Scientific article
Open access

Classical vs quantum eikonal scattering and its causal structure

Published inThe journal of high energy physics, vol. 2023, 23
Publication date2023
First online date2023-04-05

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) → 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.

  • Effective Field Theories
  • Scattering Amplitudes
  • Scattering: eikonal
  • Correction: quantum
  • Gravitation: fundamental constant
  • Approximation: classical
  • Photon: scattering
  • Scattering: gravitation
  • Gravitation: interaction
  • Higher-order: 1
  • Fundamental constant: fine structure
  • Field theory: scalar
  • Causality
  • Angular momentum
  • Isometry
  • Nonlinear
  • Spin
  • SU(2)
  • Time delay
  • Rotation
Citation (ISO format)
BELLAZZINI, Brando, ISABELLA, Giulia, RIVA, Massimiliano Maria. Classical vs quantum eikonal scattering and its causal structure. In: The journal of high energy physics, 2023, vol. 2023, p. 23. doi: 10.1007/jhep04(2023)023
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Article (Published version)
ISSN of the journal1029-8479

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