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This paper claims to complete the conservative scattering-angle computation for non-spinning black holes at fifth post-Minkowskian and second self-force order, using a new 'γ-3' propagator prescription to tame a novel divergence.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-03 08:36 UTC pith:E7APETSL

load-bearing objection A very large, carefully executed four-loop computation, but the final 5PM-2SF angle is only fixed by an admittedly opaque 'gamma-3' prescription — conditional, not complete. the 4 major comments →

arxiv 2601.16256 v4 pith:E7APETSL submitted 2026-01-22 hep-th gr-qchep-ph

Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order

Mathias Driesse , Gustav Uhre Jakobsen , Gustav Mogull , Christoph Nega , Jan Plefka , Benjamin Sauer , Johann Usovitsch This is my paper
classification hep-th gr-qchep-ph
keywords black hole scatteringpost-Minkowskian expansionsecond self-force orderworldline quantum field theoryK3 surfacescattering angleconservative dynamicsgravitational waves
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims to complete the conservative scattering-angle computation for non-spinning black holes at fifth post-Minkowskian (5PM) order and second self-force (2SF) order, i.e. order G^5 and quadratic in the mass ratio. Using the worldline quantum field theory formalism, it reduces the four-loop problem to a system of hundreds of master integrals and expresses the final scattering angle as a sum of 36 terms built from iterated integrals, including a K3 period. A spurious divergence at Lorentz factor γ=3 (velocity v/c=√8/3) appears in the potential region and must be cancelled by radiative memory contributions, but the standard Feynman-propagator prescription does not achieve this cancellation. The paper introduces the 'γ-3' prescription, which sets an otherwise undetermined coefficient c_M to 1, and verifies all available low-velocity post-Newtonian checks. A sympathetic reader would care because this is the last missing conservative ingredient at 5PM order, directly relevant for high-accuracy gravitational-wave models.

Core claim

The central claim is that the conservative 5PM-2SF scattering angle is θ^(5,2)_cons = Σ_{k=1}^{36} c_k(γ) f_k(γ), where the f_k are iterated integrals over kernels that include the K3 period ϖ_K3(x) and its derivative, and the c_k are explicit polynomials in γ and γv. The result is finite and agrees with the post-Newtonian expansion up to 5PN, including confirmation that the 5PN π² terms are purely potential. To achieve finiteness, the paper introduces the 'γ-3' prescription for the two memory-region boundary integrals, which determines the previously undetermined coefficient c_M and sets it to 1; this is the value used in the final result.

What carries the argument

The key object is the K3 period ϖ_K3(x), whose Picard-Fuchs operator is the Apery-like operator L_K3 = (1-34x²+x⁴)θ³ - 6x²(17-x²)θ² - ... . The period's singular point at x=3-2√2 (γ=3) creates the spurious divergence that must cancel between potential and memory regions. The computation of the memory boundary integrals I_1^(M) and I_2^(M) under the new γ-3 prescription—retarded propagators pointing toward the symmetric three-graviton vertex, averaged over causality directions—determines these integrals up to the coefficient c_M, which is set to 1. The 'γ-3' prescription is the mechanism that produces a finite, physically sensible answer.

Load-bearing premise

The load-bearing premise is the 'γ-3' prescription—evaluating the two memory-region boundary integrals with retarded propagators aimed at the middle three-graviton vertex and averaging causality directions—which the authors themselves describe as 'opaque' and possibly incomplete; if this projection misidentifies the conservative sector, the c_M=1 value and the resulting scattering angle would be wrong.

