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.
Highlights
NNLO predictions is by no means a simple task
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
Rather than constructing D-dimensional local integrands from first principles, we focus on their uses in the all-plus sector of Yang-Mills theory
Summary
Throughout this paper we will work in dimensional regularisation with different dimensions in play simultaneously:. D The number of dimensions in dimensional regularisation, D = 4 − 2. D The number of dimensions in which we embed D-dimensional momenta, D = 6. For oneloop integrals we will write μ2 = −( [−2 ])2 These loop momenta will often be included in. [45] but in practice we will overcome such ambiguities by decomposing into four-dimensional traces tr±(i1 · · · ik x yik+1 · · · in) = tr±(i1 · · · ikxyik+1 · · · in) − μxytr±(i1 · · · in). In general we will identify topologies T by explicitly drawing them.
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