicitly calculate the expansion of the high energy evolution operator to fourth order in the functional derivatives. Our result is infrared and ultraviolet finite, but does not coincide with the formula given in hep-ph/0501088. We resolve this discrepancy by showing that the identification of the dipole creation and annihilation operators used in hep-ph/0501088 is incomplete, and provide the required corrections to these definitions. The use of the corrected operators in the calculational framework of hep-ph/0501088 reproduces our result. We also prove that there is no discrepancy between the expansion of the JIMWLK equation and the dualization of the expansion of the weak field limit.Comment: 18 pages, Explanations added. Version to appear in PR

A zero-dimensional model for high-energy scattering in QCD

We investigate a zero-dimensional toy model originally introduced by Mueller and Salam which mimics high-energy scattering in QCD in the presence of both gluon saturation and gluon number fluctuations, and hence of Pomeron loops. Unlike other toy models of the reaction-diffusion type, the model studied in this paper is consistent with boost invariance and, related to that, it exhibits a mechanism for particle saturation close to that of the JIMWLK equation in QCD, namely the saturation of the emission rate due to high-density effects. Within this model, we establish the dominant high-energy behaviour of the S-matrix element for the scattering between a target obtained by evolving one particle and a projectile made with exactly n particles. Remarkably, we find that all such matrix elements approach the black disk limit S=0 at high rapidity Y, with the same exponential law: ~ exp(-Y) for all values of n. This is so because the S-matrix is dominated by rare target configurations which involve only few particles. We also find that the bulk distribution for a saturated system is of the Poisson type.Comment: 34 pages, 9 figures. Some explanations added on the frame-dependence of the relevant configurations (new section 3.3