What would settle it

Compute the same 5PM-2SF impulse in the worldline formalism using only retarded propagators throughout (the fully dissipative in-in setup), extract the conservative part by subtracting the even-in-velocity dissipative contributions as prescribed by the paper's own consistency conditions, and compare with the γ-3 result; a mismatch in c_M or in the γ→3 cancellation would falsify the central claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The 5PM-2SF conservative sector is now known analytically, completing the conservative two-body scattering problem at this order when combined with existing 0SF and 1SF results.
  • All low-velocity checks against post-Newtonian theory up to 5PN are satisfied, including the conjecture that 5PN π² terms are purely potential.
  • The function space for 5PM-2SF observables includes a K3 period, not just polylogarithms, so any resummation or EFT matching must accommodate such functions.
  • The relation between the discontinuity of the scattering angle and radiated energy (Eq. (15)) can now be tested with the new result at this order.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the γ-3 prescription is right, the standard Feynman-propagator 'real and even' projection is not a valid definition of the conservative sector at 2SF order; a new definition may be needed, possibly from the unitary S-matrix operator.
  • The spurious γ=3 divergence may indicate that the potential-region expansion fails before the last stable orbit; resummation or numerical relativity comparisons near γ=3 would test whether the divergence leaves a physical imprint.
  • The undetermined coefficient c_M highlights that the normalization of the memory contribution is not fixed by finiteness alone; an independent derivation of c_M from first principles would either confirm c_M=1 or revise the scattering angle.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper reports a worldline quantum field theory (WQFT) computation of the conservative scattering angle and impulse for nonspinning black-hole scattering at fifth post-Minkowskian (5PM) order and second self-force (2SF) order. The computation involves four-loop Feynman integrals, integration-by-parts reduction of hundreds of master integrals, canonical differential equations involving Calabi-Yau and K3 geometries, and a region-by-region analysis separating potential, tail, and memory contributions. The final result is expressed as a sum of 36 basis functions with coefficient polynomials. The authors find that the standard Feynman-propagator prescription fails to produce a finite conservative result because of a spurious divergence at γ=3; they introduce a new 'γ-3' prescription for the memory boundary integrals, which sets an undetermined coefficient c_M to 1. Low-velocity checks up to 4PN are satisfied, and a 5PN O(v^0) check is quoted as confirming their result, though it relies on an unpublished communication.

Significance. If the conservative-sector ambiguity were resolved, this would be a landmark calculation: the first complete 5PM-2SF conservative dynamics, with a non-trivial function space involving K3 periods and an intricate cancellation of divergences between potential and memory regions. The technical achievements—651 diagrams, four-loop IBP reduction with ~3×10^6 core hours, canonical differential equations for large sectors, and analytic boundary integrals—are substantial and the results are deposited in Zenodo, which is commendable for reproducibility. However, the central claim of 'completing' the computation is conditional on the γ-3 prescription, whose physical motivation the authors themselves describe as opaque. The undetermined coefficient c_M enters the final observable at O(v^0) in the low-velocity expansion, and the only 5PN check that could fix it is not independently documented. These issues are load-bearing and preclude acceptance in the present form.

major comments (4)
  1. [Boundary integrals and the i0+ prescription; Eqs. (9), (13), (14)] The memory boundary integrals I_1^(M) and I_2^(M) are determined only up to a single coefficient c_M by imposing the cancellations of ε-poles and the γ=3 divergence. The γ-3 prescription is then introduced as a choice that realizes these cancellations and sets c_M=1, but the manuscript states: 'we acknowledge that the physical motivation for this prescription is opaque and may not capture all conservative effects.' Since c_M appears explicitly in the final scattering angle (Tables II and III, and Eq. (14) shows a c_M-dependent term at O(v^0) in the 5PN expansion), the headline result Eq. (13) is not unique. The structure is circular: the desired cancellations fix the memory integrals up to c_M, and the prescription is then selected because it achieves exactly those cancellations. The paper should either derive γ-3 from a first-principles definition of the conservative sector (e.g., the N
  2. [Checks; Eq. (14) and Ref. [153]] The 5PN O(v^0) check that would be sensitive to c_M relies on 'upcoming work' by Porto and Riva (Ref. [153]), an unpublished communication. This is not a verifiable check and cannot support the claim that the result is confirmed. The authors should either provide the explicit comparison data in the paper or supplementary material, or clearly mark this check as pending. Without it, the only independent verifications are up to 4PN, where c_M does not enter, leaving the central value c_M=1 untested.
  3. [Results; Eq. (15)] The unitarity-type relation connecting the discontinuity of the scattering angle to the radiated energy is stated but no verification is shown. If this relation is intended as a consistency check or as a way to constrain c_M, the verification should be reported. If it is merely a statement of a known property, its role in this paper should be clarified. As written, it is an unsubstantiated assertion in a context where an independent constraint on c_M would be highly valuable.
  4. [Conclusions vs. abstract] The abstract and conclusions assert 'we have completed the computation of the conservative impulse ... at the 5PM (G^5) order'. However, the body of the paper explains that the result depends on a 'prescription-dependent' conservative dynamics and that the γ-3 prescription 'may not capture all conservative effects.' These statements are in tension. Either the result is complete and the prescription is justified, or it is conditional and the wording should be softened accordingly. As it stands, the claim of completion is stronger than what the presented evidence supports.
minor comments (4)
  1. [Full text, near Eq. (9) and Fig. 4] The manuscript contains unremoved editorial comments: '[Gustav: I would change the way we identify these coefficients]', '[Jan: no way that would require new TABLES 2 + 3]', '[Mathias: I really think ...]', and '[Jan: Improve plot]'. These are inappropriate in a submitted paper and must be removed.
  2. [Introduction, reference list] Reference [8?–10] contains a stray question mark. Please fix the citation format.
  3. [Expansion by regions, Fig. 4 caption] The caption of Fig. 4 states that the memory plot sets c_M=1, which is fine, but the sentence 'These divergences cancel for the full result if one uses Eq. (9) irrespective of the value of c_M' is slightly confusing because the full result does depend on c_M at finite v. Clarify that the cancellation of the γ→3 divergence is c_M-independent, not the full angle.
  4. [Supplementary material, Eq. (25)] The IBP relation (25) is evaluated at γ=√2. The text says this is done 'in order to simplify the known gamma dependence'. Please state explicitly what is recovered and how the full γ dependence is reconstructed, as this is important for reproducibility.

