All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops.

Jacob L Bourjaily,Enrico Herrmann,Andrew J Mcleod,Jaroslav Trnka,Cameron Langer

doi:10.1103/physrevlett.124.111603

Abstract

We give a prescriptive representation of all-multiplicity two-loop maximally-helicity-violating (MHV) amplitude integrands in fully-color-dressed (nonplanar) maximally supersymmetric Yang-Mills theory.

Highlights

We give a prescriptive representation of all-multiplicity two-loop maximally-helicity-violating (MHV) amplitude integrands in fully-color-dressed maximally supersymmetric Yang-Mills theory
These amplitude integrands should be expressible in terms of an integrand basis with “triangle power counting”
In this Letter, we show that this is the case by presenting the first fully explicit, color-dressed, prescriptive representation of all-multiplicity maximally-helicity-violating (MHV) amplitude integrands in SYM at two loops

Summary

Published by the American Physical Society

Methods (or even for BCJ [55], for example). Because individual integrands have support on poles at infinite loop momentum, the cancellation of these residues at infinity for SYM amplitudes [41] amounts to a nontrivial consistency check. The representation Eq (1) is a sum over all distinct leg distributions—including cases where the sets of legs A, B, C attached to MHV vertices are allowed to be empty Such leading singularities have the interpretation of a residue taken in a soft (and sometimes collinear) region, which sets the momentum flowing through the “doubled” propagator to zero. Recall that when a MHV vertex in a leading singularity has no external legs attached to it, the corresponding residue is to be understood as the double constraint taking the momentum through that edge to be on shell and soft. Normalizing these integrands on their associated kinematic points is a good start, but is not sufficient to define our basis.

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