Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy

TL;DR

This work clarifies how infrared factorization shapes the high-energy behavior of four-parton QCD amplitudes, extending analyses beyond NLL to NNLL and beyond. By aligning infrared-derived structures with Regge-based factorization, the authors identify when Regge factorization holds and precisely isolate non-factorizing remainder terms responsible for its breakdown, notably at NNLL due to color mixing in the t-channel. They demonstrate that, in $d=4$, hard (IR-finite) parts of the amplitude vanish up to NLL for the color-octet exchange, implying that high-energy logarithms are governed by infrared operators. The study also generalizes to color representations beyond the octet and provides explicit pole structures and predictions up to three loops (and some four-loop implications), offering a framework to test Regge theory against infrared constraints in high-energy QCD.

Abstract

We provide a complete and detailed study of the high-energy limit of four-parton scattering amplitudes in QCD, giving explicit results at two loops and higher orders, and going beyond next-to-leading logarithmic (NLL) accuracy. Building upon recent results, we use the techniques of infrared factorization to investigate the failure of the simplest form of Regge factorization, starting at next-to-next-to-leading logarithmic accuracy (NNLL) in ln(s/|t|). We provide detailed accounts and explicit expressions for the terms responsible for this breaking in the case of two-loop and three-loop quark and gluon amplitudes in QCD; in particular, we recover and explain a known non-logarithmic double-pole contribution at two-loops, and we compute all non-factorizing single-logarithmic singular contributions at three loops. Conversely, we use high-energy factorization to show that the hard functions of infrared factorization vanish in d = 4 to all orders in the coupling, up to NLL accuracy in ln(s/|t|). This provides clear evidence for the infrared origin of high-energy logarithms. Finally, we extend earlier studies to t-channel exchanges of color representations beyond the octet, which enables us to give predictions based on the dipole formula for single-pole NLL contributions at three and four loops.