Circularity Check

1 steps flagged

The 5PM-2SF conservative angle is not fully derived: c_M is fixed by imposing the required cancellations via the 'γ-3' prescription, whose physical motivation the authors call opaque.

specific steps
  1. self definitional [Boundary integrals and the i0+ prescription, Eqs. (8)-(9) and following paragraph; Results Eq. (13)-(14) and Tables II/III.]
    "imposing the cancellation of the γ=3 singularity along with maintaining the ε-pole cancellation between the potential and tail regions determines their results up to a single undetermined coefficient c_M ... evaluating I_1,2 with retarded propagators pointing towards the middle point provides such a prescription – that we term 'γ-3' – and leads to the value c_M = 1 ... Yet, we acknowledge that the physical motivation for this prescription is opaque and may not capture all conservative effects."

    Eq. (9) fixes the two memory boundary integrals I_1^(M), I_2^(M) only up to c_M by imposing exactly the cancellations (ε-pole and γ=3 divergence) that the final observable is required to have. The 'γ-3' prescription is then selected because it satisfies those same three conditions and sets c_M=1. The main result Eq. (13) is evaluated with c_M=1 (Tables II/III), and Eq. (14) shows the 5PN O(v^0) term depends on 64 c_M/5. Thus the headline number is not derived from the WQFT/integral calculation alone: c_M is an input chosen to make the cancellations work, and the physical justification is admitted to be 'opaque'. The divergence cancellation is therefore used both to determine the boundary data and to validate the final result, a circular fixing of the conservative sector.

full rationale

The bulk of the paper is a substantial, largely self-contained computation: IBP reduction with Kira, canonical differential equations, Calabi-Yau/K3 period analysis, and the potential-region result agree with the independent low-velocity 4PN literature and with Ref. [99] in the potential region. Those checks are genuine and do not rely on the contested prescription. The circularity is concentrated in the memory boundary data: Eq. (9) determines I^(M)_1,2 only up to c_M by imposing the cancellations that the final result must have, and then the 'γ-3' propagator prescription is chosen because it realizes those cancellations and yields c_M=1. The final scattering angle in Eq. (13), with the tables evaluated at c_M=1, therefore contains a parameter that is effectively an input rather than a prediction. Eq. (14) makes this explicit: c_M enters at O(v^0), i.e. at 5PN, so the independent 4PN checks cannot distinguish c_M, and the quoted 5PN check relies on an unpublished communication [153]. The authors themselves flag the prescription's motivation as 'opaque' and call for a clearer definition of the conservative sector, confirming that c_M is not uniquely fixed by the formalism. This is a partial but central circularity; hence score 6 rather than 0-2. There is no significant self-citation circularity: citations to the authors' own prior work concern formal machinery and lower-order results that are independently documented.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 0 invented entities

The only genuinely free parameter is c_M; the remaining assumptions are standard machinery, previous-work inputs, or the ad hoc γ-3 prescription. No new particles, forces, or dimensions are introduced.

