On possible implications of gluon number fluctuations in DIS data

We study the effect of gluon number fluctuations (Pomeron loops) on deep inelastic scattering (DIS) in the fixed coupling case. We find that the description of the DIS data is improved once gluon number fluctuations are included. Also the values of the parameters, like the saturation exponent and the diffussion coefficient, turn out reasonable and agree with values obtained from numerical simulations of toy models which take into account fluctuations. This outcome seems to indicate the evidence of geometric scaling violations, and a possible implication of gluon number fluctuations, in the DIS data. However, we cannot exclude the possibility that the scaling violations may also come from the diffusion part of the solution to the BK-equation, instead of gluon number fluctuations.Comment: 9 pages, 2 figures; references added, minor changes, matches published versio

Small-x physics beyond the Kovchegov equation

We note the differences between the Kovchegov equation and the Balitsky-JIMWLK equations as methods of evaluating high energy hard scattering near the unitarity limit. We attempt to simulate some of the correlations absent in the Kovchegov equation by introducing two boundaries rather than the single boundary which effectively approximates the unitarity limit guaranteed in the Kovchegov equation. We solve the problem of BFKL evolution in the presence of two boundaries and note that the resulting T-matrix now is the same in different frames, which was not the case in the single boundary case. The scaling behavior of the solution to the Kovchegov equation is apparently now lost.Comment: 38 pages, 8 figures, typos correcte

Deep inelastic and dipole scattering on finite length hot N=4\mathcal{N}=4 SYM matter

Deep inelastic scattering of $\mathcal{R}$-currents and the scattering of a small dipole on finite length hot $\mathcal{N}=4$ SYM matter are discussed. In each case we find the scale when scattering becomes strong is determined by a saturation momentum $Q^2_s \sim LT^3/x$ where $L$ is the length of the matter. For $\mathcal{R}$-currents we analyze the operator product expansion. For infinite length matter the series generated by the OPE is not Borel summable but we are able to determine the exponential part of the tunneling amplitude determining $F_2$ when $\frac{Q^2}{Q^2_s}\gg 1$ from the position of the singularity closest to the origin on the real axis of the Borel plane. In finite length matter the OPE series is not convergent but it is Borel summable. When a small dipole, and the string connecting the ends of the dipole, pass through hot matter there is an induced motion of the string in the $5^{th}$ dimension. When $T^4 L \cosh \eta$, with the $\eta$ the rapidity of the string, is large enough the string would normally break into several parts after leaving the medium, however, this cannot happen in the classical approximation in which we work.Comment: 26 page

Diffractive photon dissociation in the saturation regime from the Good and Walker picture

Combining the QCD dipole model with the Good and Walker picture, we formulate diffractive dissociation of a photon of virtuality Q^2 off a hadronic target, in the kinematical regime in which Q is close to the saturation scale and much smaller than the invariant mass of the diffracted system. We show how the obtained formula compares to the HERA data and discuss what can be learnt from such a phenomenology. In particular, we argue that diffractive observables in these kinematics provide useful pieces of information on the saturation regime of QCD.Comment: 17 pages, 7 figures, revte

Extension of the JIMWLK Equation in the Low Gluon Density Region

It has recently been realized that the Balitsky-JIMWLK equations have serious shortcomings as equations to be used in small-x evolution near the unitarity limit. A recent generalization of the Balitsky equations has been given which corrects these shortcomings. In this paper we present an equivalent discussion, but in terms of the JIMWLK equation where we show that a new (fourth order functional derivative) term should be included. We also present a stochastic version of the new equation which, however, has some unusual mathematical aspects which are not as yet well understood.Comment: 23 pages, 1 figure, corrected typos, corrected references, published versio

Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams

Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing the quantum solution for the scattering amplitude in both models. The equations of motion for the Lagrangians of the theories are also considered and the classical solutions of the equations are found. Full two-point Green functions ("effective" Pomeron propagator) and amplitude of diffractive dissociation process are calculated in the framework of RFT-0 approach. The importance of the loops contribution in the amplitude at different values of the model parameters is discussed as well as the difference between the models with and without quaternary Pomeron vertex.Comment: 34 pages, 36 figure

