Integral Coefficients for One-Loop Amplitudes

Abstract

We present a set of algebraic functions for evaluating the coefficients of the scalar integral basis of a general one-loop amplitude. The functions are derived from unitarity cuts, but the complete cut-integral procedure has been carried out in generality so that it never needs to be repeated. Where the master integrals are known explicitly, the results here can be used as a black box with tree-level amplitudes as input and one-loop amplitudes as output.

32 pages, 1 figure

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• All tree-level amplitudes in massless QCD
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• Optimizing the Reduction of One-Loop Amplitudes
• Double-Cut of Scattering Amplitudes and Stokes' Theorem
• Closed-Form Decomposition of One-Loop Massive Amplitudes
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• From multiple unitarity cuts to the coproduct of Feynman integrals
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• Two-Loop Maximal Unitarity with External Masses
• The one-loop gluon amplitude for heavy-quark production at NNLO
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• Multivariate Residues and Maximal Unitarity
• Next-to-Leading Order Gamma Gamma + 2-Jet Production at the LHC
• Single Cut Integration
• Maximal Unitarity for the Four-Mass Double Box
• Unitarity Cuts of Integrals with Doubled Propagators
• Solving for tadpole coefficients in one-loop amplitudes
• Global Residues and Two-Loop Hepta-Cuts
• Unitarity Method with Spurious Pole
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• Analytic Tadpole Coefficients of One-loop Integrals
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• Generation Function For One-loop Tensor Reduction
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• Reduction of one-loop integrals with higher poles by unitarity cut method
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• All one-loop NMHV gluon amplitudes in N=1 SYM
• Analytic structure of one-loop coefficients
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• On the Cuts of Scattering Amplitudes