free parameters (1)
  • c_M = 1 (γ-3 prescription)
    Undetermined by the cancellation conditions in Eq. (9); the γ-3 prescription sets it to 1. It enters the final θ^(5,2)_cons at O(1) in the low-velocity expansion, Eq. (14), and the authors state its physical motivation is opaque and may not capture all conservative effects.
axioms (5)
  • domain assumption The WQFT/EFT description of black holes as point particles with action (1) and straight-line backgrounds yields the classical 5PM impulse.
    The entire calculation assumes this worldline quantum field theory setup; it is standard in the field but not derived in this paper.
  • ad hoc to paper The 'γ-3' conservative prescription (retarded propagators pointing toward the middle three-graviton vertex, averaged with advanced propagators) selects the true conservative sector.
    Introduced because the standard Feynman i0+ prescription fails; authors acknowledge the physical motivation is opaque and 'may not capture all conservative effects' (Boundary integrals section and Conclusions).
  • domain assumption The method-of-regions split into potential/radiative scalings, keeping only an even number of radiative gravitons, gives the complete conservative contribution.
    Section 'Expansion by regions and divergences'; follows lower-order practice [31,36,46,55,95], but is a modelling assumption, especially for the novel memory region.
  • domain assumption The L_K3 operator, K3 periods, and ε-factorized canonical system from Refs. [116,118] are correct and complete.
    The paper uses the Picard-Fuchs operator Eq. (6) and the canonical basis from overlapping authors' previous work without re-deriving them here.
  • domain assumption The communicated 5PN tail result of Porto & Riva (Ref. [153], 'upcoming work') used in Eq. (14) is correct.
    The check supporting the c_M=1 rational term relies on an unpublished private communication that is not independently verifiable.

pith-pipeline@v1.3.0-alltime-deepseek · 36553 in / 15158 out tokens · 135624 ms · 2026-08-03T08:36:40.691701+00:00 · methodology

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read the original abstract

Using the worldline quantum field theory formalism, we compute conservative contributions to the scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian (5PM) and second self-force (2SF) order. This four-loop calculation involves non-planar Feynman integrals and requires advanced integration-by-parts reduction, novel differential-equation strategies, and efficient boundary-integral algorithms to solve a system of hundreds of master integrals in four integral families on high-performance computing systems. The resulting function space includes multiple polylogarithms as well as iterated integrals with a K3 period, which generate a spurious velocity divergence at $v/c=\sqrt{8}/3$, $\gamma=3$. This divergence is present in the potential region and must be canceled by contributions from the radiative memory region, while its dimensional-regularisation pole should cancel against the radiative tail region. As the standard use of Feynman propagators fails to ensure this cancellation, we instead propose a ($\gamma$-3) conservative prescription that realises both cancellations, leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied.

Figures

Figures reproduced from arXiv: 2601.16256 by Benjamin Sauer, Christoph Nega, Gustav Mogull, Gustav Uhre Jakobsen, Jan Plefka, Johann Usovitsch, Mathias Driesse.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Non-zero entries of the 321 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Active (red) gravitons that become radiative G. 3: Active gravitons that become radiative (red) iththiflttd [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The 5PM-2SF contribution to the scatterin l✓ (52) ()l d b FIG. 4: The 5PM-2SF contribution to the scattering [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

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Reference graph

Works this paper leans on

163 extracted references · 1 canonical work pages · cited by 17 Pith papers

  1. [6]

    Punturo et al.,The Einstein Telescope: A third-generation gravitational wave observatory,Class

    M. Punturo et al.,The Einstein Telescope: A third-generation gravitational wave observatory,Class. Quant. Grav.27(2010) 194002

    2010

  2. [7]

    S. W. Ballmer et al.,Snowmass2021 Cosmic Frontier White Paper: Future Gravitational-Wave Detector Facilities, inSnowmass 2021, 3, 2022,2203.08228

    Pith/arXiv arXiv 2021

  3. [8]

    Blanchet,Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries,Living Rev

    L. Blanchet,Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries,Living Rev. Rel.17(2014) 2 [1310.1528]

    Pith/arXiv arXiv 2014

  4. [9]

    R. A. Porto,The effective field theorist’s approach to gravitational dynamics,Phys. Rept.633(2016) 1 [1601.04914]

    Pith/arXiv arXiv 2016

  5. [10]

    Levi,Effective Field Theories of Post-Newtonian Gravity: A comprehensive review,Rept

    M. Levi,Effective Field Theories of Post-Newtonian Gravity: A comprehensive review,Rept. Prog. Phys.83 (2020) 075901 [1807.01699]

    Pith/arXiv arXiv 2020

  6. [11]

    D. A. Kosower, R. Monteiro and D. O’Connell,The SAGEX review on scattering amplitudes Chapter 14: Classical gravity from scattering amplitudes,J. Phys. A55(2022) 443015 [2203.13025]

    Pith/arXiv arXiv 2022

  7. [12]

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, L. Plante and P. Vanhove,The SAGEX review on scattering amplitudes Chapter 13: Post-Minkowskian expansion from scattering amplitudes,J. Phys. A55(2022) 443014 [2203.13024]

