High-energy QCD amplitudes at two loops and beyond
Vittorio Del Duca, Giulio Falcioni, Lorenzo Magnea, Leonardo Vernazza
TL;DR
The paper analyzes high-energy QCD amplitudes in the Regge limit, showing that naive Regge factorization breaks at NNLL due to non-factorizing color exchanges. It develops a framework that partitions amplitudes into universal Regge trajectory and impact factors plus a non-factorizing remainder sourced by infrared structure, enabling explicit two-loop factorization-breaking terms and predicting three-loop non-universal contributions using soft-collinear factorization. By intersecting soft-collinear and high-energy factorizations, the authors identify the origin of historical discrepancies and redefine the factorization scheme to extract universal pieces while encoding breakdowns in R. The results provide stringent infrared-based constraints on Reggeization and pave the way for extensions to multi-Regge kinematics and phenomenology at the LHC, as well as applications to other gauge theories.
Abstract
Recent progress in our understanding of infrared singularities of multi-parton amplitudes has shown that the simplest form of Regge factorization for high-energy gauge-theory amplitudes fails starting at next-to-next-to-leading logarithmic accuracy. We provide a framework to organize the calculation of parton amplitudes at leading power in t/s, in terms of factorizing and non-factorizing contributions. This allows us to give explicit expressions for the leading Reggeization-breaking terms in two-loop and three-loop quark and gluon amplitudes in QCD. In particular, using only infrared information, we recover a known non-factorizing, non-logarithmic double-pole contribution at two-loops, and we compute the leading non-factorizing single-logarithmic contributions at three loops.