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arxiv: 2604.20681 · v1 · submitted 2026-04-22 · ⚛️ nucl-th

Recognition: unknown

Cutoff-independent predictions from nuclear lattice effective field theory

Bing-Nan Lu, Chen-Can Wang, Jia-ai Shi

Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:01 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords chiral effective field theorynuclear forcescutoff independenceab initio calculationsnuclear binding energiesthree-nucleon forcesmomentum regulator
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The pith

A minimal chiral nuclear force fitted only to light nuclei predicts binding energies up to 40Ca with cutoff dependence of just a few MeV.

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

The paper establishes that a stripped-down chiral effective field theory interaction, limited to contact terms at next-to-leading order, one three-nucleon contact, and leading one-pion exchange, all fixed using only nuclei with up to three nucleons, can reproduce experimental binding energies for nuclei through calcium-40. This holds with remarkably small dependence on the ultraviolet cutoff, varying by only a few MeV across a wide range. The success comes from applying a lattice-style regulator based on absolute momentum that cuts off high-momentum contributions without causing the usual overbinding seen in soft forces. If correct, this shows that predictive power in nuclear ab initio work does not require the usual proliferation of complex forces and higher-order terms.

Core claim

A chiral nuclear interaction consisting of contact terms up to next-to-leading order, a single three-nucleon contact force, and leading-order one-pion exchange, all constrained strictly in the A ≤ 3 sector, accurately reproduces experimental binding energies up to 40Ca with residual cutoff dependencies of only a few MeV by using a lattice-inspired absolute-momentum regulator that suppresses high-momentum modes without complex many-body forces.

What carries the argument

The lattice-inspired absolute-momentum regulator that suppresses high-momentum modes and prevents overbinding.

If this is right

  • Binding energies for medium-mass nuclei can be predicted from parameters fixed solely in the A ≤ 3 sector.
  • Cutoff independence holds across nuclei from light to 40Ca and sub-saturated nuclear matter with residuals of a few MeV.
  • Complex many-body forces are unnecessary to resolve overbinding in soft chiral forces.
  • The same minimal interaction serves as a foundation for both continuum and lattice ab initio calculations.

Where Pith is reading between the lines

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

  • The regulator approach may extend to other observables such as nuclear radii or scattering without additional fitting.
  • Testing the interaction on nuclei heavier than 40Ca would show where the minimal form ceases to be accurate.
  • Similar absolute-momentum regulators could simplify EFT calculations in related few-body systems.

Load-bearing premise

That parameters fitted strictly to nuclei with three or fewer nucleons remain predictive for heavier nuclei without higher-order interactions or explicit many-body forces.

What would settle it

A calculation of the 40Ca binding energy at varied cutoffs within the paper's range showing deviations much larger than a few MeV.

Figures

Figures reproduced from arXiv: 2604.20681 by Bing-Nan Lu, Chen-Can Wang, Jia-ai Shi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: illustrates the equations of state (EOS) obtained within the range 300 MeV ≤ Λ ≤ 400 MeV. We compare results using 2NFs alone with those incorporating the full 2N+3N interaction, where the variation in Λ defines the corresponding uncertainty bands. With 2NFs only, the predicted E/A forms a divergent band that widens sig￾nificantly as density increases. Remarkably, the inclusion of 3NFs collapses this varia… view at source ↗
read the original abstract

Cutoff independence is an essential requirement for the predictive power of nuclear \textit{ab initio} calculations based on effective field theory (EFT). While it is conventionally assumed that such invariance necessitates high-order interactions and complex many-body forces, we present a minimal chiral nuclear force that exhibits remarkable cutoff independence across a broad range from light to medium-mass nuclei and sub-saturated nuclear matter. Our framework comprises only contact terms up to next-to-leading order, a single three-nucleon contact force, and a leading-order one-pion-exchange potential, all constrained strictly in the $A \leq 3$ sector. Despite its simplicity, this interaction accurately reproduces experimental binding energies up to $^{40}\text{Ca}$ with unexpectedly small residual cutoff dependencies of only a few MeV. We demonstrate that the use of a lattice-inspired \emph{absolute}-momentum regulator efficiently suppresses high-momentum modes, resolving the overbinding problem for soft chiral forces without invoking complex many-body forces. These results establish a robust and economic foundation for EFT-based \textit{ab initio} calculations in both continuum and lattice frameworks.

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 manuscript presents a minimal chiral EFT nuclear interaction consisting of LO one-pion exchange, NLO two-nucleon contacts, and a single three-nucleon contact, with all low-energy constants fixed exclusively to A≤3 data. It claims that a lattice-inspired absolute-momentum regulator enables cutoff-independent predictions of binding energies up to 40Ca with only a few MeV residual dependence, without requiring higher-order or additional many-body forces.

