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We present the computation of the eight-particle three-loop amplitude beyondleading logarithmic accuracy in the multi-Regge limit of planar N=4 SuperYang-Mills theory. Starting from the all-loop dispersion integral form of theamplitude, we consider the eight-particle case and by analyzing said dispersionintegral we associate it to a well-defined Fourier-Mellin transform. By usingthe properties of the Fourier-Mellin representation and its convolution productstructure, we compute the three-loop eight-particle MHV amplitude atnext-to-leading logarithmic accuracy. From this MHV result, we obtain thethree-loop eight particle amplitude in multi-Regge kinematics for all helicityconfigurations, including next-to-next-to-MHV. Finally, we find that the resultis described by combinations of single-valued multiple polylogarithms ofuniform weight, the leading singularity structure of which corresponds to theclassification shown at leading logarithmic accuracy.

The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy