Local integrands for two-loop all-plus Yang-Mills amplitudes

TL;DR

This paper derives compact, local integrand representations for two-loop all-plus Yang-Mills amplitudes, revealing their infrared properties and simplifying the rational terms after integration.

Contribution

It introduces D-dimensional local integrands for two-loop all-plus amplitudes, fixed from six-dimensional on-shell tree amplitudes, with manifest infrared behavior and simplified rational terms.

Findings

Explicit compact formulas for five- and six-gluon amplitudes

Manifest infrared behavior at the integrand level

Simplified rational terms after integration

Abstract

We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4-2epsilon dimensions.