Analytic structure of the high-energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms

Abstract

We investigate the high-energy, small-angle limit of two-body gravitational scattering. Using power counting arguments and dispersion relations in an effective field theory for the Regge regime, we derive the general loop expansion that determines how the leading Regge logarithms and their complex structure arise as a power series in $t/s$. Focusing on the tower of multi-H diagrams that govern the leading logarithmic behavior, we compute the leading double logarithm at four loops (5PM) using both effective field theory methods and the multi-Regge expansion, finding complete agreement. Finally, using the aforementioned dispersion relations, we extract the single logarithmic contribution to the imaginary part of the eikonal phase at 5PM in the Regge limit.

6 pages + appendices, 2 figures; v2: published version

References in corpus (18)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order
• Towards an S-matrix Description of Gravitational Collapse
• Infrared features of gravitational scattering and radiation in the eikonal approach
• Integrability of scattering amplitudes in N=4 SUSY
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Emergence of Calabi-Yau manifolds in high-precision black hole scattering
• Radiated momentum and radiation-reaction in gravitational two-body scattering including time-asymmetric effects
• Gravitational Regge bounds
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• Scaling similarities and quasinormal modes of D0 black hole solutions
• Soft-collinear gravity beyond the leading power
• Wave scattering event shapes at high energies
• Strong Field Scattering of Black Holes: Assessing Resummation Strategies
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• A Collinear Perspective on the Regge Limit
• Highly accurate simulations of asymmetric black-hole scattering and cross validation of effective-one-body models
• Wormholes and holographic decoherence