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arxiv: 1907.04032 · v1 · pith:PF4TYNR3new · submitted 2019-07-09 · ⚛️ nucl-th · hep-ph

Uncertainty quantification and falsification of Chiral Nuclear Potentials

Rodrigo Navarro Perez , Enrique Ruiz Arriola This is my paper

Pith reviewed 2026-05-25 00:17 UTC · model grok-4.3

classification ⚛️ nucl-th hep-ph
keywords chiral effective field theorynucleon-nucleon scatteringnuclear potentialsuncertainty quantificationGranada-2013 databaseperipheral scatteringzero-energy scattering
0
0 comments X

The pith

Chiral nuclear potentials show systematic discrepancies with NN scattering data.

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

The paper checks whether chiral effective field theories currently describe nucleon-nucleon scattering data well enough. It finds clear systematic mismatches in zero-energy scattering and in perturbative peripheral partial waves, the regimes where the expansion should perform most reliably. These mismatches appear when the chiral results are compared directly to the Granada-2013 NN-database and its partial-wave analysis. If the discrepancies are real, the chiral approach cannot yet serve as a fully model-independent framework for nuclear forces. The analysis therefore questions the present predictive power of chiral potentials for nuclear structure and reactions.

Core claim

Chiral theories at present are not describing experimental NN scattering data satisfactorily, with relevant systematic discrepancies unveiled in zero energy NN scattering and perturbative counterterm-free peripheral scattering when compared to the Granada-2013 NN-database and PWA based on coarse graining the interaction.

What carries the argument

Zero-energy NN scattering and perturbative counterterm-free peripheral scattering used as direct tests of the chiral expansion against the Granada-2013 database.

If this is right

  • Higher-order terms or adjustments in the chiral expansion are required to remove the observed discrepancies.
  • Fitting procedures for np and pp data may still introduce theoretical bias until the theory is validated.
  • Predictive calculations of nuclear structure and reactions remain limited until the discrepancies are resolved.
  • Further work is needed to confirm that the chiral hierarchy functions as intended in the tested regimes.

Where Pith is reading between the lines

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

  • Persistent mismatches could motivate development of alternative constructions for nuclear forces.
  • Ab initio calculations relying on current chiral potentials may inherit the same systematic offsets.
  • Re-analysis of the Granada-2013 database construction could help isolate whether the discrepancies originate in data handling.

Load-bearing premise

The chiral expansion supplies a model-independent hierarchy that should work best in the chosen peripheral and zero-energy regimes, with discrepancies arising from the theory rather than from data selection or analysis choices.

What would settle it

A chiral potential at the appropriate order that reproduces the Granada-2013 NN-database in zero-energy scattering and peripheral waves without systematic deviations.

Figures

Figures reproduced from arXiv: 1907.04032 by Enrique Ruiz Arriola, Rodrigo Navarro Perez.

