Abstract
We present the computation of the eight-particle three-loop amplitude beyond leading logarithmic accuracy in the multi-Regge limit of planar \( \mathcal{N} \) = 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.
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Marzucca, R., Verbeek, B. The multi-Regge limit of the eight-particle amplitude beyond leading logarithmic accuracy. J. High Energ. Phys. 2019, 39 (2019). https://doi.org/10.1007/JHEP07(2019)039
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DOI: https://doi.org/10.1007/JHEP07(2019)039