Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$

Abstract

Following a recent proposal to describe inelastic eikonal scattering processes in terms of gravitationally dressed elastic eikonal amplitudes, we motivate a collinear double graviton dressing and investigate its properties. This is derived from a generalized Wilson line operator in the worldline formalism by integrating over fluctuations of the eikonal trajectories of external particles in gravitationally interacting theories. The dressing can be expressed as a product of exponential terms -- a coherent piece with contributions to all odd orders in the gravitational coupling constant and a term quadratic in graviton modes, with the former providing classical gravitational wave observables. In particular, the coherent dressing involves $\mathcal{O}({\kappa }^3)$ subleading double graviton corrections to the Weinberg soft factor. We use this dressing to derive expressions for the waveform, radiative momentum spectrum and angular momentum. In a limiting case of the waveform, we derive the nonlinear memory effect resulting from the emission of nearly soft gravitons from a scattering process.

Matches published version; 49 pages, 1 figure, revisions of Sec. 2.3, Sec. 4.1 and Sec. 5 with broader literature review, minor revision of notation and typos corrected

References in corpus (15)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• The gravitational-wave memory effect
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• Next-to-soft corrections to high energy scattering in QCD and gravity
• Classical observables from coherent-spin amplitudes
• Resummed spinning waveforms from five-point amplitudes
• Subleading Soft Theorem for Multiple Soft Gravitons
• Tidal effects for spinning particles
• Dressed infrared quantum information
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• Classical and quantum gravitational scattering with Generalized Wilson Lines

Cited by in corpus (2)

• Dirac brackets for classical radiative observables
• Double soft graviton factors from the gravitational Wilson line