    Pith/arXiv arXiv 2022

  8. [13]

    Buonanno, M

    A. Buonanno, M. Khalil, D. O’Connell, R. Roiban, M. P. Solon and M. Zeng,Snowmass White Paper: Gravitational Waves and Scattering Amplitudes, in Snowmass 2021, 4, 2022,2204.05194

    Pith/arXiv arXiv 2021

  9. [14]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano,The gravitational eikonal: from particle, string and brane collisions to black-hole encounters, 2306.16488

    Pith/arXiv arXiv

  10. [15]

    G. U. Jakobsen,Gravitational Scattering of Compact Bodies from Worldline Quantum Field Theory, phd thesis, Humboldt-University Berlin, 8, 2023

    2023

  11. [16]

    Y. Mino, M. Sasaki and T. Tanaka,Gravitational radiation reaction to a particle motion,Phys. Rev. D 55(1997) 3457 [gr-qc/9606018]

    Pith/arXiv arXiv 1997

  12. [17]

    Poisson, A

    E. Poisson, A. Pound and I. Vega,The Motion of point particles in curved spacetime,Living Rev. Rel.14 (2011) 7 [1102.0529]

    Pith/arXiv arXiv 2011

  13. [18]

    Barack and A

    L. Barack and A. Pound,Self-force and radiation reaction in general relativity,Rept. Prog. Phys.82 (2019) 016904 [1805.10385]

    Pith/arXiv arXiv 2019

  14. [19]

    S. E. Gralla and K. Lobo,Self-force effects in post-Minkowskian scattering,Class. Quant. Grav.39 (2022) 095001 [2110.08681]

    Pith/arXiv arXiv 2022

  15. [20]

    Pretorius,Evolution of binary black hole spacetimes, Phys

    F. Pretorius,Evolution of binary black hole spacetimes, Phys. Rev. Lett.95(2005) 121101 [gr-qc/0507014]

    Pith/arXiv arXiv 2005

  16. [21]

    Boyle et al.,The SXS Collaboration catalog of binary black hole simulations,Class

    M. Boyle et al.,The SXS Collaboration catalog of binary black hole simulations,Class. Quant. Grav.36 (2019) 195006 [1904.04831]

    Pith/arXiv arXiv 2019

  17. [22]

    Damour, F

    T. Damour, F. Guercilena, I. Hinder, S. Hopper, A. Nagar and L. Rezzolla,Strong-Field Scattering of Two Black Holes: Numerics Versus Analytics,Phys. Rev. D89(2014) 081503 [1402.7307]

    Pith/arXiv arXiv 2014

  18. [23]

    Driesse, G

    M. Driesse, G. U. Jakobsen, A. Klemm, G. Mogull, C. Nega, J. Plefka et al.,Emergence of Calabi–Yau manifolds in high-precision black-hole scattering, Nature641(2025) 603 [2411.11846]

    Pith/arXiv arXiv 2025

  19. [24]

    S. J. Kovacs and K. S. Thorne,The Generation of Gravitational Waves. 4. Bremsstrahlung,Astrophys. J. 224(1978) 62

    1978

  20. [25]

    Westpfahl and M

    K. Westpfahl and M. Goller,Gravitational scattering of two relativistic particles in postlinear approximation, Lett. Nuovo Cim.26(1979) 573

    1979

  21. [26]

    L. Bel, T. Damour, N. Deruelle, J. Ibanez and J. Martin,Poincar´ e-invariant gravitational field and equations of motion of two pointlike objects: The postlinear approximation of general relativity,Gen. Rel. Grav.13(1981) 963

    1981

  22. [27]

    Damour,High-energy gravitational scattering and the general relativistic two-body problem,Phys

    T. Damour,High-energy gravitational scattering and the general relativistic two-body problem,Phys. Rev. D 97(2018) 044038 [1710.10599]

    Pith/arXiv arXiv 2018

  23. [28]

    Hopper, A

    S. Hopper, A. Nagar and P. Rettegno,Strong-field scattering of two spinning black holes: Numerics versus analytics,Phys. Rev. D107(2023) 124034 [2204.10299]

    Pith/arXiv arXiv 2023

  24. [29]

    W. D. Goldberger and I. Z. Rothstein,An Effective field theory of gravity for extended objects,Phys. Rev. D73(2006) 104029 [hep-th/0409156]

    Pith/arXiv arXiv 2006

  25. [30]

    K¨ alin and R

    G. K¨ alin and R. A. Porto,Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics, JHEP11(2020) 106 [2006.01184]

    Pith/arXiv arXiv 2020

  26. [31]

