Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles

Abstract

We generalize the scattering equations to include both massless and massive particles. We construct an expression for the tree-level n-point amplitude with n-2 gluons or gravitons and a pair of massive scalars in arbitrary spacetime dimension as a sum over the (n-3)! solutions of the scattering equations, a la Cachazo, He, and Yuan. We derive the BCJ relations obeyed by these massive amplitudes.

22 pages. v2: clarification of eqs. (5.5) and (5.6)

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• Two-Loop Scattering Amplitudes from the Riemann Sphere
• Scattering Equations and String Theory Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• A Worldsheet Theory for Supergravity
• Ambitwistor formulations of $R^2$ gravity and $(DF{)}^2$ gauge theories
• Loop-Level Double-Copy for Massive Quantum Particles
• Relations for Einstein-Yang-Mills amplitudes from the CHY representation
• Chiral approach to massive higher spins
• Scattering equations, generating functions and all massless five point tree amplitudes
• CHY-Graphs on a Torus
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• The Scattering Variety
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• BCJ relations from a new symmetry of gauge-theory amplitudes
• A String Deformation of the Parke-Taylor Factor
• Infrared behaviour of the one-loop scattering equations and supergravity integrands
• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• Off-shell BCJ Relation in Nonlinear Sigma Model
• Note on off-shell relations in nonlinear sigma model
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Fermions and the scattering equations
• Sudakov Representation of the Cachazo-He-Yuan Scattering Equations Formalism
• On-shell representation and further instances of the 2-split behavior of amplitudes
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Color-factor symmetry and BCJ relations for QCD amplitudes
• Relations and representations of QCD amplitudes