Paper and ancilary files.

# Author(s):

Robin Marzucca, Bram Verbeek

# Abstract:

We present the computation of the eight-particle three-loop amplitude beyond leading logarithmic accuracy in the multi-Regge limit of planar 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.

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