The two-loop five-point amplitude in $\mathcal{N} =4$ super-Yang-Mills theory

TL;DR

The paper computes the symbol of the two-loop five-point amplitude in N=4 sYM, including full color dependence, by constructing a complete nonplanar master-integral basis and solving canonical differential equations for the 108 masters within a 31-letter alphabet. The authors assemble the color-dressed amplitude in a Parke-Taylor–based decomposition, obtaining parity-even and parity-odd parts at the symbol level via finite-field IBP reductions. Rigorous validation against collinear factorization, the BDS planar limit, and Catani's infrared structure establishes the reliability of the nonplanar result, with ancillary files providing explicit symbols and master-integral data. This marks the first analytic nonplanar two-loop five-point result, with implications for Wilson-loop duality, subleading-color dynamics, and the application of these master integrals to QCD at NNLO.

Abstract

We compute the symbol of the two-loop five-point scattering amplitude in $\mathcal{N}$ = 4 super-Yang-Mills theory, including its full color dependence. This requires constructing the symbol of all two-loop five-point nonplanar massless master integrals, for which we give explicit results.

Figures (1)

• Figure 1: Diagram topologies entering the local representation of the two-loop five-point integrand of $\mathcal{N}\!=\!4\text{ sYM}$Carrasco:2011mn. Each diagram has an associated color structure and numerator which we suppress.