After a brief review of the BFKL approach to Regge processes in QCD and in supersymmetric (SUSY) gauge theories we propose a strategy for calculating the nextto-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross-sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high energy scattering. In the case of N = 4 SUSY it is also possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the analytic properties of the BDS amplitudes at high energies are investigated, in order to verify their self-consistency. It is found that, for the number of external particles being larger than five, these amplitudes, beyond one loop, are not in agreement with the BFKL approach which predicts the existence of Regge cuts in some physical channels.

We further investigate, in the planar limit of N = 4 supersymmetric Yang Mills theories, the high energy Regge behavior of six-point MHV scattering amplitudes. In particular, for the new Regge cut contribution found in our previous paper, we compute in the leading logarithmic approximation (LLA) the energy spectrum of the BFKL equation in the color octet channel, and we calculate explicitly the two loop corrections to the discontinuities of the amplitudes for the transitions 2 → 4 and 3 → 3. We find an explicit solution of the BFKL equation for the octet channel for arbitrary momentum transfers and investigate the intercepts of the Regge singularities in this channel. As an important result we find that the universal collinear and infrared singularities of the BDS formula are not affected by this Regge-cut contribution. Any improvement of the BDS formula should reproduce this cut to all orders in the coupling.

We present a detailed description of the Q 2 and x dependence of the structure functions F 2 and F L as extracted from the Deep Inelastic Scattering data at HERA in the small Bjorken x region. Making use of a collinearly-improved BFKL equation at next-to-leading order and a treatment of the running of the coupling using non-Abelian physical renormalization together with the BLM scale choice allows us to reach low values of Q 2 . We also provide some predictions for future leptonhadron colliders.

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We show that it is possible to describe the effective Pomeron intercept, determined from the HERA deep inelastic scattering data at small values of Bjorken x, by using next-to-leading order Balitsky-Fadin-Kuraev-Lipatov evolution together with collinear improvements. To obtain a good description over the whole range of Q(2), we use a non-Abelian physical renormalization scheme with the Brodsky-Lepage-Mackenzie optimal scale, combined with a parametrization of the running coupling in the infrared region.

We determine both real and virtual next-to-leading order corrections to the gluon induced forward jet vertex, from the high energy effective action proposed by Lipatov. For these calculations we employ the same regularization and subtraction formalism developed in our previous work on the quark-initiated vertex. We find agreement with previous results in the literature.

We investigate the stability under variation of the renormalization, factorization and energy scales entering the calculation of the cross section, at next-to-leading order in the BFKL formalism, for the production of Mueller-Navelet jets at the Large Hadron Collider, following the experimental cuts on the tagged jets. To find optimal values for the scales involved in this observable it is possible to look for regions of minimal sensitivity to their variation. We show that the scales found with this logic are more natural, in the sense of being more similar to the squared transverse momenta of the tagged jets, when the BFKL kernel is improved with a resummation of collinear contributions than when the treatment is at a purely next-to-leading order. We also discuss the good perturbative convergence of the ratios of azimuthal angle correlations, which are quite insensitive to collinear resummations and well described by the original BFKL framework.

Ratios of azimuthal angle correlations between two jets produced at large rapidity separation are studied in the N = 4 maximally supersymmetric Yang-Mills (MSYM) theory. It is shown that these observables, which directly prove the SL(2,C) symmetry present in gauge theories in the Regge limit, exhibit an excellent perturbative convergence. They are compared to those calculated in QCD for different renormalization schemes concluding that the momentum-substraction scheme with the Brodsky-Lepage-Mackenzie scale-fixing procedure captures the bulk of the MSYM results.