Classical vs Quantum Eikonal Scattering and its Causal Structure

Abstract

We study the eikonal scattering of two gravitationally interacting bodies, in the regime of large angular momentum and large center of mass energy. We show that eikonal exponentiation of the scattering phase matrix is a direct consequence of the group contraction $SU(2)\to ISO(2)$, from rotations to the isometries of the plane, in the large angular momentum limit. We extend it to all orders in the scattering angle, and for all masses and spins. The emergence of the classical limit is understood in terms of the continuous-spin representations admitted by $ISO(2)$. We further investigate the competing classical vs quantum corrections to the leading classical eikonal scattering, and find several interesting examples where quantum corrections are more important than Post-Minkowskian's. As a case of study, we analyse the scattering of a photon off a massless neutral scalar field, up to next-to-leading order in the Newton constant, and to leading order in the fine structure constant. We investigate the causal structure of the eikonal regime and establish an infinite set of non-linear positivity bounds, of which positivity of time delay is the simplest.

32 pages + Appendices and References, 5 Figures, published version

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• Iterative structure of finite loop integrals
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• Infrared features of gravitational scattering and radiation in the eikonal approach
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Cited by in corpus (17)

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• Bethe-Salpeter equation for classical gravitational bound states
• Boundary to bound dictionary for generic Kerr orbits
• Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations
• The EFT Bootstrap at Finite $M_{PL}$
• Causality and quasi-normal modes in the GREFT
• Positivity Bounds on parity-violating scalar-tensor EFTs
• Wave scattering event shapes at high energies
• Non-Forward UV/IR Relations
• Feynman Integrals from Positivity Constraints
• Spinning waveforms of scalar radiation in quadratic modified gravity
• Amplitudes and partial wave unitarity bounds
• IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry
• On-shell approach to scalar hair in spinning binaries