The Seven-Point Two-Loop Full-Color All-Plus Helicity Yang-Mills Amplitude

TL;DR

This paper presents a compact analytic form of the seven-gluon two-loop full-color Yang-Mills amplitude, combining unitarity cuts and recursion methods, and explores potential relations among two-loop partial amplitudes.

Contribution

It introduces a new compact analytic expression for the seven-gluon two-loop amplitude and an n-point form for the polylogarithmic part, advancing computational techniques in gauge theory.

Findings

Derived a compact analytic form of the amplitude.

Proposed an n-point form for the polylogarithmic piece.

Explored potential relations among two-loop partial amplitudes.

Abstract

The seven-gluon two-loop full-color Yang-Mills amplitude is presented in a compact analytic form where we use the methods of four-dimensional unitarity cuts to obtain the polylogarithmic pieces and augmented recursion to obtain the rational pieces. Furthermore, an $n$-point form for the full-color polylogarithmic piece is presented. We use these results to probe for potential relations amongst the two-loop partial amplitudes.