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

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/vertical bar t vertical bar). 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/vertical bar t vertical bar). 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 NU contributions at three and four loops.