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arxiv: 2511.11457 · v2 · pith:F6I3RFIGnew · submitted 2025-11-14 · ✦ hep-th · gr-qc· hep-ph

Analytic structure of the high-energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms

Francesco Alessio , Vittorio Del Duca , Riccardo Gonzo , Emanuele Rosi , Ira Z. Rothstein , Michael Saavedra This is my paper

Pith reviewed 2026-05-21 18:15 UTC · model grok-4.3

classification ✦ hep-th gr-qchep-ph
keywords gravitational scatteringhigh-energy limitRegge regimepost-Minkowskian expansionmulti-H diagramseikonal phasedispersion relationsloop amplitudes
0
0 comments X

The pith

Multi-H diagrams produce the leading double logarithm in gravitational scattering at 5PM order.

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

The paper examines two-body gravitational scattering in the high-energy small-angle limit. It applies power counting arguments and dispersion relations inside an effective field theory for the Regge regime to show how leading Regge logarithms appear as a power series in t/s. The authors isolate the tower of multi-H diagrams that control the dominant logarithmic terms and compute the leading double logarithm at four loops, which is 5PM order. They verify this result by independent calculation in the multi-Regge expansion. Dispersion relations are then used to extract the single-logarithmic piece of the imaginary part of the eikonal phase at the same order in the Regge limit.

Core claim

In the high-energy small-angle limit of gravitational two-body scattering, power counting and dispersion relations in an effective field theory for the Regge regime determine that the leading Regge logarithms arise as a power series in t/s from a tower of multi-H diagrams. The leading double logarithm is computed explicitly at four loops (5PM) and agrees between the effective field theory method and the multi-Regge expansion. Dispersion relations then give the single logarithmic contribution to the imaginary part of the eikonal phase at 5PM in the Regge limit.

What carries the argument

The tower of multi-H diagrams that govern the leading logarithmic behavior, together with dispersion relations in the Regge effective field theory.

If this is right

  • The analytic structure of the amplitude at higher loop orders is fixed by the same class of multi-H diagrams.
  • Agreement between effective field theory and multi-Regge methods supports using either for logarithmic terms at 5PM and beyond.
  • The single logarithmic term in the imaginary part of the eikonal phase is accessible at 5PM via dispersion relations.
  • Classical 5PM logarithms in gravitational scattering are determined by this loop expansion.

Where Pith is reading between the lines

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

  • The same dispersion relations could isolate subleading logarithms at higher post-Minkowskian orders.
  • The framework may extend to resummation of the full tower of Regge logarithms in the eikonal phase.
  • Similar power-counting techniques could apply to high-energy scattering in other long-range force theories.

Load-bearing premise

Power counting arguments and dispersion relations remain valid in the effective field theory for the Regge regime, allowing the expansion in powers of t/s to capture the leading logarithmic behavior without additional non-perturbative effects.

What would settle it

A mismatch between the coefficient of the leading double logarithm computed from four-loop multi-H diagrams in effective field theory and the corresponding multi-Regge expansion result would falsify the central claim.

Figures

Figures reproduced from arXiv: 2511.11457 by Emanuele Rosi, Francesco Alessio, Ira Z. Rothstein, Michael Saavedra, Riccardo Gonzo, Vittorio Del Duca.

Figure 1
Figure 1. Figure 1: FIG. 1: Vertical and horizontal wavy lines denote [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Momenta parametrisation for [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The scalar massless kite integral topology [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

We investigate the high-energy, small-angle limit of two-body gravitational scattering. Using power counting arguments and dispersion relations in an effective field theory for the Regge regime, we derive the general loop expansion that determines how the leading Regge logarithms and their complex structure arise as a power series in $t/s$. Focusing on the tower of multi-H diagrams that govern the leading logarithmic behavior, we compute the leading double logarithm at four loops (5PM) using both effective field theory methods and the multi-Regge expansion, finding complete agreement. Finally, using the aforementioned dispersion relations, we extract the single logarithmic contribution to the imaginary part of the eikonal phase at 5PM in the Regge limit.

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

2 major / 2 minor

Summary. The manuscript investigates the high-energy, small-angle limit of two-body gravitational scattering. Using power counting arguments and dispersion relations in an effective field theory for the Regge regime, the authors derive the general loop expansion for leading Regge logarithms as a power series in t/s. Focusing on multi-H diagrams, they compute the leading double logarithm at four loops (5PM) via both EFT methods and the multi-Regge expansion, reporting complete agreement. They then apply the dispersion relations to extract the single logarithmic contribution to the imaginary part of the eikonal phase at 5PM in the Regge limit.

