Reducing full one-loop amplitudes to scalar integrals at the integrand level

Abstract

We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation

updated version

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• Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices
• OPITeR: A program for tensor reduction of multi-loop Feynman Integrals
• NLO QCD predictions for $\mathbf{t}\bar{\mathbf{t}}\mathbf{\gamma }$ with realistic photon isolation
• Next-to-Leading-Order Corrections to Weak Boson Production with a Massive Quark Jet Pair at Hadron Colliders
• Studies of Quantum Chromodynamics at the LHC
• Automated calculations for multi-leg processes
• Hard QCD at hadron colliders
• An interface between the POWHEG BOX and MadGraph5_aMC@NLO
• Illustrations of Integrand-Basis Building at Two Loops
• On the finite basis topologies for multi-loop high-multiplicity Feynman integrals
• Stable One-Dimensional Integral Representations of One-Loop N-Point Functions in the General Massive Case: I - Three Point Functions
• Augmented Recursion For One-loop Amplitudes
• Probing B-Anomalies via Dimuon Tails at a Future Collider
• Analytic Computations of Massive One-Loop Amplitudes
• NLO QCD predictions for off-shell $t\bar{t}W$ production in association with a light jet at the LHC
• Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
• Generalized unitarity method for unstable particles
• Peaks and cusps: anomalous thresholds and LHC physics
• Next-to-Leading Order QCD Corrections to Heavy-Flavour Production in Neutral Current DIS
• Five-Point Two-Loop Amplitudes from Numerical Unitarity
• NNLO QED contribution to the $\mu e\to \mu e$ elastic scattering
• Numerical evaluation of one-loop QCD amplitudes
• Light-by-light scattering amplitudes from generalized unitarity in massive QED
• Massive particles and unitarity cuts
• On Higgs boson plus gluon amplitudes at one loop
• Analytic structure of one-loop coefficients
• Proton structure at the LHC
• Scattering Amplitudes for Monopoles: Pairwise Little Group and Pairwise Helicity
• Electroweak corrections to Higgs boson production via W W fusion at the future LHeC
• The $\gamma \gamma$ decay of the Higgs boson in FDR
• Monte Carlo evaluation of divergent one-loop integrals without contour deformation
• A new method for finding more symmetry relations of Feynman integrals
• Higgs + Multi-jets in Gluon Fusion
• An Automated Approach for $q\bar{q}\to b\bar{b}b\bar{b}$ at Next-to-Leading Order QCD
• Higgs production via vector-boson fusion at the LHC
• Precise evaluation of the Cut Constructible part of one loop amplitudes within D-dimensional unitarity
• Automated computation of scattering amplitudes
• The HiggsTools Handbook: Concepts and observables for deciphering the Nature of the Higgs Sector
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Extended Projection Method for Massive Fermion
• GoSam applications for automated NLO calculations
• Optimising hadronic collider simulations using amplitude neural networks
• Higher-Order QCD prediction for dark matter pair associated with a b-jet production at the LHC
• Chinese Magic in Loop Integrals
• Recent news and results in the computation of NLO processes with new techniques
• Quantum point particle approximation of spinning black holes and compact stars
• Universal Decomposition of Phase-Space Integrands
• Monte Carlo Event Generators
• NLO automated tools for QCD and beyond
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• Production of t anti-t b anti-b at the LHC at NLO QCD
• Equivalence of Coefficients Extraction of One-loop Master Integrals
• Phenomenological studies of top-pair production at Next-to-Leading order
• $t\bar{t}jj$ -- NLO QCD corrections to top quark pair production and decays at the LHC
• Next-to-leading order QCD corrections to ttbb production at the LHC
• Automated NLO/NLL Monte Carlo programs for the LHC
• Higgs probes of top quark contact interactions and their interplay with the Higgs self-coupling
• Co-homology of Differential Forms and Feynman diagrams
• Recent Developments in Higher-Order Calculations: Hard Functions at NLO with GoSam
• Applications of higher order QCD
• Complete NLO corrections to off-shell $\mathbf{t}\bar{\mathbf{t}}$ production in the $\mathbf{\ell }+\mathbf{j}$ decay channel
• On the Cuts of Scattering Amplitudes
• QCD Amplitudes: new perspectives on Feynman integral calculus
• A stroll through the loop-tree duality
• Monte Carlo Event Generators for Future Lepton Colliders
• Complete NLO corrections to $t\bar{t}\gamma$ and $t\bar{t}\gamma \gamma$