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The Last of the Finite Loop Amplitudes in QCD
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We use on-shell recursion relations to determine the one-loop QCD scattering amplitudes with a massless external quark pair and an arbitrary number (n-2) of positive-helicity gluons. These amplitudes are the last of the unknown infrared- and ultraviolet-finite loop amplitudes of QCD. The recursion relations are similar to ones applied at tree level, but contain new non-trivial features corresponding to poles present for complex momentum arguments but absent for real momenta. We present the relations and the compact solutions to them, valid for all n. We also present compact forms for the previously-computed one-loop n-gluon amplitudes with a single negative helicity and the rest positive helicity.
Forward citations
Cited by 2 Pith papers
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$N$-Photon Amplitudes in EFT from Recursion Relations and Effective Vertices
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Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
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