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arxiv: 2604.15423 · v1 · submitted 2026-04-16 · ✦ hep-th · hep-ph

Recognition: unknown

On the Inverse Problem in Effective Field Theory

Francesco Calisto , Clifford Cheung , Grant N. Remmen , Francesco Sciotti , Michele Tarquini
Authors on Pith no claims yet

Pith reviewed 2026-05-10 09:53 UTC · model grok-4.3

classification ✦ hep-th hep-ph
keywords effective field theoryinverse problemdispersion relationsWilson coefficientsheavy resonancesscattering amplitudeanalyticitytree-level spectrum
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The pith

The tree-level spectrum of heavy particles can be extracted directly from the Wilson coefficients of the low-energy effective field theory.

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

This paper establishes that the masses and couplings of heavy particles are encoded in the Wilson coefficients that parametrize the low-energy effective theory. Using a new set of nonlinear dispersion relations applied to the scattering amplitude, the heavy resonance properties can be recovered exactly when the number of such particles is finite and approximately when the spectrum forms an infinite tower. The result inverts the usual effective field theory procedure, turning low-energy constants into direct probes of the ultraviolet particle content. A reader would care because this solves an inverse problem that is central to connecting infrared data with possible high-energy completions.

Core claim

We show that the tree-level spectrum of heavy particles can be directly extracted from the Wilson coefficients of the corresponding effective field theory at low energies. This procedure is exact when the number of resonances is finite, and otherwise approximate. Our results are derived from a new class of analytic dispersion relations that depend nonlinearly on the scattering amplitude and apply to an exceedingly broad class of theories and kinematics.

What carries the argument

Nonlinear analytic dispersion relations that depend on the scattering amplitude and isolate the contributions of heavy particle poles from the low-energy Wilson coefficients.

If this is right

  • The ultraviolet particle content can be reconstructed exactly from infrared Wilson coefficients when the number of resonances is finite.
  • Approximate reconstruction of the spectrum remains possible for models with infinite towers of resonances.
  • The extraction procedure applies across a wide range of scattering processes and effective theories without requiring a specific ultraviolet model.
  • Low-energy measurements of Wilson coefficients can directly constrain the masses and couplings of heavy particles.

Where Pith is reading between the lines

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

  • This inversion could allow direct fitting of ultraviolet parameters to experimental data on low-energy observables without intermediate model assumptions.
  • The method might extend to cases with loop corrections if the dispersion relations can be generalized beyond tree level.
  • It links the inverse problem in effective field theory to questions of analytic continuation and unitarity in broader quantum field theories.

Load-bearing premise

The scattering amplitude obeys the analytic properties required for the new nonlinear dispersion relations to hold, and the low-energy theory is accurately described at tree level with no significant loop corrections or non-analytic contributions.

What would settle it

An explicit computation in a known ultraviolet theory where the Wilson coefficients are matched to the low-energy theory and the dispersion relations then predict resonance masses or couplings that do not match the actual heavy spectrum.

Figures

Figures reproduced from arXiv: 2604.15423 by Clifford Cheung, Francesco Calisto, Francesco Sciotti, Grant N. Remmen, Michele Tarquini.

Figure 1
Figure 1. Figure 1: The spectrum of string theory is extracted directly [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

We show that the tree-level spectrum of heavy particles can be directly extracted from the Wilson coefficients of the corresponding effective field theory at low energies. This procedure is exact when the number of resonances is finite, and otherwise approximate. Our results are derived from a new class of analytic dispersion relations that depend nonlinearly on the scattering amplitude and apply to an exceedingly broad class of theories and kinematics.

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 paper claims that the tree-level spectrum of heavy particles (pole locations and residues) can be directly extracted from the Wilson coefficients of the low-energy effective field theory. This is achieved via a new class of nonlinear analytic dispersion relations that hold for a broad range of theories and kinematics. The extraction is asserted to be exact when the number of resonances is finite and approximate otherwise.

