An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM

TL;DR

This paper presents a comprehensive algorithm to explicitly construct two-loop seven-point MHV amplitudes in N=4 super-Yang-Mills theory, combining cluster polylogarithms, symbol completion, and collinear limits.

Contribution

It introduces a novel algorithm that integrates various mathematical tools to derive explicit analytic formulas for complex scattering amplitudes.

Findings

Explicit formula for the seven-point two-loop MHV amplitude

Integration of cluster polylogarithms into amplitude construction

Method for fixing additive constants using collinear limits

Abstract

We describe a general algorithm which builds on several pieces of data available in the literature to construct explicit analytic formulas for two-loop MHV amplitudes in N=4 super-Yang-Mills theory. The non-classical part of an amplitude is built from $A_3$ cluster polylogarithm functions; classical polylogarithms with (negative) cluster X-coordinate arguments are added to complete the symbol of the amplitude; beyond-the-symbol terms proportional to $\pi^2$ are determined by comparison with the differential of the amplitude; and the overall additive constant is fixed by the collinear limit. We present an explicit formula for the seven-point amplitude $R_7^{(2)}$ as a sample application.