Particularities of the NNLLA BFKL

TL;DR

The article analyzes the peculiarities of the NNLLA BFKL framework, arguing that the conventional factorized amplitudes used in LLA and NLLA break down at NNLLA due to three-Reggeon cuts and imaginary parts in unitarity relations. It details how these effects modify the derivation, necessitating the inclusion of Regge cuts in the BFKL kernel and revealing a loss of universality when imaginary parts are included. The work also discusses the structure and impact of the three-Reggeon cut on MRK amplitudes and outlines the theoretical steps needed to extend NNLLA BFKL, highlighting both the challenges and the directions for future calculation. Overall, the paper emphasizes that NNLLA requires new ingredients beyond Reggeized-gluon exchange to achieve a consistent high-energy description in QCD.

Abstract

Peculiar properties of the BFKL approach in the next-to-next-to-leading logarithmic approximation (NNLLA) are discussed. In this approximation the scheme of derivation of the BFKL equation must be changed because of violation of the simple factorized form of amplitudes with multi-Reggeon exchanges and necessity to take into account imaginary parts of amplitudes in the unitarity relations.