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 next-to-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of v
arious 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 discuss the recent proposal in hep-th/0611312 where it was shown that the critical anomalous dimension associated to the onset of non-linear effects in the high energy limit of QCD coincides with the critical exponent governing the radius of the b
lack hole formed in the spherically symmetric collapse of a massless scalar field. We argue that a new essential ingredient in this mapping between gauge theory and gravity is continuous self-similarity, not present in the scalar field case but in the spherical collapse of a perfect fluid with barotropic equation of state. We identify this property with geometric scaling, present in DIS data at small values of Bjorken x. We also show that the Choptuik exponent in dimension five tends to the QCD critical value in the traceless limit of the energy momentum tensor.
We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbati
ve convergence. We provide estimates of these decorrelations for large rapidity differences at the Tevatron, LHC and HERA.
The azimuthal angle correlation of Mueller-Navelet jets at hadron colliders is studied in the NLO BFKL formalism. We highlight the need of collinear improvements in the kernel to obtain good convergence properties and we obtain better fits for the Te
vatron data than at LO accuracy. We also estimate these correlations for larger rapidity differences available at the LHC.