    K¨ alin, Z

    G. K¨ alin, Z. Liu and R. A. Porto,Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach,Phys. Rev. Lett.125(2020) 261103 [2007.04977]

    Pith/arXiv arXiv 2020

  27. [32]

    K¨ alin, Z

    G. K¨ alin, Z. Liu and R. A. Porto,Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order,Phys. Rev. D102(2020) 124025 [2008.06047]

    Pith/arXiv arXiv 2020

  28. [33]

    Mogull, J

    G. Mogull, J. Plefka and J. Steinhoff,Classical black hole scattering from a worldline quantum field theory, JHEP02(2021) 048 [2010.02865]

    Pith/arXiv arXiv 2021

  29. [34]

    G. U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory,Phys. Rev. Lett. 126(2021) 201103 [2101.12688]

    Pith/arXiv arXiv 2021

  30. [35]

    Dlapa, G

    C. Dlapa, G. K¨ alin, Z. Liu and R. A. Porto,Dynamics of binary systems to fourth Post-Minkowskian order from the effective field theory approach,Phys. Lett. B 14 831(2022) 137203 [2106.08276]

    Pith/arXiv arXiv 2022

  31. [36]

    Dlapa, G

    C. Dlapa, G. K¨ alin, Z. Liu and R. A. Porto, Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-Eccentricity Expansion,Phys. Rev. Lett.128(2022) 161104 [2112.11296]

    Pith/arXiv arXiv 2022

  32. [37]

    Mougiakakos, M

    S. Mougiakakos, M. M. Riva and F. Vernizzi, Gravitational Bremsstrahlung in the post-Minkowskian effective field theory,Phys. Rev. D104(2021) 024041 [2102.08339]

    Pith/arXiv arXiv 2021

  33. [38]

    M. M. Riva and F. Vernizzi,Radiated momentum in the post-Minkowskian worldline approach via reverse unitarity,JHEP11(2021) 228 [2110.10140]

    Pith/arXiv arXiv 2021

  34. [39]

    Dlapa, G

    C. Dlapa, G. K¨ alin, Z. Liu, J. Neef and R. A. Porto, Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order,Phys. Rev. Lett.130(2023) 101401 [2210.05541]

    Pith/arXiv arXiv 2023

  35. [40]

    Dlapa, G

    C. Dlapa, G. K¨ alin, Z. Liu and R. A. Porto, Bootstrapping the relativistic two-body problem,JHEP 08(2023) 109 [2304.01275]

    Pith/arXiv arXiv 2023

  36. [41]

    Z. Liu, R. A. Porto and Z. Yang,Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics,JHEP06(2021) 012 [2102.10059]

    Pith/arXiv arXiv 2021

  37. [42]

    Mougiakakos, M

    S. Mougiakakos, M. M. Riva and F. Vernizzi, Gravitational Bremsstrahlung with Tidal Effects in the Post-Minkowskian Expansion,Phys. Rev. Lett.129 (2022) 121101 [2204.06556]

    Pith/arXiv arXiv 2022

  38. [43]

    M. M. Riva, F. Vernizzi and L. K. Wong,Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion,Phys. Rev. D106(2022) 044013 [2205.15295]

    Pith/arXiv arXiv 2022

  39. [44]

    G. U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies,Phys. Rev. Lett. 128(2022) 011101 [2106.10256]

    Pith/arXiv arXiv 2022

  40. [45]

    G. U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, SUSY in the sky with gravitons,JHEP01(2022) 027 [2109.04465]

    Pith/arXiv arXiv 2022

  41. [46]

    G. U. Jakobsen and G. Mogull,Conservative and Radiative Dynamics of Spinning Bodies at Third Post-Minkowskian Order Using Worldline Quantum Field Theory,Phys. Rev. Lett.128(2022) 141102 [2201.07778]

    Pith/arXiv arXiv 2022

  42. [47]

    G. U. Jakobsen and G. Mogull,Linear response, Hamiltonian, and radiative spinning two-body dynamics,Phys. Rev. D107(2023) 044033 [2210.06451]

    Pith/arXiv arXiv 2023

  43. [48]

    G. U. Jakobsen, G. Mogull, J. Plefka and B. Sauer,All things retarded: radiation-reaction in worldline quantum field theory,JHEP10(2022) 128 [2207.00569]

    Pith/arXiv arXiv 2022

  44. [49]

    Shi and J

    C. Shi and J. Plefka,Classical double copy of worldline quantum field theory,Phys. Rev. D105(2022) 026007 [2109.10345]

    Pith/arXiv arXiv 2022

  45. [50]

