QCD analysis of deep inelastic lepton-hadron scattering in the region of small values of the bjorken parameter x

We present the new framework based on BFKL and DGLAP evolution equations in which the leading in(Q(_2)) and in(l/x) terms are treated on equal footing. We introduce a pair of coupled integro-difFerential equations for the quark singlet and the unintegrated gluon distribution. The observable structure functions are calculated using high energy factorisation approach. We also include the sub-leading in (l/x) effects via consistency constraint. We argue that the use of this constraint leads to more stable solution to the Pomeron intercept than that based on the NLO calculation of the BFKL equation alone and generates resummation to all orders of the major part of the subleading in (l/x) effects. The global fit to all available deep inelastic data is performed using a simple parametrisation of the non-perturbative region. We also present the results for the longitudinal structure function and the charm component of the F(_2) structure function. Next; we extend this approach to the low Q(^2) domain. At small distances we use the perturbative approach based on the unified BFKL/DGLAP equations and for large distances we use Vector Meson Dominance Model and, for the higher mass qq states, the additive quark approach. We show the results for the total cross section and for the ratio of the longitudinal and transverse structure functions. Finally, we calculate the dijet production and consider the decorrelation effects in the azimuthal distributions caused by the diffusion in the transverse momentum k(_r) of the exchanged gluon. Using the gluon distribution which is fixed by the fit to the DIS data we are able to make absolute predictions. We show the results for the dF(_r)/dɸ, the total cross section and also the distributions in Q(^2) as well as in the longitudinal momentum fraction of the gluon. Our theoretical predictions are confronted with the measurements made using ZEUS detector at HERA

Momentum sum rule and factorization of double parton distributions

We show that the momentum sum rule is a necessary condition for factorization of double parton distributions into a product of two single parton distributions for small values of the parton momentum fractions x and large enough values of the evolution scale Q. This is a somewhat surprising result since the momentum sum rule involves integration over all values of the momentum fraction. In essence, the momentum sum rule provides a proper relation between the double and single parton distributions, which is necessary for the small x factorization at large $Q$.Comment: 11 pages, 4 figures, version published in Phys. Rev.

Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation

Nonlinear evolution equation at small x with impact parameter dependence is analyzed numerically. Saturation scales and the radius of expansion in impact parameter are extracted as functions of rapidity. Running coupling is included in this evolution, and it is found that the solution is sensitive to the infrared regularization. Kinematical effects beyond leading logarithmic approximation are taken partially into account by modifying the kernel which includes the rapidity dependent cuts. While the local nonlinear evolution is not very sensitive to these effects, the kinematical constraints cannot be neglected in the evolution with impact parameter.Comment: 22 pages, 37 figures, RevTe

Algebraic models for the hierarchy structure of evolution equations at small x

We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the equations that include the processes of pomeron splittings. We examine the algebraic structures of the governing equation hierarchies, as well as the asymptotic behavior of their solutions in the large-rapidity limit.Comment: 12 pages, 5 figures; minor changes in the revised versio

Small x nonlinear evolution with impact parameter and the structure function data

The nonlinear Balitsky-Kovchegov equation at small x is solved numerically, incorporating impact parameter dependence. Confinement is modeled by including effective gluon mass in the dipole evolution kernel, which regulates the splitting of dipoles with large sizes. It is shown, that the solution is sensitive to different implementations of the mass in the kernel. In addition, running coupling effects are taken into account in this analysis. Finally, a comparison of the calculations using the dipole framework with the inclusive data from HERA on the structure functions F2 and FL is performed.Comment: 19 pages, 11 figures. Minor revision. One reference added, two figures update

Saturation momentum at fixed and running QCD coupling

A relationship, linking the saturation momentum in the case of fixed and running QCD coupling, respectively, is derived from the Balitsky-Kovchegov equation. It relies on the linear instability of the evolution equation in the dilute regime. The leading orders of the saturation momenta are mapped onto each other exactly. For subleading terms a qualitative correspondence is achieved with a relative error going to zero for large rapidities. The relationship can also be derived for the Balitsky-Kovchegov equation with a cutoff accounting for low-density effects and is satisfied by the corresponding isoline functions. Further implications arise for the existence of travelling-wave solutions in the two situations.Comment: revised version, 6 pages, no figure

QCD saturation in the dipole sector with correlations

In this paper we study the description of saturation in Balitsky, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (B-JIMWLK) picture when restricted to observables made up only from dipole operators. We derive a functional form of the evolution equation for the dipole probability distribution and find a one-parameter family of exact solutions to the dipole evolution equations.Comment: 9 pages, v2: references and comments added, v3: version to appear in Phys. Lett. B (title changed in journal

Geometric Scaling at RHIC and LHC

We present a new phenomenological model of the dipole scattering amplitude to demonstrate that the RHIC data for hadron production in d-Au collisions for all available rapidities are compatible with geometric scaling, just like the small-x inclusive DIS data. A detailed comparison with earlier geometric scaling violating models of the dipole scattering amplitude in terms of an anomalous dimension gamma is made. In order to establish whether the geometric scaling violations expected from small-x evolution equations are present in the data a much larger range in transverse momentum and rapidity must be probed. Predictions for hadron production in p-Pb and p-p collisions at LHC are given. We point out that the fall-off of the transverse momentum distribution at LHC is a sensitive probe of the variation of gamma in a region where x is much smaller than at RHIC. In this way, the expectation for the rise of gamma from small-x evolution can be tested.Comment: 11 pages, 6 figures, minor changes, references added; version to appear in Phys.Rev.