Figure 1
Figure 1. Figure 1: Top panel: Point-like (solid-blue) and extended (dashed-red) proton-proton Coulomb interaction as a function of distance. Bottom panel: Coarse grained NN potential (red dots) plus the chiral 1π +2π exchange potentials when rc = 1.8fm (blue line) compared with the wave function at a CM corresponding to a back-to-back NN collision on the Fermi surface in nuclear matter (brown line). whereas they become singu… view at source ↗
Figure 2
Figure 2. Figure 2: The pp total (red) and total elastic (blue) cross section as a function of the CM momentum. We mark the single π-production and the ∆-production for reference. 2.1 The scattering amplitude The elastic scattering process is described by the scattering ma￾trix S whose matrix elements in the CM system are defined as S(kˆ f ,kˆ i) ≡ hkˆ f |S|kˆ ii with kˆ i and kˆ f the incoming and outgoing directions respect… view at source ↗
Figure 3
Figure 3. Figure 3: Abundance plots for pp (top panels) and np (bottom panels) scattering data. Full data base (left panel). Standard 3σ criterion (middle panels). Self-consistent 3σ criterion (right panels). We show accepted data (blue), rejected data (red) and recovered data (green). At present only 3π exchanges have been considered starting by Ref. [36]. A particularly attractive scheme to represent the ana￾lytical propert… view at source ↗
Figure 4
Figure 4. Figure 4: The LAB energy complex plane, showing the partial waves left cut structure due to multiple pion (and σ,ρω) ex￾change along with the right cut structure due to pion production. T left LAB = (...,−375.3,−260.6,−166.8,−93.8,−41.7,−10.4)MeV. The outer/inner circles correspond to LAB energies of 350/125MeV respectively. equation which besides facing technical difficulties poses the￾oretical issues in practice s… view at source ↗
Figure 5
Figure 5. Figure 5: Momentum space components of potentials as a function of the momentum transfer for several potentials: AV18 [55] and the Granada DS-OPE [58, 59], DS-χTPE [60, 61] and Gauss-OPE [62]. This can be generalized to higher orders in p or equivalently in L. Here, the first fourteen operators are the same charge￾independent ones used in the Argonne v14 potential and are given by O n=1,14 = 1, τ1·τ2, σ1·σ2,(σ1·σ2)(… view at source ↗
Figure 6
Figure 6. Figure 6: np Phase shifts for 10 high quality fits in all partial waves with J ≤ 5 as a function of the LAB energy. We show the Nijmegen PWA Nijm I, NijmII Reid93 [54] the AV18 [55], CD Bonn [56], Spectator [57], and the Granada DS-OPE [58, 59], DS-χTPE [60, 61] and Gauss-OPE [62]. for the previous high quality potentials at their time (defined by their χ 2/N ∼ 1). Our observation is that for the Granada poten￾tials… view at source ↗
Figure 7
Figure 7. Figure 7: Momentum space local components of potentials as a function of the momentum transfer for several potentials: AV18 [55] and the Granada DS-OPE [58, 59], DS-χTPE [60, 61] and Gauss-OPE [62]. 76. S. Wesolowski, N. Klco, R.J. Furnstahl, D.R. Phillips, A. Tha￾paliya, J. Phys. G43, 074001 (2016) 77. R. Navarro Perez, J.E. Amaro, E. Ruiz Arriola, Phys. Rev. ´ C91, 054002 (2015). 78. R. Navarro Perez, J.E. Amaro, … view at source ↗
read the original abstract

Are chiral theories at present describing experimental NN scattering data satisfactorily ?. Will the chiral approach offer a framework where fitting and selecting the existing np and pp data can be done without theoretical bias ?. While predictive power in theoretical nuclear physics has been a major concern in the study of nuclear structure and reactions, the Effective Field Theory (EFT) based on chiral expansions has emerged after Weinberg as a model independent hierarchy for many body forces and much progress has been achieved over the last decades. We review some of the issues involved which point to being close to the solution, but also that work remains still to be done to validate the theory. We analyze several examples including zero energy NN scattering and perturbative counterterm -- free peripheral scattering where one would expect these methods to work best and unveil relevant systematic discrepancies when a fair comparison to the Granada-2013 NN-database and partial wave analysis (PWA) based on coarse graining the interaction is undertaken.

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

3 major / 2 minor

Summary. The paper claims that chiral EFT nuclear potentials do not satisfactorily describe experimental NN scattering data. It identifies relevant systematic discrepancies in zero-energy NN scattering and perturbative counterterm-free peripheral scattering when compared to the Granada-2013 NN-database and its coarse-grained partial-wave analysis (PWA). The work questions whether chiral expansions provide a model-independent hierarchy suitable for unbiased data fitting and selection, while reviewing progress and remaining validation issues in the approach.