    Bastianelli, F

    F. Bastianelli, F. Comberiati and L. de la Cruz,Light bending from eikonal in worldline quantum field theory, JHEP02(2022) 209 [2112.05013]

    Pith/arXiv arXiv 2022

  46. [51]

    Comberiati and C

    F. Comberiati and C. Shi,Classical Double Copy of Spinning Worldline Quantum Field Theory,JHEP04 (2023) 008 [2212.13855]

    Pith/arXiv arXiv 2023

  47. [52]

    Wang,Binary dynamics from worldline QFT for scalar QED,Phys

    T. Wang,Binary dynamics from worldline QFT for scalar QED,Phys. Rev. D107(2023) 085011 [2205.15753]

    Pith/arXiv arXiv 2023

  48. [53]

    Ben-Shahar,Scattering of spinning compact objects from a worldline EFT,JHEP03(2024) 108 [2311.01430]

    M. Ben-Shahar,Scattering of spinning compact objects from a worldline EFT,JHEP03(2024) 108 [2311.01430]

    Pith/arXiv arXiv 2024

  49. [54]

    Bhattacharyya, D

    A. Bhattacharyya, D. Ghosh, S. Ghosh and S. Pal, Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory,JHEP04(2024) 015 [2401.05492]

    Pith/arXiv arXiv 2024

  50. [55]

    G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer and Y. Xu,Conservative Scattering of Spinning Black Holes at Fourth Post-Minkowskian Order,Phys. Rev. Lett.131(2023) 151401 [2306.01714]

    Pith/arXiv arXiv 2023

  51. [56]

    G. U. Jakobsen, G. Mogull, J. Plefka and B. Sauer, Dissipative Scattering of Spinning Black Holes at Fourth Post-Minkowskian Order,Phys. Rev. Lett.131 (2023) 241402 [2308.11514]

    Pith/arXiv arXiv 2023

  52. [57]

    G. U. Jakobsen, G. Mogull, J. Plefka and B. Sauer, Tidal effects and renormalization at fourth post-Minkowskian order,Phys. Rev. D109(2024) L041504 [2312.00719]

    Pith/arXiv arXiv 2024

  53. [58]

    Neill and I

    D. Neill and I. Z. Rothstein,Classical Space-Times from the S Matrix,Nucl. Phys. B877(2013) 177 [1304.7263]

    Pith/arXiv arXiv 2013

  54. [59]

    A. Luna, I. Nicholson, D. O’Connell and C. D. White, Inelastic Black Hole Scattering from Charged Scalar Amplitudes,JHEP03(2018) 044 [1711.03901]

    Pith/arXiv arXiv 2018

  55. [60]

    D. A. Kosower, B. Maybee and D. O’Connell, Amplitudes, Observables, and Classical Scattering, JHEP02(2019) 137 [1811.10950]

    Pith/arXiv arXiv 2019

  56. [61]

    Cristofoli, R

    A. Cristofoli, R. Gonzo, D. A. Kosower and D. O’Connell,Waveforms from amplitudes,Phys. Rev. D106(2022) 056007 [2107.10193]

    Pith/arXiv arXiv 2022

  57. [62]

    N. E. J. Bjerrum-Bohr, J. F. Donoghue and P. Vanhove,On-shell Techniques and Universal Results in Quantum Gravity,JHEP02(2014) 111 [1309.0804]

    Pith/arXiv arXiv 2014

  58. [63]

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, G. Festuccia, L. Plant´ e and P. Vanhove,General Relativity from Scattering Amplitudes,Phys. Rev. Lett.121(2018) 171601 [1806.04920]

    Pith/arXiv arXiv 2018

  59. [64]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon and M. Zeng,Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order,Phys. Rev. Lett.122(2019) 201603 [1901.04424]

    Pith/arXiv arXiv 2019

  60. [65]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon and M. Zeng,Black Hole Binary Dynamics from the Double Copy and Effective Theory,JHEP10 (2019) 206 [1908.01493]

    Pith/arXiv arXiv 2019

  61. [66]

    N. E. J. Bjerrum-Bohr, L. Plant´ e and P. Vanhove, Post-Minkowskian radial action from soft limits and velocity cuts,JHEP03(2022) 071 [2111.02976]

    Pith/arXiv arXiv 2022

  62. [67]

    Cheung and M

    C. Cheung and M. P. Solon,Classical gravitational scattering atO(G 3) from Feynman diagrams,JHEP 06(2020) 144 [2003.08351]