Jet quenching parameter \hat q in the stochastic QCD vacuum with Landau damping

We argue that the radiative energy loss of a parton traversing the quark-gluon plasma is determined by Landau damping of soft modes in the plasma. Using this idea, we calculate the jet quenching parameter of a gluon. The calculation is done in SU(3) quenched QCD within the stochastic vacuum model. At the LHC-relevant temperatures, the result depends on the gluon condensate, the vacuum correlation length, and the gluon Debye mass. Numerically, when the temperature varies from T=T_c to T=900 MeV, the jet quenching parameter rises from \hat q=0 to approximately 1.8 GeV^2/fm. We compare our results with the predictions of perturbative QCD and other calculations.Comment: 20 pages, 6 figures, discussions and references added; final version to appear in Eur. Phys. J.

Confining QCD Strings, Casimir Scaling, and a Euclidean Approach to High-Energy Scattering

We compute the chromo-field distributions of static color-dipoles in the fundamental and adjoint representation of SU(Nc) in the loop-loop correlation model and find Casimir scaling in agreement with recent lattice results. Our model combines perturbative gluon exchange with the non-perturbative stochastic vacuum model which leads to confinement of the color-charges in the dipole via a string of color-fields. We compute the energy stored in the confining string and use low-energy theorems to show consistency with the static quark-antiquark potential. We generalize Meggiolaro's analytic continuation from parton-parton to gauge-invariant dipole-dipole scattering and obtain a Euclidean approach to high-energy scattering that allows us in principle to calculate S-matrix elements directly in lattice simulations of QCD. We apply this approach and compute the S-matrix element for high-energy dipole-dipole scattering with the presented Euclidean loop-loop correlation model. The result confirms the analytic continuation of the gluon field strength correlator used in all earlier applications of the stochastic vacuum model to high-energy scattering.Comment: 65 pages, 13 figures, extended and revised version to be published in Phys. Rev. D (results unchanged, 2 new figures, 1 new table, additional discussions in Sec.2.3 and Sec.5, new appendix on the non-Abelian Stokes theorem, old Appendix A -> Sec.3, several references added

Elastic and quasi-elastic pppp and γ⋆p\gamma^\star p scattering in the Dipole Model

We have in earlier papers presented an extension of Mueller's dipole cascade model, which includes sub-leading effects from energy conservation and running coupling as well as colour suppressed saturation effects from pomeron loops via a ``dipole swing''. The model was applied to describe the total and diffractive cross sections in $pp$ and $\gamma^*p$ collisions, and also the elastic cross section in $pp$ scattering. In this paper we extend the model to describe the corresponding quasi-elastic cross sections in $\gamma^*p$, namely the exclusive production of vector mesons and deeply virtual compton scattering. Also for these reactions we find a good agrement with measured cross sections. In addition we obtain a reasonable description of the $t$-dependence of the elastic $pp$ and quasi-elastic $\gamma^\star p$ cross sections

S-Matrix Unitarity, Impact Parameter Profiles, Gluon Saturation and High-Energy Scattering

A model combining perturbative and non-perturbative QCD is developed to compute high-energy reactions of hadrons and photons and to investigate saturation effects that manifest the S-matrix unitarity. Following a functional integral approach, the S-matrix factorizes into light-cone wave functions and the universal amplitude for the scattering of two color-dipoles which are represented by Wegner-Wilson loops. In the framework of the non-perturbative stochastic vacuum model of QCD supplemented by perturbative gluon exchange, the loop-loop correlation is calculated and related to lattice QCD investigations. With a universal energy dependence motivated by the two-pomeron (soft + hard) picture that respects the unitarity condition in impact parameter space, a unified description of pp, pip, Kp, gamma* p, and gamma gamma reactions is achieved in good agreement with experimental data for cross sections, slope parameters, and structure functions. Impact parameter profiles for pp and longitudinal gamma* p reactions and the gluon distribution of the proton xG(x,Q^2,b) are calculated and found to saturate in accordance with S-matrix unitarity. The c.m. energies and Bjorken x at which saturation sets in are determined.Comment: 65 pages with 13 figures, Introduction, Sec. 3, and Conclusion extende