Significance. If the central claim holds after addressing quantitative gaps, the result would highlight limitations in current chiral power counting for peripheral and low-energy regimes, strengthening the case for rigorous uncertainty quantification and falsification protocols in nuclear EFT. This could influence how chiral potentials are validated against data and motivate refinements to the hierarchy or reference analyses.

major comments (3)
  1. [Abstract] Abstract: The claim that 'relevant systematic discrepancies' exist is stated without quantitative measures such as χ² per degree of freedom, explicit error budgets, or falsification thresholds. This makes it impossible to assess whether the discrepancies are statistically significant or load-bearing for the falsification conclusion.
  2. [Introduction / comparison section] The central comparison relies on the Granada-2013 database and coarse-grained PWA as the benchmark. No explicit test is provided to demonstrate that the coarse-graining procedure or data-selection cuts do not introduce effective-range or peripheral-wave systematics correlated with the chiral power counting; this assumption is load-bearing for attributing discrepancies to the EFT rather than the reference.
  3. [Discussion of peripheral waves] The assertion that the chosen regimes (zero energy and perturbative peripheral scattering) are where the chiral expansion 'should work best' is presented without a derivation or reference to the expected convergence pattern in those channels; if the hierarchy does not apply as assumed, the falsification test is not model-independent.
minor comments (2)
  1. Notation for the chiral orders and counterterm counting should be standardized across figures and text to avoid ambiguity in the uncertainty quantification.
  2. The manuscript would benefit from a table summarizing the quantitative discrepancy measures (e.g., residuals or pull distributions) for each peripheral wave and zero-energy parameter.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and detailed report. The comments highlight areas where the presentation can be strengthened, and we address each major point below with plans for revision where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that 'relevant systematic discrepancies' exist is stated without quantitative measures such as χ² per degree of freedom, explicit error budgets, or falsification thresholds. This makes it impossible to assess whether the discrepancies are statistically significant or load-bearing for the falsification conclusion.

    Authors: We agree that the abstract would benefit from explicit quantitative indicators to support the claim of relevant discrepancies. The body of the manuscript already contains direct comparisons to the Granada-2013 PWA that demonstrate systematic deviations, but we will revise the abstract to include references to χ² per degree of freedom values, brief error budget information, and a statement on the implications for falsification thresholds drawn from the detailed analysis. revision: yes

  2. Referee: [Introduction / comparison section] The central comparison relies on the Granada-2013 database and coarse-grained PWA as the benchmark. No explicit test is provided to demonstrate that the coarse-graining procedure or data-selection cuts do not introduce effective-range or peripheral-wave systematics correlated with the chiral power counting; this assumption is load-bearing for attributing discrepancies to the EFT rather than the reference.

    Authors: The Granada-2013 database and its coarse-grained PWA are established, largely model-independent benchmarks in the NN scattering literature. The systematic nature of the discrepancies across multiple independent channels and regimes supports attribution to the chiral EFT rather than reference artifacts. While a dedicated correlation test is not performed in the present work, we will add a concise discussion of the robustness and design goals of the coarse-graining procedure in the revised manuscript to address this concern. revision: partial

  3. Referee: [Discussion of peripheral waves] The assertion that the chosen regimes (zero energy and perturbative peripheral scattering) are where the chiral expansion 'should work best' is presented without a derivation or reference to the expected convergence pattern in those channels; if the hierarchy does not apply as assumed, the falsification test is not model-independent.

    Authors: The selection of these regimes is grounded in the chiral power counting, under which peripheral waves (higher partial waves) suppress short-range contributions and zero energy minimizes higher-order corrections. We will revise the relevant sections to include explicit references to the literature on expected convergence patterns in peripheral and low-energy chiral EFT scattering, thereby strengthening the justification for the test. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to Granada-2013 benchmark; no load-bearing reduction in derivation chain

full rationale

The paper's central claim of systematic discrepancies rests on comparison to the Granada-2013 NN-database and its coarse-grained PWA. This reference is cited from prior author work but is presented as derived from experimental data rather than from the chiral potentials under test. No quoted equations or steps show a self-definitional loop, a fitted parameter renamed as prediction, or an ansatz smuggled via self-citation that forces the falsification result. The benchmark remains externally falsifiable against raw NN data, keeping any self-citation non-load-bearing and the overall chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that chiral EFT supplies a model-independent hierarchy and on the external validity of the Granada-2013 database as an unbiased benchmark; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Chiral expansions provide a model-independent hierarchy for many-body forces
    Invoked explicitly in the abstract as the foundation of the EFT approach after Weinberg.

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