Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy

TL;DR

The paper tests high-energy factorization in N=4 SYM by examining the high-energy limit of two- and three-loop four-point amplitudes. It derives the three-loop Regge trajectory and the two- and three-loop coefficient functions, confirming consistency with the Bern-Dixon-Smirnov iterative structure and Regge factorization beyond NLL. The results provide essential building blocks for NNLL BFKL evolution in MSYM and enable cross-checks for higher-leg amplitudes in the high-energy limit.

Abstract

By taking the high-energy limit of the two-loop and the three-loop four-point amplitudes in the maximally supersymmetric N=4 Yang-Mill theory (MSYM), we test the validity of the loop expansion of the high-energy amplitude, beyond the next-to-leading-logarithmic (NLL) accuracy. We compute the three-loop Regge trajectory, and the two-loop and three-loop coefficient functions. These quantities are relevant for the BFKL evolution beyond NLL, as well as building MSYM two-loop and three-loop amplitudes with many legs in the high-energy limit, which in turn may be used as a powerful check of the evaluation of the corresponding exact amplitudes.