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The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity

by Arpan Bhattacharyya, Saptaswa Ghosh, Sounak Pal

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Submission summary

Authors (as registered SciPost users): Arpan Bhattacharyya · Saptaswa Ghosh · Sounak Pal
Submission information
Preprint Link: scipost_202505_00020v1  (pdf)
Date submitted: May 9, 2025, 7:16 p.m.
Submitted by: Ghosh, Saptaswa
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

In this paper, we compute the celestial amplitude arising from higher curvature corrections to Einstein gravity, incorporating phase dressing. The inclusion of such corrections leads to effective modifications of the theory's ultraviolet (UV) behaviour. In the eikonal limit, we find that, in contrast to Einstein's gravity, where the $s$ and $t$-channel contributions cancel, these contributions remain non-vanishing in the presence of higher curvature terms. We examine the analytic structure of the resulting amplitude and derive a dispersion relation for the phase-dressed eikonal amplitude in quadratic gravity. Furthermore, we investigate the celestial conformal block expansion of the Mellin-transformed conformal shadow amplitude within the framework of celestial conformal field theory (CCFT). As a consequence, we compute the corresponding operator product expansion (OPE) coefficients using the Burchnall-Chaundy expansion. In addition, we evaluate the OPE via the Euclidean OPE inversion formula across various kinematic channels and comment on its applicability and implications. Finally, we briefly explore the Carrollian amplitude associated with the corresponding quadratic EFT.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Has been resubmitted

Reports on this Submission

Report #2 by Anonymous (Referee 2) on 2025-7-9 (Invited Report)

Report

In this paper, the authors discuss Celestial amplitudes corresponding to the eikonal resummation of scalar amplitudes interacting via gravity. They consider this in the context of quadratic gravity and then discuss several interesting features of the resulting celestial amplitude including dispersion relations, OPEs, shadowed correaltors. The paper potentially contains several interesting and useful results. However, a few crucial points require clarification before I can recommend this for publication. I list these in the attached file.

Attachment


Recommendation

Ask for major revision

  • validity: good
  • significance: good
  • originality: good
  • clarity: ok
  • formatting: excellent
  • grammar: excellent

Author:  Saptaswa Ghosh  on 2025-07-10  [id 5628]

(in reply to Report 2 on 2025-07-09)
Category:
answer to question
pointer to related literature

Dear Editor,

Please see the attached file for point-wise response to the Referee report.

Best,
Authors

Attachment:

response_ref2.pdf

Report #1 by Anonymous (Referee 1) on 2025-6-11 (Invited Report)

Report

The authors compute celestial amplitudes involving higher curvature corrections to Einstein gravity. In particular, they consider quadratic gravity shown in Eq.(3.1). As they summarize in the introduction and conclusion, the main new results are

1) Eikonal amplitudes for the quadratic EFT of gravity

2) UV and IR behaviour with the EFT corrections

3) Celestial Born amplitude with the EFT corrections and the shadow corrector associated with it. They also showed two methods of extracting the celestial OPEs

These are interesting new results of celestial amplitudes presented in a well-written manuscript.

However, as the authors have pointed out, their work is highly motivated and based on existing work in the literature. To meet the standard of Sci Post, I am willing to reconsider this paper for publication, provided the following comments and questions are addressed.

Requested changes

1) In the third paragraph of the introduction, Ref.[30] was not the first example of computing shadow correlators for celestial amplitude. Actually Ref.[20] provided the first example for four-point. I invite the authors revise the references for that sentence.

2) Above Eq.(2.3), the expression for the holomorphic conformal weight holds for the scalar case but not for the spinning case as the authors explain in Eq.(2.6). I would recommend the authors to revise the sentences above Eq.(2.3).

3) The quadratic gravity is introduced from section 3. It might be useful to discuss a bit more about the basic properties of the quadratic gravity. Including some useful references might be helpful. For example, it might be helpful to explain how the mass of the massive mode of it is related to the parameters in Eq.(3.1). And is it clear that the amplitudes computed in quadratic gravity are unitary?

4) The sentence below Eq.(3.11) is confusing. From Eq.(3.10), the Einstein gravity term is still present with the distributional nature. The EFT correction term behaves better but the entire celestial amplitude is not improved by that.

5) In Eq.(3.15), the authors computed the eikonal phase in quadratic gravity by perform Fourier transform on the modified Born amplitudes, following the same procedure in GR. It might be useful to explain why in the presence of the EFT corrections, the eikonal phase can still be computed in the same way as GR. Or are there other similar examples that existed in the literature can justify this point.

6) Although the authors presented a nice discussion on the delta function on page 11, it is not very clear how the author obtained the (e-1) factor in Eq.(3.22). I hope the authors could explain a bit more below Eq.(3.22).

7) In Eq.(4.11), the authors did not thow the contribution from GR. I am wondering if the authors had tried to compute it. If it is not doable for general conformal dimensions, one might try to take some specific limit of the conformal dimension. See, e.g. 2501.05805.

8) In Eq.(5.1), the physical meaning of n in the second line seems to be related to the number of particles. It might be helpful to clarify it.

I hope the comments and questions above might help the authors improve the manuscript.

Recommendation

Ask for minor revision

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

Author:  Saptaswa Ghosh  on 2025-06-18  [id 5581]

(in reply to Report 1 on 2025-06-11)
Category:
answer to question
pointer to related literature
suggestion for further work

Dear Editor,

Please see the attached file for point-wise response to the Referee report.

Best,
Authors

Attachment:

Response_ref1.pdf

Anonymous on 2025-06-20  [id 5583]

(in reply to Saptaswa Ghosh on 2025-06-18 [id 5581])

I thank the authors for the response. The authors have addressed the questions and concerns I had previously in their response. I would be happy to recommend the revised version for publications.

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