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Eikonal amplitudes from curved backgrounds

by Tim Adamo, Andrea Cristofoli, Piotr Tourkine

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Submission summary

Authors (as registered SciPost users): Andrea Cristofoli
Submission information
Preprint Link: scipost_202205_00033v1  (pdf)
Date accepted: 2022-06-28
Date submitted: 2022-05-31 16:00
Submitted by: Cristofoli, Andrea
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

Eikonal exponentiation in QFT describes the emergence of classical physics at long distances in terms of a non-trivial resummation of infinitely many diagrams. Long ago, 't Hooft proposed a beautiful correspondence between ultra-relativistic scalar eikonal scattering and one-to-one scattering in a background shockwave space-time, bypassing the need to resum. In this spirit, we propose here a covariant method for computing one-to-one amplitudes in curved background space-times which gives rise what we conjecture to be a general expression for the eikonal amplitude. We show how the one-to-one scattering amplitude for scalars on any stationary space-time reduces to a boundary term that captures the long-distance behavior of the background and has the structure of an exponentiated eikonal amplitude. In the case of scalar scattering on Schwarzschild, we recover the known results for gravitational scattering of massive scalars in the eikonal regime. For Kerr, we find a remarkable exponentiation of the tree-level amplitude for gravitational scattering between a massive scalar and a massive particle of infinite spin. This amplitude exhibits a Kawai-Lewellen-Tye-like factorization, which we use to evaluate the eikonal amplitude in momentum space, and study its analytic properties.

Published as SciPost Phys. 13, 032 (2022)


Reports on this Submission

Anonymous Report 2 on 2022-6-15 (Invited Report)

Report

The authors clarified all the points raised and I strongly suggest the new version for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2022-6-12 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202205_00033v1, delivered 2022-06-12, doi: 10.21468/SciPost.Report.5226

Strengths

1-Relevant and Timely
2-Scientifically sound
3-Well written

Weaknesses

1- Deals only with linear level results

Report

This paper by Adamo, Cristofoli and Tourkine proposes an alternative derivation of the two-to-two eikonal amplitude in QFT in terms of a one-to-one amplitude in curved spacetime.

This paper is relevant and timely, considering the recent explosion in research linking the field of scattering amplitudes with the solution of the two-body problem in general relativity.

The research is scientifically sound, and the manuscript is well written. Furthermore, the previously requested changes have been dealt with to my satisfaction, and so I recommend its publication in SciPost

Requested changes

The previously requested changes have been dealt with to my satisfaction.

  • validity: high
  • significance: good
  • originality: high
  • clarity: high
  • formatting: good
  • grammar: good

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