High energy scattering in the saturation regime including running coupling and rare fluctuation effects

The analytic result for the $S$-matrix in the saturation regime including the running coupling is obtained. To get this result we solve the Balitsky and Kovchegov-Weigert evolution equations in the saturation regime, which include running coupling corrections. We study also the effect of rare fluctuations on top of the running coupling. We find that the rare fluctuations are less important in the running coupling case as compared to the fixed coupling case.Comment: 10 page

Holographic Pomeron: Saturation and DIS

We briefly review the approach to dipole-dipole scattering in holographic QCD developed in ARXIV:1202.0831. The Pomeron is modeled by exchanging closed strings between the dipoles and yields Regge behavior for the elastic amplitude. We calculate curvature corrections to this amplitude in both a conformal and confining background, identifying the holographic direction with the virtuality of the dipoles. The it wee-dipole density is related to the string tachyon diffusion in both virtuality and the transverse directions. We give an explicit derivation of the dipole saturation momentum both in the conformal and confining metric. Our holographic result for the dipole-dipole cross section and the it wee-dipole density in the conformal limit are shown to be identical in form to the BFKL pomeron result when the non-critical string transverse dimension is $D_\perp=3$. The total dipole-dipole cross section is compared to DIS data from HERA

Treading on the cut: Semi inclusive observables at high energy

We develop the formalizm for calculating semi inclusive observables at high energy in the JIMWLK/KLWMIJ approach. We consider several examples including diffractive processes, elastic and inclusive over the target degrees of freedom, scattering with fixed total transverse momentum transfer and inclusive gluon production. We discuss evolution of these observables with respect to various rapidity variables involved in their definitions (total rapidity, rapidity gap, width of diffractive interval etc.). We also discuss the dipole model limit of these observables and derive closed simple (as opposed to functional) differential equations in this approximation. We point out that there are some interesting differences between the full JIMWLK/KLWMIJ evolution and the dipole model evolution of diffractive cross section. In particular we show that in the dipole approximation the target does not diffract beyond the valence rapidity interval, consistently with the intuition suggested by the Pomeron fan diagramms. On the other hand such diffractive processes do exist in the full JIMWLK/KLWMIJ approach, albeit suppressed by the factor 1/N_c^2.Comment: 37 pages, 3 figures. A few remarks added. To appear in PR

Invariant color calculus and generalized Balitsky-Kovchegov hierarchy

We derive generalization of the Balitsky-Kovchegov (BK) equation for a dipole, which consists of a parton and an antiparton of arbitrary charge. At first, we develop one method of indexless transformation of color expressions. The method is based on an evaluation of the Casimir operator on a tensor product. From the JIMWLK equation we derive the evolution equation for a single parton and prove gluon Reggeization in an arbitrary color channel. We show that there is a color duplication of such Regge poles. Higher t-channel color exchange has its own Regge pole, which residue is proportional to the quadratic Casimir. Taking a fundamental representation, we derive the usual BK equation and shed new light on the meaning of linear and nonlinear terms. Finally, we discuss a linearized version of the generalized BK equation.Comment: 10 pages, 1 figure; final version, improved English, slyle correction

Duality symmetry of BFKL equation: reggeized gluons vs color dipoles

We show that the duality symmetry of the BFKL equation can be interpreted as a symmetry under rotation of the BFKL Kernel in the transverse space from s-channel (color dipole model) to t-channel (reggeized gluon formulation). We argue that the duality symmetry holds also in the non-forward case due to a very special structure of the non-forward BFKL Kernel, which can be written as a sum of three forward BFKL Kernels. The duality symmetry is established by identifying the dual coordinates with the transverse coordinates of a non-diagonal dipole scattered off the target.Comment: 13 pages, 5 figure

AdS black disk model for small-x DIS

Using the approximate conformal invariance of QCD at high energies we consider a simple AdS black disk model to describe saturation in DIS. Deep inside saturation the structure functions have the same power law scaling, F_T ~ F_L ~ 1/x^w, where w is related to the expansion rate of the black disk with energy. Furthermore, the ratio F_L /F_T is given by the universal value (1+w)/(3+w), independently of the target. For virtual photon-photon scattering at high energies we obtain explicit expressions and ratios for the total cross sections of transverse and longitudinal photons in terms of the single parameter w.Comment: 5 pages. Minor correction

