# The multi-Regge limit of the eight-particle amplitude beyond leading logarithmic accuracy

Marzucc, Robin (0000 0001 2294 713X, grid.7942.8, Center for Cosmology, Particle Physics and Phenomenology (CP3), UCLouvain, Chemin du Cyclotron 2, 1348, Louvain-La-Neuve, Belgium) ; Verbeek, Bram (0000 0001 2294 713X, grid.7942.8, Center for Cosmology, Particle Physics and Phenomenology (CP3), UCLouvain, Chemin du Cyclotron 2, 1348, Louvain-La-Neuve, Belgium)

11 July 2019

Abstract: We present the computation of the eight-particle three-loop amplitude beyond leading logarithmic accuracy in the multi-Regge limit of planar N $\mathcal{N}$ = 4 Super Yang-Mills theory. Starting from the all-loop dispersion integral form of the amplitude, we consider the eight-particle case and by analyzing said dispersion integral we associate it to a well-defined Fourier-Mellin transform. By using the properties of the Fourier-Mellin representation and its convolution product structure, we compute the three-loop eight-particle MHV amplitude at next-to-leading logarithmic accuracy. From this MHV result, we obtain the three-loop eight particle amplitude in multi-Regge kinematics for all helicity configurations, including next-to-next-to-MHV. Finally, we find that the result is described by combinations of single-valued multiple polylogarithms of uniform weight, the leading singularity structure of which corresponds to the classification shown at leading logarithmic accuracy.

Published in: JHEP 1907 (2019) 039 DOI: 10.1007/JHEP07(2019)039
arXiv: 1811.10570