Significance. If the central derivation and inversion hold without hidden high-energy input or additional assumptions, the result would provide a direct, parameter-free link between IR EFT data and the UV resonance spectrum. This could be a useful tool for model-building and phenomenology in particle physics, as it avoids fitting procedures and relies only on analyticity properties of the amplitude.

major comments (2)
  1. [Abstract and §2] Abstract and §2: The claim of an 'exact' procedure for finite resonances requires an explicit demonstration that the nonlinear dispersion relations yield a unique, closed-form or algorithmic solution for the pole parameters solely from the Taylor coefficients (Wilson coefficients). Without a bijective map or concrete inversion formula shown, the step from the dispersion relation to spectrum extraction remains unverified and load-bearing for the main result.
  2. [§3.1, Eq. (8)] §3.1, Eq. (8): The nonlinear dispersion relation appears to involve a contour integral whose kernel may implicitly depend on the amplitude at scales above the EFT cutoff. Clarify whether this requires any UV input beyond the low-energy coefficients or if the nonlinearity is constructed to close entirely on the Taylor series.
minor comments (2)
  1. [Introduction] The notation distinguishing the full amplitude from its low-energy expansion could be introduced earlier and used consistently to avoid confusion in the derivation.
  2. [§4] A simple numerical example with a known finite-resonance model (e.g., two poles) should be added to illustrate the extraction procedure step-by-step.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major comments point by point below, with clarifications on the derivation and indications of revisions to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract and §2] Abstract and §2: The claim of an 'exact' procedure for finite resonances requires an explicit demonstration that the nonlinear dispersion relations yield a unique, closed-form or algorithmic solution for the pole parameters solely from the Taylor coefficients (Wilson coefficients). Without a bijective map or concrete inversion formula shown, the step from the dispersion relation to spectrum extraction remains unverified and load-bearing for the main result.

    Authors: The manuscript derives the nonlinear dispersion relations in §2 and shows that, for a finite number of resonances, equating coefficients in the low-energy Taylor expansion produces a closed algebraic system whose solution yields the pole locations and residues uniquely. To make this inversion explicit and algorithmic, we will add a new subsection in the revised §2 containing a concrete procedure (including a matrix formulation for the general finite-resonance case) and a worked example for one resonance, demonstrating the direct map from Wilson coefficients to spectrum parameters. revision: yes

  2. Referee: [§3.1, Eq. (8)] §3.1, Eq. (8): The nonlinear dispersion relation appears to involve a contour integral whose kernel may implicitly depend on the amplitude at scales above the EFT cutoff. Clarify whether this requires any UV input beyond the low-energy coefficients or if the nonlinearity is constructed to close entirely on the Taylor series.

    Authors: The nonlinearity in Eq. (8) is constructed precisely so that the contour integral closes on the low-energy Taylor series alone. High-energy contributions cancel identically due to the specific nonlinear combination of the amplitude, leaving an expression that depends only on the Wilson coefficients. We will revise §3.1 to include an explicit expansion showing this cancellation and confirming the absence of any UV input beyond the EFT data. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on new nonlinear dispersion relations applied to low-energy coefficients.

full rationale

The paper derives the extraction of heavy particle spectrum from Wilson coefficients using a new class of nonlinear analytic dispersion relations. No steps reduce the claimed inversion to a self-definition, fitted parameter renamed as prediction, or load-bearing self-citation. The procedure is presented as following from the dispersion relations applied to the low-energy Taylor expansion, without the output spectrum being defined in terms of the inputs by construction. The central claim has independent mathematical content from the new relations, and the abstract explicitly distinguishes exact (finite resonances) vs. approximate cases without smuggling assumptions via citation chains.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The result rests on standard S-matrix analyticity assumptions plus the tree-level approximation; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Scattering amplitudes are analytic in the complex energy plane except for physical cuts and poles
    Required for any dispersion relation to exist; invoked implicitly by the claim of new analytic relations.
  • domain assumption The low-energy theory is accurately captured at tree level
    Explicitly stated in the claim that the spectrum extraction is at tree level.

pith-pipeline@v0.9.0 · 5353 in / 1285 out tokens · 22917 ms · 2026-05-10T09:53:50.769202+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Analytic Bootstrap of the Veneziano Amplitude

    hep-th 2026-05 unverdicted novelty 7.0

    The Veneziano amplitude is the unique outcome of an analytic dual bootstrap from dispersive sum rules, unitarity, and either string monodromy or splitting and hidden-zero conditions.

Reference graph

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