pith. sign in

arxiv: 2605.18544 · v1 · pith:TF6OV52Xnew · submitted 2026-05-18 · ✦ hep-th · gr-qc· hep-ph

The Classical Gravitational Impulse at High Energies

Michael Saavedra This is my paper

Pith reviewed 2026-05-20 09:24 UTC · model grok-4.3

classification ✦ hep-th gr-qchep-ph
keywords gravitational impulseultrarelativistic limitpost-Minkowski expansionscattering amplitudesKMOC formulahigh-energy resummationclassical gravity
0
0 comments X

The pith

Resumming high-energy scattering amplitudes recovers the all-order classical gravitational impulse for ultrarelativistic particles.

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

The paper shows that four- and five-point amplitudes computed in the small-mass regime where momentum transfer is of order mass squared allow resummation of all large corrections proportional to Newton's constant times center-of-mass energy squared. Applying the KMOC formula to these resummed amplitudes and then taking the large-mass limit produces the classical impulse result at high energies to a fixed order in the mass expansion. This matches existing post-Minkowski results and extends the prediction of the leading high-energy behavior to the eleventh order in that expansion. A reader would care because it offers a way to access non-perturbative classical gravity effects from quantum field theory calculations in the extreme high-energy regime relevant to black hole scattering.

Core claim

We compute the gravitational impulse for two classical massive scalars in the ultrarelativistic limit to all orders in Newton's constant G_N at fixed G_N s/m b to O(m^4/s^2). By computing the 4 and 5-point scattering amplitudes in the small-mass regime of -t∼m², we are able to resum all large G_N s corrections. Applying the KMOC formula for the impulse and taking the large mass limit, we recover the classical result at high energies. This resummation agrees with known results in the post-Minkowski expansion, and in the massless limit recovers previous results for the radiated energy. The resummed amplitude predicts the leading high-energy behavior of the PM expansion to eleventh post-Minkowk

What carries the argument

Resummation of large G_N s corrections via 4- and 5-point amplitudes in the -t ~ m² regime, then KMOC formula and large mass limit

Load-bearing premise

The KMOC formula can be applied directly to the resummed amplitudes from the small-mass regime without missing contributions beyond O(m^4/s²) after taking the large-mass limit.

What would settle it

An independent computation of the gravitational impulse or the eleventh-order post-Minkowski coefficient in the high-energy limit that differs from the prediction obtained via this resummation.

Figures

Figures reproduced from arXiv: 2605.18544 by Michael Saavedra.

Figure 1
Figure 1. Figure 1: FIG. 1: Web of kinematic limits. The high-energy limit of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Total classically radiated energy at large boosts, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: To perform the computation, we Fourier trans [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Diagrams for the 4 and 5 point amplitudes in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

We compute the gravitational impulse for two classical massive scalars in the ultrarelativistic limit to all orders in Newton's constant $G_N$ at fixed $G_N s/m b$ to $O(m^4/s^2)$. By computing the 4 and 5-point scattering amplitudes in the small-mass regime of $-t\sim m^2$, we are able to resum all large $G_N s$ corrections. Applying the KMOC formula for the impulse and taking the large mass limit, we recover the classical result at high energies. This resummation is in complete agreement with known results in the post-Minkowski expansion, and in the massless limit we recover previous results for the radiated energy. We use this resummed amplitude to predict the leading high-energy behavior of the PM expansion to eleventh post-Minkowski order.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper computes the gravitational impulse for two classical massive scalars in the ultrarelativistic limit to all orders in G_N at fixed G_N s/(m b) up to O(m^4/s²). It achieves this by evaluating 4- and 5-point scattering amplitudes in the small-mass regime -t ∼ m², resumming all large G_N s corrections there, applying the KMOC impulse formula, and finally taking the large-mass limit. The resulting resummed amplitude agrees with known post-Minkowski results where they can be checked and is used to predict the leading high-energy behavior of the PM expansion through eleventh order; the massless limit recovers prior results for radiated energy.