One gluon, two gluon: multigluon production via high energy evolution

We develop an approach for calculating the inclusive multigluon production within the JIMWLK high energy evolution. We give a formal expression of multigluon cross section in terms of a generating functional for arbitrary number of gluons $n$. In the dipole limit the expression simplifies dramatically. We recover the previously known results for single and double gluon inclusive cross section and generalize those for arbitrary multigluon amplitude in terms of Feynman diagramms of Pomeron - like objects coupled to external rapidity dependent field $s(\eta)$. We confirm the conclusion that the AGK cutting rules in general are violated in multigluon production. However we present an argument to the effect that for doubly inclusive cross section the AGK diagramms give the leading contribution at high energy, while genuine violation only occurs for triple and higher inclusive gluon production. We discuss some general properties of our expressions and suggest a line of argument to simplify the approach further.Comment: 32 pages, one reference corrected. to appear in JHE

Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution

We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary matrix $R$ which represents the single gluon scattering matrix. We discuss the peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We develop a perturbative expansion in the RFT framework, and find several eigenstates of the zeroth order Hamiltonian. The zeroth order of this perturbation preserves the number of $s$ - channel gluons. The eigenstates have a natural interpretation in terms of the $t$ - channel exchanges. Studying the single $s$ - channel gluon sector we find the eigenstates which include the reggeized gluon and five other colored Reggeons. In the two ($s$ - channel) gluon sector we study only singlet color exchanges. We find five charge conjugation even states. The bound state of two reggeized gluons is the standard BFKL Pomeron. The intercepts of the other Pomerons in the large $N$ limit are $1+\omega_P=1+2\omega$ where $1+\omega$ is the intercept of the BFKL Pomeron, but their coupling in perturbation theory is suppressed by at least $1/N^2$ relative to the double BFKL Pomeron exchange. For the $[27,27]$ Pomeron we find $\omega_{[27,27]}=2\omega+O(1/N)>2\omega$. We also find three charge conjugation odd exchanges, one of which is the unit intercept Bartels-Lipatov-Vacca Odderon, while another one has an interecept greater than unity. We explain in what sense our calculation goes beyond the standard BFKL/BKP calculation. We make additional comments and discuss open questions in our approach.Comment: 58 pages, 4 figures, Extended version. To appear in JHE

An infrared approach to Reggeization

We present a new approach to Reggeization of gauge amplitudes based on the universal properties of their infrared singularities. Using the "dipole formula", a compact ansatz for all infrared singularities of massless amplitudes, we study Reggeization of singular contributions to high-energy amplitudes for arbitrary color representations, and any logarithmic accuracy. We derive leading-logarithmic Reggeization for general cross-channel color exchanges, and we show that Reggeization breaks down for the imaginary part of the amplitude at next-to-leading logarithms and for the real part at next-to-next-to-leading logarithms. Our formalism applies to multiparticle amplitudes in multi-Regge kinematics, and constrains possible corrections to the dipole formula starting at three loops.Comment: 4 page

Inclusive gluon production in the dipole approach: AGK cutting rules

We consider single gluon production in the dipole model and reproduce the result of Kovchegov and Tuchin for the adjoint (gluonic) dipole structure of the inclusive cross section. We show the validity of the adjoint dipole structure to any order of evolution deriving and solving the non-linear evolution for the non-diagonal cross section of a dipole scattering off the target. The form of the solution to this equation restores the dipole interpretation for non-diagonal cross sections, that appear in gluon production. Using this formalism, we analyse the single inclusive production cross section in terms of the contributions of different multiplicities, and we derive the Abramovskii-Gribov-Kancheli(AGK) cutting rules for two Pomeron exchange. The cutting rules, which were found in this formalism, fully reproduce the original AGK rules for the total cross section. However, for the case of gluon production, the AGK rules are violated already for one gluon emission from the vertex.Comment: 32 pages, 16 figure