HET SEMINAR<br>Hexagon Functions: Bootstrapping an NMHV Amplitude through Four Loops

In recent years, tremendous progress has been made in calculating scattering amplitudes in planar N=4 super Yang-Mills. For six particles, the two properties of maximal transcendentality and dual conformal symmetry have allowed construction of the Hexagon Functions, a complete basis for six-point amplitudes. Armed with this basis, my collaborators and I construct the six-point NMHV ratio function through four loops, finding a unique analytic expression. Plotting our results, we find remarkable similarities in the behavior of the ratio function between different loop orders, if not to the extent observed for the MHV case.