    Pith/arXiv arXiv 2020

  63. [68]

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, L. Plant´ e and P. Vanhove,The amplitude for classical gravitational scattering at third Post-Minkowskian order,JHEP08 (2021) 172 [2105.05218]

    Pith/arXiv arXiv 2021

  64. [69]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano,Universality of ultra-relativistic gravitational scattering,Phys. Lett. B811(2020) 135924 [2008.12743]

    Pith/arXiv arXiv 2020

  65. [70]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo and 15 G. Veneziano,The eikonal approach to gravitational scattering and radiation atO(G 3),JHEP07(2021) 169 [2104.03256]

    Pith/arXiv arXiv 2021

  66. [71]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano,Radiation Reaction from Soft Theorems, Phys. Lett. B818(2021) 136379 [2101.05772]

    Pith/arXiv arXiv 2021

  67. [72]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano,Classical gravitational observables from the Eikonal operator,Phys. Lett. B843(2023) 138049 [2210.12118]

    Pith/arXiv arXiv 2023

  68. [73]

    Heissenberg,Angular Momentum Loss due to Tidal Effects in the Post-Minkowskian Expansion,Phys

    C. Heissenberg,Angular Momentum Loss due to Tidal Effects in the Post-Minkowskian Expansion,Phys. Rev. Lett.131(2023) 011603 [2210.15689]

    Pith/arXiv arXiv 2023

  69. [74]

    Damour,Radiative contribution to classical gravitational scattering at the third order inG,Phys

    T. Damour,Radiative contribution to classical gravitational scattering at the third order inG,Phys. Rev. D102(2020) 124008 [2010.01641]

    Pith/arXiv arXiv 2020

  70. [75]

    Herrmann, J

    E. Herrmann, J. Parra-Martinez, M. S. Ruf and M. Zeng,Radiative classical gravitational observables atO(G 3) from scattering amplitudes,JHEP10(2021) 148 [2104.03957]

    Pith/arXiv arXiv 2021

  71. [76]

    P. H. Damgaard, K. Haddad and A. Helset,Heavy Black Hole Effective Theory,JHEP11(2019) 070 [1908.10308]

    Pith/arXiv arXiv 2019

  72. [77]

    P. H. Damgaard, L. Plante and P. Vanhove,On an exponential representation of the gravitational S-matrix,JHEP11(2021) 213 [2107.12891]

    Pith/arXiv arXiv 2021

  73. [78]

    P. H. Damgaard, E. R. Hansen, L. Plant´ e and P. Vanhove,The relation between KMOC and worldline formalisms for classical gravity,JHEP09 (2023) 059 [2306.11454]

    Pith/arXiv arXiv 2023

  74. [79]

    Aoude, K

    R. Aoude, K. Haddad and A. Helset,On-shell heavy particle effective theories,JHEP05(2020) 051 [2001.09164]

    Pith/arXiv arXiv 2020

  75. [80]

    Accettulli Huber, A

    M. Accettulli Huber, A. Brandhuber, S. De Angelis and G. Travaglini,From amplitudes to gravitational radiation with cubic interactions and tidal effects, Phys. Rev. D103(2021) 045015 [2012.06548]

    Pith/arXiv arXiv 2021

  76. [81]

    Brandhuber, G

    A. Brandhuber, G. Chen, G. Travaglini and C. Wen, Classical gravitational scattering from a gauge-invariant double copy,JHEP10(2021) 118 [2108.04216]

    Pith/arXiv arXiv 2021

  77. [82]

    Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon et al.,Scattering Amplitudes and Conservative Binary Dynamics atO(G 4),Phys. Rev. Lett.126(2021) 171601 [2101.07254]

    Pith/arXiv arXiv 2021

  78. [83]

    Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon et al.,Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G4),Phys. Rev. Lett.128(2022) 161103 [2112.10750]

    Pith/arXiv arXiv 2022

  79. [84]

    Z. Bern, D. Kosmopoulos, A. Luna, R. Roiban and F. Teng,Binary Dynamics through the Fifth Power of Spin at O(G2),Phys. Rev. Lett.130(2023) 201402 [2203.06202]

    Pith/arXiv arXiv 2023

  80. [85]

    Z. Bern, D. Kosmopoulos, A. Luna, R. Roiban, T. Scheopner, F. Teng et al.,Quantum field theory, worldline theory, and spin magnitude change in orbital evolution,Phys. Rev. D109(2024) 045011 [2308.14176]

    Pith/arXiv arXiv 2024

Showing first 80 references.