Numerical tools for the theoretical study of QCD at small x

In this contribution we present the status of two numerical tools designed to study the small x limit of QCD. The first one is a Monte Carlo simulation of the BFKL evolution equation. In design of this approach emphasis has been placed on exploiting the linear behaviour that many variants of the BFKL evolution possess. This allows us to design a procedure which can be used to study theoretical and phenomenological aspects of different kernels. The second one is a semi-analytic approach to study Lipatov's effective action which describes Reggeon interactions. The study of the properties of this action is very complicated and we propose using a computational tool to handle the large amount of non--local vertices and the derivation of higher order corrections.Comment: 7 pages, 3 figures. International Workshop on Diffraction in High-Energy Physics -DIFFRACTION 2006 - September 5-10 2006 Adamantas, Milos island, Greec

A Monte Carlo study of double logarithms in the small x region

We investigate the effect of the resummation of collinear double logarithms in the BFKL gluon Green function using the Monte Carlo event generator BFKLex. The resummed collinear terms in transverse momentum space were calculated in Ref. [1] and correspond to the addition to the NLO BFKL kernel of a Bessel function of the first kind whose argument contains the strong coupling and a double logarithm of the ratio of the squared transverse momenta of the reggeized gluons. We discuss how these additional terms improve the collinear convergence of the whole approach and reduce the asymptotic growth with energy of cross sections. Taking advantage of the Monte Carlo implementation, we show how the new results reduce the diffusion of the gluon ladder into infrared and ultraviolet transverse momentum scales, while strongly affecting final state configurations by reducing the mini-jet multiplicity.Comment: 12 pages, 5 figure

Applications of Lipatov's high energy effective action to NLO BFKL jet phenomenology

We report on recent progress in the evaluation of next-to-leading order (NLO) observables using Lipatov's QCD high energy effective action. We calculate both real and virtual corrections to the quark induced forward jet vertex at NLO, making use of a new regularization method and a subtraction mechanism. As a new result we determine the real part of the NLO Mueller-Tang impact factor which is the only missing element for a complete NLO BFKL description of dijet events with a rapidity gap.Comment: 4 pages, 29 figures, proceedings of the XX Workshop on Deep-Inelastic Scattering and Related Subjects, 26-30 March, University of Bonn (2012

NLO jet production in k_T factorization

We discuss the inclusive production of jets in the central region of rapidity in the context of k_T-factorization at next-to-leading order (NLO). Calculations are performed in the Regge limit making use of the NLO BFKL results. We introduce a jet cone definition and carry out a proper phase--space separation into multi-Regge and quasi-multi-Regge kinematic regions. We discuss two situations: scattering of highly virtual photons, which requires a symmetric energy scale to separate impact factors from the gluon Green's function, and hadron-hadron collisions, where a non-symmetric scale choice is needed.Comment: 7 pages, 1 figure, prepared for the 12th International Conference on Elastic and Diffractive Scattering, DESY, Hamburg, 21-25 May 200

QCD coherence and jet rates in small x deep inelastic scattering

The contributions to the deep inelastic scattering structure function which arise from emission of zero, one, two or three resolvable gluons and any number of unresolvable ones are computed to order ${\bar \alpha}_{S}^{3}$. Coherence effects are taken into account via angular ordering and are demonstrated to yield (at the leading logarithm level) the identical results to those obtained assuming the multi-Regge kinematics of BFKL.Comment: 14 pages. Extensively rewritten. To be published in Physics Letters

Order-by-order Analytic Solution to the BFKL Equation

We propose a regularization of the BFKL equation which allows for its solution in each order of perturbation theory by means of a sum over multiple poles. This sum can be presented in a rather simple formula for the Fourier transform in the azimuthal angle of the gluon Green function. In order to test our method, we have compared a few orders in the expansion to previous results by Del Duca, Dixon, Duhr and Pennington, finding agreement. Our formalism is general and can be applied to other, more complicated, kernels.Comment: 23 pages, 1 figur

The High Energy Radiation Pattern from BFKLex

We discuss a recent study on high-energy jet production in the multi-Regge limit done with the use of the Monte Carlo event generator BFKLex which includes collinear improvements in the form of double-log contributions. We will show results for the average transverse momentum and azimuthal angle of the final state jets when at least one of them is very forward in rapidity and another one is very backward. We also discuss the introduction of a new observable which accounts for the average rapidity ratio among subsequent emissions.Comment: 6 pages, presented by G. Chachamis at the XXIV International Workshop on Deep-Inelastic Scattering and Related Subjects, 11-15 April 2016, DESY Hamburg, German

A semi-infinite matrix analysis of the BFKL equation

The forward BFKL equation is discretised in virtuality space and it is shown that the diffusion into infrared and ultraviolet momenta can be understood in terms of a semi-infinite matrix. The square truncation of this matrix can be exponentiated leading to asymptotic eigenstates sharing many features with the BFKL gluon Green's function in the limit of large matrix size. This truncation is closely related to a representation of the XXX Heisenberg spin $= - \frac{1}{2}$ chain with SL(2) invariance where the Hamiltonian acts on a symmetric double copy of the harmonic oscillator. A simple modification of the BFKL matrix suppressing the infrared modes generates evolution with energy compatible with unitarity.Comment: Small changes, same conclusions, matching the published version in EPJ