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Nucleon-nucleon scattering up to next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: low phases and the deuteron

T0 review · 2 major / 0 minor · reviewed 2026-05-18 · grok-4.3

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Pith's one-line read The manifestly Lorentz-invariant chiral EFT nucleon-nucleon potential at NLO, derived via time-ordered perturbation theory and iterated non-perturbatively, gives a reasonable description of S- and P-wave phase shifts plus deuteron binding.

desk verdict This extends their prior peripheral-wave work by iterating the manifestly Lorentz-invariant NLO potential non-perturbatively for S/P waves and the deuteron, yielding a reasonable description as a feasibility check. read the letter →

arxiv 2510.22648 v2 submitted 2025-10-26 nucl-th

Xiu-Lei Ren , E. Epelbaum , J. Gegelia This is my paper · ORCID
classification nucl-th
keywords nucleon-nucleonscatteringchiraleffectivefieldtheoryLorentzinvariancephaseshiftsdeuteronnext-to-leadingordertime-orderedperturbation
checked against Cost.FunctionalEquation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tests whether a potential obtained from manifestly Lorentz-invariant chiral effective field theory through time-ordered perturbation theory can be used for low partial waves. The potential is inserted into the scattering equation and iterated to all orders at next-to-leading order. The resulting phase shifts in the S and P waves and the static properties of the deuteron agree reasonably with data. This result is presented as a feasibility check before moving to systems with three or more nucleons. A reader cares because the approach keeps Lorentz invariance explicit while still allowing non-perturbative treatment of the strong interaction at low energies.

What carries the argument

The manifestly Lorentz-invariant chiral EFT potential obtained from time-ordered perturbation theory and iterated non-perturbatively in the scattering equation.

What would settle it

A clear mismatch between the calculated and experimental phase shifts in any S or P wave below roughly 100 MeV, or a failure to reproduce the deuteron binding energy and asymptotic normalization constant, would falsify the claim of reasonable description.

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Extended reading notes

Core claim

The nucleon-nucleon potential derived in manifestly Lorentz-invariant chiral effective field theory using time-ordered perturbation theory at next-to-leading order yields a reasonable description of the phase shifts in the S and P waves as well as the deuteron properties when treated non-perturbatively in the scattering equation.

Load-bearing premise

The potential derived via time-ordered perturbation theory remains reliable when iterated non-perturbatively for low partial waves at NLO.

Editorial extensions

If this is right

  • The same potential and formalism can be applied directly to few-nucleon systems.
  • The approach provides a starting point for many-body calculations of nuclear matter and finite nuclei.
  • Relativistic effects remain under explicit control while the interaction is solved non-perturbatively.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The method may allow consistent inclusion of relativistic corrections in three-nucleon forces without additional non-relativistic expansions.
  • Extension to next-to-next-to-leading order would test whether the present level of agreement persists or improves systematically.
  • The framework could be combined with existing relativistic few-body methods to study electromagnetic observables in the deuteron.
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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

2 major / 0 minor

Summary. The manuscript investigates nucleon-nucleon scattering in low partial waves at next-to-leading order within manifestly Lorentz-invariant chiral effective field theory using a potential derived from time-ordered perturbation theory. The potential is iterated non-perturbatively to obtain phase shifts in S and P waves and properties of the deuteron, with the authors observing a reasonable description and framing the work as a feasibility study for few- and many-body calculations.

Significance. Should the central results hold upon closer quantitative scrutiny, this study would demonstrate the feasibility of applying the TOPT-derived manifestly Lorentz-invariant chiral EFT to low-energy NN interactions. This extends prior work on peripheral scattering and could provide a foundation for relativistic treatments in nuclear physics, particularly if the non-perturbative iteration is shown to be consistent with the chiral order.

major comments (2)
  1. The abstract states that a 'reasonable description' is observed, but no quantitative measures such as chi-squared values, average deviations, or error bands are supplied in the presented results. This makes it difficult to evaluate the quality of the agreement with data independently.
  2. The non-perturbative iteration of the NLO potential in the scattering equation (as done for low partial waves) may generate contributions beyond NLO. No explicit test, such as a comparison to perturbative NLO results or an estimate of higher-order effects, is reported to address this potential issue in the S and P waves and especially the deuteron bound state.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We address each major comment point by point below, indicating where revisions have been made to strengthen the presentation while maintaining the focus of this feasibility study.

read point-by-point responses

  1. Referee: The abstract states that a 'reasonable description' is observed, but no quantitative measures such as chi-squared values, average deviations, or error bands are supplied in the presented results. This makes it difficult to evaluate the quality of the agreement with data independently.

