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

TL;DR

This paper tests the validity of the high-energy amplitude expansion beyond NLL accuracy in N=4 SYM by computing three-loop Regge trajectories and coefficient functions, aiding BFKL evolution and amplitude evaluations.

Contribution

It provides the first computation of three-loop Regge trajectories and coefficient functions in N=4 SYM beyond NLL accuracy, extending the understanding of high-energy amplitude behavior.

Findings

Validated the loop expansion beyond NLL in N=4 SYM.

Computed three-loop Regge trajectory and coefficient functions.

Provided tools for high-energy amplitude analysis and BFKL evolution.

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.