One-loop Scattering Equations and Amplitudes from Forward Limit

Abstract

We show that the forward limit of tree-level scattering equations with two massive particles yields the SL(2,C)-covariant form of the one-loop scattering equations recently proposed by Geyer et al. We clarify several properties about these equations and the formulas at one loop. We then argue that in the bi-adjoint scalar theory, such forward limit yields the correct one-loop massless amplitudes, which leads to a new formula for the latter.

17 pages

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Cited by in corpus (66)

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• New Representations of the Perturbative S-Matrix
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Gluons and gravitons at one loop from ambitwistor strings
• Double-Copy Constructions and Unitarity Cuts
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• 1-loop Amplitudes from the Halohedron
• An Algebraic Approach to the Scattering Equations
• Elliptic scattering equations
• One-loop Correlators and BCJ Numerators from Forward Limits
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• General Solution of the Scattering Equations
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• Connected formulas for amplitudes in standard model
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Integrands of loop amplitudes within loop-tree duality
• Superstring loop amplitudes from the field theory limit
• CHY Loop Integrands from Holomorphic Forms
• Collinear limits beyond the leading order from the scattering equations
• One-loop monodromy relations on single cuts
• The Polynomial Form of the Scattering Equations is an H-Basis
• CHY-Graphs on a Torus
• From 4d Ambitwistor Strings to On Shell Diagrams and Back
• On integrands and loop momentum in string and field theory
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Scattering Forms, Worldsheet Forms and Amplitudes from Subspaces
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Double Soft Limit of Graviton Amplitude from the Cachazo-He-Yuan Formalism
• One-loop off-shell amplitudes from classical equations of motion
• Transmuting CHY formulae
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• One-Loop Yang-Mills Integrands from Scattering Equations
• The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes
• Effective observables for electromagnetic duality from novel amplitude decomposition
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• A Combinatoric Shortcut to Evaluate CHY-forms
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• One-loop diagrams with quadratic propagators from the worldsheet
• CHY formula and MHV amplitudes
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• On differential operators and unifying relations for $1$-loop Feynman integrands
• BCJ Numerators from Differential Operator of Multidimensional Residue
• One-loop integrand from generalised scattering equations
• Note on recursion relations for the $\mathcal{Q}$-cut representation
• Double Soft Theorem for Generalised Biadjoint Scalar Amplitudes
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Off-Shell Yang-Mills Amplitude in the CHY Formalism
• Advanced tools for basis decompositions of genus-one string integrals
• Note on solutions of scattering equations
• Tree and $1$-loop fundamental BCJ relations from soft theorems
• CHY Theory for Several Fields
• CHY-construction of Planar Loop Integrands of Cubic Scalar Theory
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• On-shell recursion relations for generic integrands
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands