Scattering of Gravitons and Spinning Massive States from Compact Numerators

Abstract

We provide a new efficient diagrammatic tool, in the context of the scattering equations, for computation of covariant $D$-dimensional tree-level $n$-point amplitudes with pairs of spinning massive particles using compact exponential numerators. We discuss how this framework allows non-integer spin extensions of recurrence relations for amplitudes developed for integer spin. Our results facilitate the on-going program for generating observables in classical general relativity from on-shell tree amplitudes through the Kawai-Lewellen-Tye relations and generalized unitarity.

arXiv comment32 pages, 5 figures, version to be published in JHEP

References in corpus (116)

• General relativity as an effective field theory: The leading quantum corrections
• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Amplitudes, Observables, and Classical Scattering
• The Effective Field Theorist's Approach to Gravitational Dynamics
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Black holes and the double copy
• Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
• Scattering Equations and KLT Orthogonality
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• The Momentum Kernel of Gauge and Gravity Theories
• Classical Space-Times from the S Matrix
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• From Boundary Data to Bound States
• Quantum Corrections to the Schwarzschild and Kerr Metrics
• Observables and amplitudes for spinning particles and black holes
• Explicit BCJ Numerators from Pure Spinors
• The simplest massive S-matrix: from minimal coupling to Black Holes
• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• Perturbative Quantum Gravity and its Relation to Gauge Theory
• Classical and quantum scattering in post-Minkowskian gravity
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
• On-shell Techniques and Universal Results in Quantum Gravity
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Kerr Black Holes as Elementary Particles
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• $\pi \pi$ Scattering in Three Flavour ChPT
• Radiative contribution to classical gravitational scattering at the third order in $G$
• On Post-Minkowskian Hamiltonians in General Relativity
• On-shell heavy particle effective theories
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Universality of ultra-relativistic gravitational scattering
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Radiation Reaction from Soft Theorems
• Bending of Light in Quantum Gravity
• Gravitational spin Hamiltonians from the S matrix
• Heavy Black Hole Effective Theory
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Double copy for massive quantum particles with spin
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• The Duality Between Color and Kinematics and its Applications
• Classical Physics and Quantum Loops
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• On the Coupling of Gravitons to Matter
• Light-like Scattering in Quantum Gravity
• Universality in the classical limit of massless gravitational scattering
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Post-Minkowskian Scattering Angle in Einstein Gravity
• Complete Hamiltonian for spinning binary systems at first post-Minkowskian order
• Gravity and Yang-Mills Amplitude Relations
• Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension
• Recursion Relations for Gauge Theory Amplitudes with Massive Vector Bosons and Fermions
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• Classical potential for general spinning bodies
• Proof of Gravity and Yang-Mills Amplitude Relations
• Berends-Giele recursions and the BCJ duality in superspace and components
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• BCJ numerators from reduced Pfaffian
• The Polynomial Form of the Scattering Equations
• Expansion of Einstein-Yang-Mills Amplitude
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• Graviton-Photon Scattering
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• All-Multiplicity Amplitudes with Massive Scalars
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Leading quantum gravitational corrections to scalar QED
• Scattering Equations and Feynman Diagrams
• Integration Rules for Scattering Equations
• Scattering Equations and String Theory Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• The double copy for heavy particles
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Tidal effects for spinning particles
• The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
• Helicity amplitudes for QCD with massive quarks
• Gravitational shock waves and scattering amplitudes
• String theory and the mapping of gravity into gauge theory
• Simple encoding of higher derivative gauge and gravity counterterms
• Strings, extended objects, and the classical double copy
• Constraints on a Massive Double-Copy and Applications to Massive Gravity
• Loop-Level Double-Copy for Massive Quantum Particles
• One-loop Correlators and BCJ Numerators from Forward Limits
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• $\Lambda$ Scattering Equations
• Analytic Representations of Yang-Mills Amplitudes
• Generalized string theory mapping relations between gravity and gauge theory
• Soft Matters, or the Recursions with Massive Spinors
• Scalar-Graviton Amplitudes
• Kaluza-Klein from Colour-Kinematics Duality for Massive Fields
• Gravitino Interactions from Yang-Mills Theory
• Recursion relations for scattering amplitudes with massive particles
• One-Loop Yang-Mills Integrands from Scattering Equations
• String theory and the KLT-relations between gravity and gauge theory including external matter
• New relations for graviton-matter amplitudes
• Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
• New Factorization Relations for Yang Mills Amplitudes
• Transmuting off-shell CHY integrals in the double-cover framework
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• Factorizations for tree amplitudes in the double-cover framework: from gravity to other theories

Cited by in corpus (12)

• Compton Black-Hole Scattering for $s\le 5/2$
• Classical Solutions and their Double Copy in Split Signature
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Generalizations of the Double-Copy: the KLT Bootstrap
• Classical Spin Gravitational Compton Scattering
• Classical Limit of Higher-Spin String Amplitudes
• Effective Field Theories and Cosmological Scattering Equations
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Color-Kinematic Numerators for Fermion Compton Amplitudes
• Next-to-MHV Yang-Mills kinematic algebra
• NS-NS Spacetimes from Amplitudes
• A Novel On-Shell Recursive Relation