Significance. If the results hold, this advances understanding of the analytic structure and logarithmic tower in high-energy gravitational amplitudes. The explicit 5PM double-log computation with complete agreement between two independent methods (EFT and multi-Regge) is a clear strength, as is the parameter-free derivation grounded in dispersion relations and power counting. This provides a concrete benchmark for classical 5PM effects and could inform eikonal resummations.

major comments (2)
  1. [§4] §4 (power counting for multi-H diagrams): The argument that these diagrams alone govern the leading double logarithm at 5PM relies on the t/s expansion cleanly isolating the log tower; a more explicit demonstration that other diagram classes do not contribute at the same order in the Regge regime would be needed to fully support the isolation step before the extraction.
  2. [§5] §5, dispersion relation (around Eq. (12)): The extraction of the single-log imaginary part assumes the analytic structure (branch cuts and residues) is fully captured by the stated power counting without subleading non-perturbative contributions; if this assumption is incomplete, the 5PM single-log term could receive uncontrolled corrections, directly affecting the final claim.
minor comments (2)
  1. [Abstract] The abstract and introduction could more clearly distinguish the double-log computation (which has the two-method agreement) from the single-log extraction (which relies on the dispersion step).
  2. [Introduction] Notation for the eikonal phase and its imaginary part should be defined consistently when first introduced to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript's significance and for the constructive major comments. We address each point below with clarifications grounded in the paper's EFT power counting and dispersion relations framework, and indicate the revisions incorporated.

read point-by-point responses

  1. Referee: [§4] §4 (power counting for multi-H diagrams): The argument that these diagrams alone govern the leading double logarithm at 5PM relies on the t/s expansion cleanly isolating the log tower; a more explicit demonstration that other diagram classes do not contribute at the same order in the Regge regime would be needed to fully support the isolation step before the extraction.

    Authors: We agree that an expanded demonstration improves clarity. In the revised manuscript we have augmented §4 with an explicit classification of diagram topologies in the Regge EFT. Using the established power-counting rules (where each additional graviton exchange or non-multi-H topology introduces extra factors of t/s or suppresses the double-logarithmic enhancement), we show that only the multi-H class contributes to the leading O((t/s)^0 log^2) term at four loops. This classification is now presented with a table summarizing the scaling of representative non-multi-H diagrams, confirming they enter only at subleading orders in the t/s expansion. revision: yes

  2. Referee: [§5] §5, dispersion relation (around Eq. (12)): The extraction of the single-log imaginary part assumes the analytic structure (branch cuts and residues) is fully captured by the stated power counting without subleading non-perturbative contributions; if this assumption is incomplete, the 5PM single-log term could receive uncontrolled corrections, directly affecting the final claim.

    Authors: We appreciate the referee's emphasis on the robustness of the analytic assumptions. The dispersion relations are applied strictly within the perturbative Regge EFT, where the power counting isolates the leading branch-cut structure generated by the multi-H diagrams. Subleading non-perturbative contributions (e.g., from instantons or non-perturbative Regge poles) are exponentially suppressed in the high-energy limit and do not affect the perturbative single-log term at fixed loop order. We have added a clarifying paragraph in §5 that makes this separation explicit and notes consistency with the independent multi-Regge computation, which reproduces the same single-log coefficient without invoking the dispersion relations. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation uses external EFT power counting and dispersion relations with independent multi-Regge cross-check

full rationale

The paper derives the general loop expansion for leading Regge logarithms via power counting and dispersion relations in the Regge-regime EFT, then explicitly computes the four-loop double logarithm using both EFT methods and the multi-Regge expansion, reporting agreement. The single-log imaginary part is extracted from the same dispersion relations. No quoted step reduces a reported result to a fitted parameter, self-defined quantity, or load-bearing self-citation chain; the central extraction is cross-validated by an independent expansion and remains falsifiable against external benchmarks. This is the normal non-circular outcome for a computation grounded in prior literature assumptions rather than tautological redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard domain assumptions of effective field theory in the Regge regime and dispersion relations; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Power counting arguments determine the general loop expansion for leading Regge logarithms in the effective field theory for the Regge regime
    Invoked to derive how logarithms arise as a power series in t/s.
  • domain assumption Dispersion relations apply in the high-energy small-angle limit to extract imaginary parts of the eikonal phase
    Used to obtain the single logarithmic contribution at 5PM.

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discussion (0)

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