Second-order Post-Minkowskian scattering in arbitrary dimensions

Abstract

We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten.

51 pages, 1 figure, version to appear in JHEP

References in corpus (35)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• 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
• From Boundary Data to Bound States
• Eikonal Quantum Gravity and Planckian Scattering
• Observables and amplitudes for spinning particles and black holes
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• The simplest massive S-matrix: from minimal coupling to Black Holes
• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• Kerr Black Holes as Elementary Particles
• On Post-Minkowskian Hamiltonians in General Relativity
• On-shell heavy particle effective theories
• Scattering at Planckian Energies
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• 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
• Heavy Black Hole Effective Theory
• Classical Physics and Quantum Loops
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Next-to-soft corrections to high energy scattering in QCD and gravity
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• High energy scattering in gravity and supergravity
• High-energy string-brane scattering: leading eikonal and beyond
• The Subleading Eikonal in Supergravity Theories
• Microscopic unitary description of tidal excitations in high-energy string-brane collisions
• Gravitino one-loop contribution to Planckian Scattering
• Eikonal Scattering in Kaluza-Klein Gravity

Cited by in corpus (64)

• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Gravitational Bremsstrahlung from Reverse Unitarity
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• SUSY in the Sky with Gravitons
• Tidal Effects in the Post-Minkowskian Expansion
• Sixth post-Newtonian nonlocal-in-time dynamics of binary systems
• On an Exponential Representation of the Gravitational S-Matrix
• Classical Gravity from Loop Amplitudes
• Radiative contributions to gravitational scattering
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• A worldsheet for Kerr
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Inelastic Exponentiation and Classical Gravitational Scattering at One Loop
• Tidal effects in quantum field theory
• Classical Solutions and their Double Copy in Split Signature
• Classical observables from coherent-spin amplitudes
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Mining the Geodesic Equation for Scattering Data
• Classical Yang-Mills observables from amplitudes
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Angular momentum of zero-frequency gravitons
• The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
• Infrared Divergences and the Eikonal Exponentiation
• Gravitational shock waves and scattering amplitudes
• Exponentiation of the leading eikonal with spin
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Eikonal amplitudes from curved backgrounds
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Horizon radiation reaction forces
• Light bending from eikonal in worldline quantum field theory
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• Post-Minkowskian Theory Meets the Spinning Effective-One-Body Approach for Two-Body Scattering
• Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory
• Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity
• Simplifying $D$-Dimensional Physical-State Sums in Gauge Theory and Gravity
• A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Large Gauge Effects and the Structure of Amplitudes
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• The Reissner-Nordström-Tangherlini solution from scattering amplitudes of charged scalars
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering
• General Relativity from Intersection Theory
• Machine Learning Post-Minkowskian Integrals
• On the classical limit of the (sub)${}^n$-leading soft graviton theorems in $D=4$ without deflection
• Fixing the non-relativistic expansion of the 1PM potential
• Yang-Mills observables: from KMOC to eikonal through EFT
• The Radial Action from Probe Amplitudes to All Orders
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order
• NS-NS Spacetimes from Amplitudes
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework