An on-shell construction using BCFW trees plus vacuum-pair phase-space integrals with inclusion-exclusion signs reproduces the known one- and two-loop all-plus four-gluon amplitudes.
Analytic all-plus-helicity gluon amplitudes in QCD
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abstract
We detail the calculation of two-loop all-plus helicity amplitudes for pure Yang-Mills theory. The four dimensional unitarity methods and augmented recursion techniques we have developed, together with a knowledge of the singular structure of the amplitudes allow us to compute these in compact analytic forms. Specifically we present the computation and analytic results for the six- and seven-gluon leading colour two-loop amplitudes these being the first QCD two-loop amplitudes beyond five-points.
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The paper decomposes two-loop Yang-Mills gluon amplitudes into color structures via trace and structure-constant bases and organizes relations between the resulting partial amplitudes.
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Perturbative construction of amplitudes from on-shell trees with vacuum pairs: the all-plus four-gluon amplitude through order $\boldsymbol{g}^{\boldsymbol{6}}$
An on-shell construction using BCFW trees plus vacuum-pair phase-space integrals with inclusion-exclusion signs reproduces the known one- and two-loop all-plus four-gluon amplitudes.
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Color Decompositions of the Two Loop Amplitudes of Yang-Mills theory
The paper decomposes two-loop Yang-Mills gluon amplitudes into color structures via trace and structure-constant bases and organizes relations between the resulting partial amplitudes.