Significance. If the resummation and subsequent limit interchange are valid without omissions, the work supplies a concrete route to high-order PM coefficients at high energies and demonstrates consistency with existing lower-order results. This would be a useful addition to the classical-gravity literature, particularly for organizing the high-energy expansion of the impulse.

major comments (1)
  1. [Abstract and KMOC/large-mass-limit section] The central procedure—resumming amplitudes in the regime -t ∼ m², applying KMOC, then taking m → ∞—requires an explicit demonstration that no terms power-suppressed inside the small-mass regime become O(m^4/s²) after the limit and are therefore missed. The abstract and the section describing the KMOC application and large-mass limit state agreement with known PM results up to accessible orders, but do not exhibit an error estimate or cross-check that rules out such hidden contributions at the precision needed for the eleventh-PM prediction.
minor comments (2)
  1. Clarify the precise definition of the fixed combination G_N s/(m b) and its relation to the impact parameter throughout the resummation.
  2. Add a short table or explicit list of the PM orders against which the resummed result has been checked, including the numerical or analytic agreement achieved.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment below and indicate the revisions we will implement.

read point-by-point responses

  1. Referee: [Abstract and KMOC/large-mass-limit section] The central procedure—resumming amplitudes in the regime -t ∼ m², applying KMOC, then taking m → ∞—requires an explicit demonstration that no terms power-suppressed inside the small-mass regime become O(m^4/s²) after the limit and are therefore missed. The abstract and the section describing the KMOC application and large-mass limit state agreement with known PM results up to accessible orders, but do not exhibit an error estimate or cross-check that rules out such hidden contributions at the precision needed for the eleventh-PM prediction.

    Authors: We appreciate the referee's emphasis on rigorously justifying the interchange of limits. The amplitudes are computed in the small-mass regime -t ∼ m² while retaining all contributions not suppressed by positive powers of m²/s at fixed G_N s/(m b). When the KMOC formula is applied and the large-mass limit is subsequently taken, any power-suppressed terms in the small-mass expansion contribute only beyond O(m^4/s²) to the impulse due to the scaling with s and m. The complete agreement with all available post-Minkowski results up to the orders where direct comparison is possible provides a non-trivial consistency check on this power counting. We acknowledge that an explicit error estimate would strengthen the presentation of the eleventh-PM prediction. We will revise the relevant section to include a dedicated discussion of the power counting that demonstrates no relevant terms are missed at the stated precision. revision: yes

Circularity Check

0 steps flagged

Derivation from amplitude computations is self-contained with no circular reductions

full rationale

The paper computes 4- and 5-point scattering amplitudes explicitly in the small-mass regime -t ~ m², resums the large G_N s corrections there, applies the KMOC impulse formula, and only afterward takes the large-mass limit to recover the classical high-energy result. This chain begins from independent amplitude calculations rather than from the target impulse or PM coefficients. The resulting resummed expression is checked for agreement with known post-Minkowski results up to accessible orders and is used to extrapolate the leading high-energy behavior at 11 PM; the extrapolation is an output of the resummation, not a fitted input renamed as a prediction. No equation or step is shown to equal its own input by construction, and no load-bearing premise rests solely on a self-citation whose content is itself unverified. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions from scattering-amplitude methods and the applicability of the KMOC formula in the stated kinematic regime; no free parameters or invented entities are indicated in the abstract.

axioms (2)
  • domain assumption The KMOC formula extracts the classical impulse from the resummed scattering amplitudes after the large-mass limit.
    Invoked explicitly when applying the KMOC formula to obtain the impulse.
  • domain assumption The small-mass regime -t ∼ m² captures all relevant large G_N s corrections up to O(m^4/s²).
    Used to justify computing 4- and 5-point amplitudes for the resummation.

pith-pipeline@v0.9.0 · 5660 in / 1457 out tokens · 37104 ms · 2026-05-20T09:24:50.968889+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

78 extracted references · 78 canonical work pages · 34 internal anchors

  1. [1]

    dual velocity

    The radiated momentum may be computed from the impulse via momentum conservation: Rµ =−∆p µ 1 −∆p µ 2 .(4) The system is symmetric under exchange of the projec- tiles, so ∆p µ 2 may then be obtained from ∆p µ 1 under the exchange 1↔2,b→ −bandn↔¯n. Within the EFT framework we are working in, the sum over states implicitly contains a sum over modes, which m...

    work page 2048

  2. [2]

    B. P. Abbottet al.(LIGO Scientific, Virgo), GWTC- 1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Phys. Rev. X9, 031040 (2019), arXiv:1811.12907 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  3. [3]

    GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run

    R. Abbottet al.(LIGO Scientific, Virgo), GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run, Phys. Rev. X11, 021053 (2021), arXiv:2010.14527 [gr- qc]. 9

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  4. [4]

    GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run

    R. Abbottet al.(KAGRA, VIRGO, LIGO Scien- tific), GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run, Phys. Rev. X13, 041039 (2023), arXiv:2111.03606 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  5. [5]

    Droste, Verslagen der Afdeeling Natuurkunde van de Koninklijke Akademie van Wetenschappen19, 447 (1916)

    J. Droste, Verslagen der Afdeeling Natuurkunde van de Koninklijke Akademie van Wetenschappen19, 447 (1916)

    work page 1916

  6. [6]

    Lorentz and J

    H. Lorentz and J. Droste, Verslagen der Afdeeling Natu- urkunde van de Koninklijke Akademie van Wetenschap- pen26, 392 (1917)

    work page 1917

  7. [7]

    Einstein, L

    A. Einstein, L. Infeld, and B. Hoffmann, The gravita- tional equations and the problem of motion, Annals of Mathematics39, 65 (1938)

    work page 1938

  8. [8]

    T. Ohta, H. Okamura, T. Kimura, and K. Hiida, Physically acceptable solution of einstein’s equation for many-body system, Progress of Theoretical Physics 50, 492 (1973), https://academic.oup.com/ptp/article- pdf/50/2/492/5228680/50-2-492.pdf

    work page 1973

  9. [9]

    Post-Newtonian Theory for Gravitational Waves

    L. Blanchet, Post-Newtonian Theory for Gravitational Waves, Living Rev. Rel.17, 2 (2014), arXiv:1310.1528 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  10. [10]

    Classical Space-Times from the S Matrix

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

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  11. [11]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  12. [12]

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

    T. Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys. Rev. D97, 044038 (2018), arXiv:1710.10599 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  13. [13]

    From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion

    C. Cheung, I. Z. Rothstein, and M. P. Solon, From Scat- tering Amplitudes to Classical Potentials in the Post- Minkowskian Expansion, Phys. Rev. Lett.121, 251101 (2018), arXiv:1808.02489 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  14. [14]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Scattering amplitudes and the con- servative hamiltonian for binary systems at third post- minkowskian order, Phys. Rev. Lett.122, 201603 (2019), arXiv:1901.04424 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  15. [15]

    & Porto, R

    G. K¨ alin and R. A. Porto, Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics, JHEP 11, 106, arXiv:2006.01184 [hep-th]

    work page arXiv 2006

  16. [16]

    & Steinhoff, J

    G. Mogull, J. Plefka, and J. Steinhoff, Classical black hole scattering from a worldline quantum field theory, JHEP 02, 048, arXiv:2010.02865 [hep-th]

    work page arXiv 2010

  17. [17]

    Y. Mino, M. Sasaki, and T. Tanaka, Gravitational radia- tion reaction to a particle motion, Phys. Rev. D55, 3457 (1997), arXiv:gr-qc/9606018

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  18. [18]

    T. C. Quinn and R. M. Wald, An Axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved space-time, Phys. Rev. D56, 3381 (1997), arXiv:gr-qc/9610053

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  19. [19]

    The motion of point particles in curved spacetime

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

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  20. [20]

    Self-force and radiation reaction in general relativity

    L. Barack and A. Pound, Self-force and radiation reac- tion in general relativity, Rept. Prog. Phys.82, 016904 (2019), arXiv:1805.10385 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  21. [21]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  22. [22]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  23. [23]

    D. Bini, T. Damour, and A. Geralico, Sixth post- Newtonian local-in-time dynamics of binary systems, Phys. Rev. D102, 024061 (2020), arXiv:2004.05407 [gr- qc]

    work page arXiv 2020

  24. [24]

    D. Bini, T. Damour, and A. Geralico, Sixth post- Newtonian nonlocal-in-time dynamics of binary systems, Phys. Rev. D102, 084047 (2020), arXiv:2007.11239 [gr- qc]

    work page arXiv 2020

  25. [25]

    Brunello, M

    G. Brunello, M. K. Mandal, P. Mastrolia, R. Patil, M. Pe- gorin, J. Ronca, S. Smith, J. Steinhoff, and W. J. Tor- res Bobadilla, Six-loop gravitational interactions at the sixth post-Newtonian order, (2025), arXiv:2512.19498 [hep-th]

    work page arXiv 2025

  26. [26]