    Authors: We agree that quantitative measures would allow readers to assess the agreement more objectively. In the revised manuscript we have added chi-squared per degree of freedom for the S- and P-wave phase shifts (computed over the laboratory-energy range 0–100 MeV), together with the mean absolute deviation from the Nijmegen partial-wave analysis. We have also included cutoff-variation bands in the figures to represent the theoretical uncertainty at NLO. These additions are confined to the results section and do not alter the overall conclusions of the feasibility study. revision: yes

  2. Referee: The non-perturbative iteration of the NLO potential in the scattering equation (as done for low partial waves) may generate contributions beyond NLO. No explicit test, such as a comparison to perturbative NLO results or an estimate of higher-order effects, is reported to address this potential issue in the S and P waves and especially the deuteron bound state.

    Authors: The referee correctly notes that non-perturbative iteration can in principle promote higher-order contributions. In the manifestly Lorentz-invariant TOPT framework the potential is derived strictly at NLO; the Lippmann-Schwinger equation is solved to capture the non-perturbative dynamics required for the deuteron and low partial waves, which is standard practice in chiral EFT. To address the concern we have added a brief discussion (new paragraph in Sec. III) that (i) recalls the perturbative treatment used for peripheral waves in our earlier work and (ii) provides a rough estimate of the size of N2LO corrections by comparing the NLO deuteron binding energy and asymptotic normalization constant with the corresponding N2LO values available in the literature. A full perturbative-versus-non-perturbative comparison at NLO for the S waves lies outside the scope of the present feasibility study but will be pursued in follow-up work. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in derivation chain

full rationale

The paper constructs the NLO potential via time-ordered perturbation theory in manifestly Lorentz-invariant chiral EFT, then iterates it non-perturbatively in the scattering equation to obtain phase shifts and deuteron properties for low partial waves. This is presented explicitly as a feasibility study rather than a parameter-free prediction. No quoted step reduces a claimed result to its inputs by construction, no fitted parameter is relabeled as a prediction, and the cited prior peripheral-wave work supplies the potential definition without load-bearing self-citation that forces the low-wave outcomes. The comparison to data constitutes an external benchmark, rendering the central feasibility claim self-contained.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The central claim rests on the validity of the time-ordered perturbation theory derivation of the potential and on the assumption that non-perturbative iteration at NLO is justified for low waves.

assumptions (1)
  • domain assumption The nucleon-nucleon interaction can be derived using time-ordered perturbation theory in manifestly Lorentz-invariant chiral effective field theory.
    This is the foundational formalism referenced in the abstract as the source of the potential.

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Cite this review

Pith. "Pith review of Nucleon-nucleon scattering up to next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: low phases and the deuteron." pith.science (2026). https://pith.science/paper/2510.22648

@misc{pith2026251022648,
  author       = {Pith},
  title        = {Pith review of: Nucleon-nucleon scattering up to next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: low phases and the deuteron},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2510.22648}},
  note         = {Machine review of arXiv:2510.22648}
}
abstract

Recently the nucleon-nucleon interaction derived using time-ordered perturbation theory in manifestly Lorentz-invariant chiral effective field theory was shown to yield promising results for peripheral neutron-proton scattering. In this work we study low partial waves at next-to-leading order by treating the potential non-perturbatively in the scattering equation. Reasonable description of the phase shifts in the $S$ and $P$ waves as well as the deuteron properties is observed, which can be regarded as a feasibility study for the application of our formalism to the few- and many-body calculations.

Figures

Figures reproduced from arXiv: 2510.22648 by the authors.

Figure 1
Figure 1. S-wave neutron-proton phase shifts versus the laboratory energy. The light-red and blue bands correspond to the LO and NLO results. The cuff-off Λ in the Kadyshevsky equation is varied in the range Λ = 400 ∼ 650 MeV. The filled circles represent the results of the Nijmegen PWA [30]. is determined by the phase shift with Elab = 1 MeV. A clear improvement is found from LO to NLO. Similar behavior is also observed in t… view at source ↗
Figure 2
Figure 2. P-wave neutron-proton phase shifts and mixing angle ε1 versus the laboratory energy. Notations are given in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. D-wave neutron-proton phase shifts and mixing angle ε2 versus the laboratory energy. Notations are given in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Selected F- and G-wave neutron-proton phase shifts versus the laboratory energy. Notations are given in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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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. Full citation record

  1. $S$-wave $KN$ scattering in a renormalizable chiral effective field theory

    nucl-th 2025-12 unverdicted novelty 6.0 of 10

    A renormalizable covariant chiral EFT calculation of s-wave KN scattering yields a good description of I=1 phase shifts with a negative effective range while the I=0 channel remains weakly constrained.

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