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Cartographing gravity-mediated scattering amplitudes: scalars and photons

by Benjamin Knorr, Samuel Pirlo, Chris Ripken, Frank Saueressig

Submission summary

Authors (as Contributors): Benjamin Knorr · Chris Ripken · Frank Saueressig
Submission information
Arxiv Link: (pdf)
Date submitted: 2022-05-10 21:20
Submitted by: Knorr, Benjamin
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
Approach: Theoretical


The effective action includes all quantum corrections arising in a given quantum field theory. Thus it serves as a powerful generating functional from which quantum-corrected scattering amplitudes can be constructed via tree-level computations. In this work we use this framework for studying gravity-mediated two-to-two scattering processes involving scalars and photons as external particles. We construct a minimal basis of interaction monomials capturing all contributions to these processes. This classification goes beyond the expansions used in effective field theory since it retains the most general momentum dependence in the propagators and couplings. In this way, we derive the most general scattering amplitudes compatible with a relativistic quantum field theory. Comparing to tree-level scattering in general relativity, we identify the differential cross sections which are generated by the non-trivial momentum dependence of the interaction vertices.

Current status:
In refereeing

Submission & Refereeing History

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Submission 2205.01738v1 on 10 May 2022

Reports on this Submission

Anonymous Report 1 on 2022-9-7 (Invited Report)


The general idea of enumerating these form factors is good. The paper represents significant work in organizing the form factors.


It seems that the authors are excluding important non-local effects. See report.


This paper contains a good deal of content which is potentially useful. However, it seems also incomplete because it neglects the nonlocalities which come with quantum calculations. This is briefly discussed, but is just dismissed without any resolution.

The basic problem is that with quantum corrections there can be inverse powers of d’Alambertians which seem not to be captured in this formfactor expansion. An extreme version of this is seen in the Riegert anomaly action R.J. Riegert, Phys. Lett. 134B (1984) 56 , which has powers of 1/Box^2 . But also the Barvinsky Vilkovisky expansion at third order in the curvature has many logs in the numerators and 1/Box factor in the denominator. Another example is the recent nonlocal action of Donoghue Phys. Rev. D105} 105025 (2022) which have various nonlocal factors when expressed in terms of the curvature. These quantum effects seem common, but they also seem to be missed by the work or the present paper.

The issue is mentioned briefly on page 8. But the authors say only that these effects are excluded from their parametrization. While this is true, it is not sufficient. I understand fully their comment about BV removing the structure with the Riemann tensor. But there are other nonlocalities besides these. These effects do occur regularly. If the authors work is to be useful, they need to explain clearly how their parameterization is to be used in the face of these nonlocalities. The immediate worry is that they are useless if there are sufficient nonlocal terms. Maybe this is too extreme a conclusion – I can’t really see through the effects of these – but it certainly needs more comment that a casual dismissal.

I recommend that the paper be returned to the authors for a full discussion of the non-analytic effects which they are excluding. Please address directly Riegert and Barvinsky-Vilkovisky actions and say how they fit into the formfactor scheme that they are using. . If the effects are being ignored, how are their results to be used? Is there a need to generalize this work to include the quantum nonlocalities.?

Requested changes

See report

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