Some analytic results for two-loop scattering amplitudes

TL;DR

This paper provides analytic expressions for finite two-loop eight-point MHV scattering amplitudes in planar N=4 SYM, utilizing momentum twistors and motives to simplify results into classical polylogarithms.

Contribution

It introduces a new analytic approach for calculating two-loop scattering amplitudes using momentum twistors and motives, simplifying complex integrals into classical polylogarithms.

Findings

Analytic formulas for finite two-loop eight-point MHV amplitudes.

Simplification of results using motives and classical polylogarithms.

Focus on a restricted kinematic regime with two cross-ratios.

Abstract

We present analytic results for the finite diagrams contributing to the two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a recently proposed representation for the integrand of the amplitude in terms of (momentum) twistors and focus on a restricted kinematics in which the answer depends only on two independent cross-ratios. The theory of motives can be used to vastly simplify the results, which can be expressed as simple combinations of classical polylogarithms.