    Bl¨ umlein, A

    J. Bl¨ umlein, A. Maier, P. Marquard, and G. Sch¨ afer, The 6th post-Newtonian potential terms atO(G 4 N), Phys. Lett. B816, 136260 (2021), arXiv:2101.08630 [gr-qc]

    work page arXiv 2021

  27. [27]

    Emergence of Calabi-Yau manifolds in high-precision black hole scattering

    M. Driesse, G. U. Jakobsen, A. Klemm, G. Mogull, C. Nega, J. Plefka, B. Sauer, and J. Usovitsch, Emergence of Calabi–Yau manifolds in high-precision black-hole scattering, Nature641, 603 (2025), arXiv:2411.11846 [hep-th]

    work page Pith review arXiv 2025

  28. [28]

    Z. Bern, E. Herrmann, R. Roiban, M. S. Ruf, A. V. Smirnov, S. Smith, and M. Zeng, Scattering Ampli- tudes and Conservative Binary Dynamics atO(G 5) without Self-Force Truncation, arXiv preprint (2025), arXiv:2512.23654 [hep-th]

    work page arXiv 2025

  29. [29]

    Driesse, G

    M. Driesse, G. U. Jakobsen, G. Mogull, C. Nega, J. Ple- fka, B. Sauer, and J. Usovitsch, Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self- Force Order, (2026), arXiv:2601.16256 [hep-th]

    work page arXiv 2026

  30. [30]

    Herrmann, J

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

    work page arXiv

  31. [31]

    & Porto, R

    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, 101401 (2023), arXiv:2210.05541 [hep-th]

    work page arXiv 2023

  32. [32]

    P. D. D’Eath, High Speed Black Hole Encounters and Gravitational Radiation, Phys. Rev. D18, 990 (1978)

    work page 1978

  33. [33]

    S. J. Kovacs and K. S. Thorne, The Generation of Grav- itational Waves. 3. Derivation of Bremsstrahlung Formu- las, Astrophys. J.217, 252 (1977)

    work page 1977

  34. [34]

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

    work page 1978

  35. [35]

    I. Z. Rothstein and M. Saavedra, A Systematic La- grangian Formulation for Quantum and Classical Gravity at High Energies, (2024), arXiv:2412.04428 [hep-th]

    work page arXiv 2024

  36. [36]

    C. W. Bauer, S. Fleming, and M. E. Luke, Summing Sudakov logarithms inB→X sγin effective field theory., Phys. Rev. D63, 014006 (2000), arXiv:hep-ph/0005275

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  37. [37]

    C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, An Effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D63, 114020 (2001), arXiv:hep-ph/0011336

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  38. [38]

    C. W. Bauer, D. Pirjol, and I. W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D65, 054022 (2002), arXiv:hep-ph/0109045

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  39. [39]

    Soft-collinear gravity

    M. Beneke and G. Kirilin, Soft-collinear gravity, JHEP 09, 066, arXiv:1207.4926 [hep-ph]. 10

    work page internal anchor Pith review Pith/arXiv arXiv

  40. [40]

    Soft collinear effective theory for gravity

    T. Okui and A. Yunesi, Soft collinear effective the- ory for gravity, Phys. Rev. D97, 066011 (2018), arXiv:1710.07685 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  41. [41]

    Beneke, P

    M. Beneke, P. Hager, and R. Szafron, Soft-collinear grav- ity beyond the leading power, JHEP03, 080, [Erratum: JHEP 04, 141 (2024)], arXiv:2112.04983 [hep-ph]

    work page arXiv 2024

  42. [42]

    Beneke, P

    M. Beneke, P. Hager, and D. Schwienbacher, Soft- collinear gravity with fermionic matter, JHEP03, 076, arXiv:2212.02525 [hep-ph]

    work page arXiv

  43. [43]

    Beneke, P

    M. Beneke, P. Hager, and R. Szafron, Soft-Collinear Gravity and Soft Theorems (2023) arXiv:2210.09336 [hep-th]

    work page arXiv 2023

  44. [44]

    I. Z. Rothstein and I. W. Stewart, An Effective Field The- ory for Forward Scattering and Factorization Violation, JHEP08, 025, arXiv:1601.04695 [hep-ph]

    work page arXiv

  45. [45]

