Higher-order Contributions to QCD Amplitudes in Regge Kinematics (Mini-review)

The famous Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation was derived using the hypothesis that amplitudes of non-abelian gauge theories with adjoint representation of the gauge group in cross-channels are given by the Reggeized gauge boson contributions. The hypothesis is true in the leading logarithmic approximation, wherein the equation was originally derived, and in the next-to-leading one. But in the next-to-next-to-leading logarithmic approximation this is not so, since in this approximation the Regge cuts begin to contribute. Calculations of their contributions to elastic scattering amplitudes in Quantum Chromodynamics and their role in derivation of the BFKL equation are discussed.