From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
Arthur E. Lipstein, Lionel Mason
TL;DR
This work develops a direct $d\log$ framework for planar N=4 sYM amplitudes, centering on the 1-loop MHV case and the Kermit diagram. By embedding the Feynman iε prescription within momentum-twistor variables, it yields a compact dilogarithm expression for generic diagrams, with dual conformal invariance preserved up to the reference twistor. Divergent cases are regulated using mass regularization, and the method extends naturally to higher loops, where building blocks like multiple Kermits produce higher polylogs (e.g., Li4). The approach provides a simpler, potentially non-planar extensible route to integrated amplitudes and their symbols, aligning with known results while offering new computational tools.
Abstract
Recently, loop integrands for certain Yang-Mills scattering amplitudes and correlation functions have been shown to be systematically expressible in dlog form, raising the possibility that these loop integrals can be performed directly without Feynman parameters. We do so here to give a new description of the planar 1-loop MHV amplitude in N = 4 super Yang-Mills theory. We explicitly incorporate the standard Feynman i epsilon prescription into the integrands. We find that the generic MHV diagram contributing to the 1-loop MHV amplitude, known as Kermit, is dual conformal invariant up to the choice of reference twistor explicit in our axial gauge (the generic MHV diagram was already known to be finite). The new formulae for the amplitude are nontrivially related to previous ones in the literature. The divergent diagrams are evaluated using mass regularization. Our techniques extend directly to higher loop diagrams, and we illustrate this by sketching the evaluation of a non-trivial 2-loop example. We expect this to lead to a simple and efficient method for computing amplitudes and correlation functions with less supersymmetry and without the assumption of planarity.