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

Understand

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.