Significance. If the reported cutoff independence and predictive accuracy hold under detailed scrutiny, the result would be significant for nuclear ab initio theory: it offers a simple, economical framework that could streamline calculations in both lattice and continuum settings while addressing overbinding issues for soft interactions. The approach challenges the conventional need for complex many-body forces in this mass range and highlights the potential of regulator design to enhance EFT predictivity.

major comments (3)
  1. Abstract: the central claim that binding energies up to 40Ca are reproduced with 'only a few MeV' residual cutoff dependence is stated without quantitative details on the precise binding-energy values, error bars, fitting procedure, data selection criteria, or numerical methods employed. This leaves the load-bearing assertion of cutoff independence only partially supported.
  2. Regulator section (implied in formalism and results): the absolute-momentum regulator is presented as efficiently suppressing high-momentum modes without artifacts, yet no explicit comparison is shown with a conventional momentum cutoff applied to the same interaction. Without this test, it remains unclear whether the small residual dependence is a genuine EFT feature or an artifact of the regulator choice effectively renormalizing the low-energy constants in a cutoff-dependent manner when the many-body space enlarges to 40Ca.
  3. Results on 40Ca: parameters are fitted strictly to A≤3 systems, and the application to 40Ca is offered as a prediction; however, the manuscript does not demonstrate that the single 3N contact plus NLO contacts remain sufficient without cutoff-dependent absorption of higher-order or many-body contributions, contrary to standard chiral EFT experience where three- and four-body forces become essential in this regime.
minor comments (2)
  1. The explicit functional form of the absolute-momentum regulator should be provided with an equation number in the formalism section to allow reproducibility.
  2. Clarify the precise definition of 'cutoff independence' (e.g., variation across which specific cutoff values) and include a table summarizing binding energies versus cutoff for key nuclei.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the positive assessment of the significance of our work and for the detailed comments. We address each of the major comments below.

read point-by-point responses

  1. Referee: Abstract: the central claim that binding energies up to 40Ca are reproduced with 'only a few MeV' residual cutoff dependence is stated without quantitative details on the precise binding-energy values, error bars, fitting procedure, data selection criteria, or numerical methods employed. This leaves the load-bearing assertion of cutoff independence only partially supported.

    Authors: We acknowledge that the abstract could be more informative. In the revised manuscript, we will include quantitative details such as the specific binding energies for nuclei up to 40Ca, the range of residual cutoff dependence (a few MeV), and references to the fitting procedure and numerical methods described in the main text. This will better support the central claim. revision: yes

  2. Referee: Regulator section (implied in formalism and results): the absolute-momentum regulator is presented as efficiently suppressing high-momentum modes without artifacts, yet no explicit comparison is shown with a conventional momentum cutoff applied to the same interaction. Without this test, it remains unclear whether the small residual dependence is a genuine EFT feature or an artifact of the regulator choice effectively renormalizing the low-energy constants in a cutoff-dependent manner when the many-body space enlarges to 40Ca.

    Authors: The absolute-momentum regulator is specifically chosen in our lattice EFT framework to suppress high-momentum components in a manner consistent with the EFT power counting. We believe the small residual dependence observed is a genuine feature, as evidenced by the consistent predictions across cutoffs. However, to address the referee's concern, we will add a paragraph in the formalism section discussing the properties of this regulator compared to conventional ones and why it avoids the renormalization artifacts mentioned. A full numerical comparison may require additional computations, but we will clarify the distinction. revision: partial

  3. Referee: Results on 40Ca: parameters are fitted strictly to A≤3 systems, and the application to 40Ca is offered as a prediction; however, the manuscript does not demonstrate that the single 3N contact plus NLO contacts remain sufficient without cutoff-dependent absorption of higher-order or many-body contributions, contrary to standard chiral EFT experience where three- and four-body forces become essential in this regime.

    Authors: Our calculations show that the minimal set of interactions, constrained only in A≤3, provides predictions for 40Ca binding energies with only a few MeV cutoff dependence, which indicates that the single 3N contact is sufficient in this regulator scheme. This does not contradict standard chiral EFT because the absolute-momentum regulator effectively handles the high-momentum contributions differently than soft regulators that lead to overbinding. We will expand the discussion in the results section to explicitly address this point and explain how our approach differs from conventional expectations. revision: no

Circularity Check

0 steps flagged

No significant circularity; extrapolation and regulator effects are demonstrated rather than constructed

full rationale

The paper constrains all LECs strictly to A≤3 data, then performs explicit many-body calculations to obtain binding energies and cutoff dependence up to 40Ca. This is a standard EFT extrapolation test whose outcomes are not forced by the fitting procedure itself. The lattice-inspired absolute-momentum regulator is introduced as an independent technical choice whose UV suppression is verified numerically by comparing cutoff variations; it is not defined in terms of the target cutoff independence. No quoted equation or claim reduces the reported predictions to the input fits by construction, and no self-citation chain is invoked to justify uniqueness or forbid alternatives. The central results therefore remain independent of the fitted inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard chiral EFT power counting, a new regulator, and parameters fitted to light nuclei; no new particles or forces are postulated.

free parameters (1)
  • NLO contact strengths and 3N contact strength
    Determined by fitting to A≤3 binding energies and scattering observables.
axioms (2)
  • domain assumption Chiral EFT power counting remains valid up to NLO for nuclear forces
    Justifies truncation at NLO contacts plus LO OPE without higher-order or many-body terms.
  • ad hoc to paper Absolute-momentum lattice regulator suppresses high-momentum modes without artifacts
    Invoked to explain why cutoff dependence remains small.

pith-pipeline@v0.9.0 · 5486 in / 1469 out tokens · 67570 ms · 2026-05-09T23:01:10.605437+00:00 · methodology

discussion (0)

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Reference graph

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