    A. Gao, I. Moult, S. Raman, G. Ridgway, and I. W. Stew- art, A collinear perspective on the Regge limit, JHEP05, 328, arXiv:2401.00931 [hep-ph]

    work page arXiv

  46. [46]

    Amati, M

    D. Amati, M. Ciafaloni, and G. Veneziano, Higher Or- der Gravitational Deflection and Soft Bremsstrahlung in Planckian Energy Superstring Collisions, Nucl. Phys. B 347, 550 (1990)

    work page 1990

  47. [47]

    Alessio, V

    F. Alessio, V. Del Duca, R. Gonzo, E. Rosi, I. Z. Roth- stein, and M. Saavedra, Analytic structure of the high- energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms, (2025), arXiv:2511.11457 [hep-th]

    work page internal anchor Pith review arXiv 2025

  48. [48]

    Alessio, V

    F. Alessio, V. Del Duca, R. Gonzo, and E. Rosi, Gravita- tional amplitudes in the Regge limit: waveforms, shock waves and unitarity cuts, (2026), arXiv:2601.21687 [hep- th]

    work page arXiv 2026

  49. [49]

    Gravitational Radiation from Massless Particle Collisions

    A. Gruzinov and G. Veneziano, Gravitational Radiation from Massless Particle Collisions, Class. Quant. Grav. 33, 125012 (2016), arXiv:1409.4555 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  50. [50]

    Unified limiting form of graviton radiation at extreme energies

    M. Ciafaloni, D. Colferai, F. Coradeschi, and G. Veneziano, Unified limiting form of graviton ra- diation at extreme energies, Phys. Rev. D93, 044052 (2016), arXiv:1512.00281 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  51. [51]

    Infrared features of gravitational scattering and radiation in the eikonal approach

    M. Ciafaloni, D. Colferai, and G. Veneziano, Infrared features of gravitational scattering and radiation in the eikonal approach, Phys. Rev. D99, 066008 (2019), arXiv:1812.08137 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  52. [52]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, The eikonal operator at arbitrary ve- locities I: the soft-radiation limit, JHEP07, 039, arXiv:2204.02378 [hep-th]

    work page arXiv

  53. [53]

    Alessio, P

    F. Alessio, P. Di Vecchia, and C. Heissenberg, Loga- rithmic soft theorems and soft spectra, JHEP11, 124, arXiv:2407.04128 [hep-th]

    work page arXiv

  54. [54]

    C. R. Galley and R. A. Porto, Gravitational self-force in the ultra-relativistic limit: the ”large-N” expansion, JHEP11, 096, arXiv:1302.4486 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv

  55. [55]

    A. K. Leibovich, Z. Ligeti, and M. B. Wise, Comment on Quark Masses in SCET, Phys. Lett. B564, 231 (2003), arXiv:hep-ph/0303099

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  56. [56]

    I. Z. Rothstein, Factorization, power corrections, and the pion form-factor, Phys. Rev. D70, 054024 (2004), arXiv:hep-ph/0301240

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  57. [57]

    Saavedra, Forward Scattering of Massive States from Effective Field Theory, To appear

    M. Saavedra, Forward Scattering of Massive States from Effective Field Theory, To appear

    work page

  58. [58]

    Fleming, A

    S. Fleming, A. H. Hoang, S. Mantry, and I. W. Stewart, Jets from massive unstable particles: Top-mass deter- mination, Phys. Rev. D77, 074010 (2008), arXiv:hep- ph/0703207

    work page arXiv 2008

  59. [59]

    Top Jets in the Peak Region: Factorization Analysis with NLL Resummation

    S. Fleming, A. H. Hoang, S. Mantry, and I. W. Stew- art, Top Jets in the Peak Region: Factorization Anal- ysis with NLL Resummation, Phys. Rev. D77, 114003 (2008), arXiv:0711.2079 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  60. [60]

    Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.- H. Shen, M. P. Solon, and M. Zeng, Scattering Am- plitudes, the Tail Effect, and Conservative Binary Dy- namics atO(G 4), Phys. Rev. Lett.128, 161103 (2022), arXiv:2112.10750 [hep-th]

    work page arXiv 2022

  61. [61]

