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

TL;DR

This paper thoroughly investigates the high-energy limit of four-parton scattering amplitudes in QCD, analyzing factorization failures beyond NLL accuracy, and providing explicit two- and three-loop results, revealing the infrared origin of high-energy logarithms.

Contribution

It offers the first detailed analysis of Regge factorization failure beyond NLL in QCD amplitudes and extends predictions to higher loops and color representations.

Findings

Identifies the breakdown of Regge factorization at NNLL accuracy.

Provides explicit two- and three-loop amplitude expressions.

Shows that infrared effects explain high-energy logarithms.

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.