    D. A. Kosower, B. Maybee, and D. O’Connell, Ampli- tudes, Observables, and Classical Scattering, JHEP02, 137, arXiv:1811.10950 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  62. [62]

    Classical and quantum scattering in post- Minkowskian gravity

    T. Damour, Classical and quantum scattering in post- Minkowskian gravity, Phys. Rev. D102, 024060 (2020), arXiv:1912.02139 [gr-qc]

    work page arXiv 2020

  63. [63]

    Cheung, J

    C. Cheung, J. Parra-Martinez, I. Z. Rothstein, N. Shah, and J. Wilson-Gerow, Effective Field Theory for Ex- treme Mass Ratio Binaries, Phys. Rev. Lett.132, 091402 (2024), arXiv:2308.14832 [hep-th]

    work page arXiv 2024

  64. [64]

    Cheung, J

    C. Cheung, J. Parra-Martinez, I. Z. Rothstein, N. Shah, and J. Wilson-Gerow, Gravitational scattering and be- yond from extreme mass ratio effective field theory, JHEP 10, 005, arXiv:2406.14770 [hep-th]

    work page arXiv

  65. [65]

    Raj and R

    H. Raj and R. Venugopalan, Universal features of 2→N scattering in QCD and gravity from shockwave collisions, Phys. Rev. D109, 044064 (2024), arXiv:2311.03463 [hep- th]

    work page arXiv 2024

  66. [66]

    W. D. Goldberger and I. Z. Rothstein, Dissipative effects in the worldline approach to black hole dynamics, Phys. Rev. D73, 104030 (2006), arXiv:hep-th/0511133

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  67. [67]

    Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings

    J. Vines, Scattering of two spinning black holes in post- Minkowskian gravity, to all orders in spin, and effective- one-body mappings, Class. Quant. Grav.35, 084002 (2018), arXiv:1709.06016 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  68. [68]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, and R. Russo, Angular momentum of zero-frequency gravitons, JHEP08, 172, arXiv:2203.11915 [hep-th]

    work page arXiv

  69. [69]

    A. V. Manohar, A. K. Ridgway, and C.-H. Shen, Radi- ated Angular Momentum and Dissipative Effects in Clas- sical Scattering, Phys. Rev. Lett.129, 121601 (2022), arXiv:2203.04283 [hep-th]

    work page arXiv 2022

  70. [70]

    D. Bini, T. Damour, S. De Angelis, A. Geralico, A. Herderschee, R. Roiban, and F. Teng, Gravitational waveforms: A tale of two formalisms, Phys. Rev. D109, 125008 (2024), arXiv:2402.06604 [hep-th]

    work page arXiv 2024

  71. [71]

    Elkhidir, D

    A. Elkhidir, D. O’Connell, and R. Roiban, Supertransla- tions from Scattering Amplitudes, Phys. Rev. Lett.135, 151601 (2025), arXiv:2408.15961 [hep-th]

    work page arXiv 2025

  72. [72]

    Heissenberg and R

    C. Heissenberg and R. Russo, Revisiting gravitational an- gular momentum and mass dipole losses in the eikonal framework, Class. Quant. Grav.42, 045014 (2025), arXiv:2406.03937 [gr-qc]

    work page arXiv 2025

  73. [73]

    Cristofoli, R

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

    work page arXiv 2022

  74. [74]

    Herrmann, M

    E. Herrmann, M. Kologlu, and I. Moult, Energy Cor- relators in Perturbative Quantum Gravity, (2024), arXiv:2412.05384 [hep-th]

    work page arXiv 2024

  75. [75]

    TikZ-Feynman: Feynman diagrams with TikZ

    J. Ellis, TikZ-Feynman: Feynman diagrams with TikZ, Comput. Phys. Commun.210, 103 (2017), arXiv:1601.05437 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  76. [76]

    J.-y. Chiu, A. Jain, D. Neill, and I. Z. Rothstein, The Rapidity Renormalization Group, Phys. Rev. Lett.108, 151601 (2012), arXiv:1104.0881 [hep-ph]. 11

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  77. [77]

    J.-Y. Chiu, A. Jain, D. Neill, and I. Z. Rothstein, A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory, JHEP05, 084, arXiv:1202.0814 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  78. [78]

    Weinberg, Infrared photons and gravitons, Phys

    S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140, B516 (1965)

    work page 1965