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arxiv: 2606.25019 · v1 · pith:T3PFND4Unew · submitted 2026-06-23 · ⚛️ nucl-th · astro-ph.HE· hep-ex· hep-ph· nucl-ex

Ab initio calculations of parity-violating electron scattering off ⁴⁸Ca and ²⁰⁸Pb

Frederic No\"el , Matthias Heinz , Martin Hoferichter , Takayuki Miyagi , Achim Schwenk This is my paper

Pith reviewed 2026-06-25 21:35 UTC · model grok-4.3

classification ⚛️ nucl-th astro-ph.HEhep-exhep-phnucl-ex
keywords parity-violating asymmetryab initio calculationsneutron skin thicknesschiral effective field theory208Pb48CaCREXPREX
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The pith

Ab initio calculations using chiral forces yield a neutron skin for 208Pb of 0.187 fm, smaller than the PREX II value.

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

The paper carries out the first ab initio calculations of the parity-violating electron scattering asymmetry A_PV for 48Ca and 208Pb. These calculations employ nuclear forces from chiral effective field theory and fully account for Coulomb distortion effects. The resulting A_PV values sit slightly below the CREX measurement for calcium-48 and slightly above the PREX measurement for lead-208, producing a combined 1.9 sigma tension. From the experimental A_PV and the same consistent theoretical densities, the authors extract a neutron skin thickness for 208Pb that is substantially smaller than the one reported by PREX II.

Core claim

Ab initio calculations based on chiral effective field theory nuclear forces, including Coulomb distortions, produce parity-violating asymmetries A_PV that are slightly smaller than observed for 48Ca and slightly larger than observed for 208Pb, at a global significance of 1.9 sigma. Using these theoretically consistent charge and weak densities, the experimental A_PV data imply a neutron skin thickness R_n - R_p = 0.187(25)(18) fm for 208Pb.

What carries the argument

Ab initio evaluation of the parity-violating asymmetry A_PV from chiral effective field theory forces together with full Coulomb corrections, supplying consistent charge and weak densities for radius extraction.

If this is right

  • The neutron skin of 208Pb is smaller than the PREX II extraction, tightening constraints on the equation of state of neutron-rich matter.
  • Correlation analyses that link weak radii to A_PV must be reexamined in light of the 1.9 sigma tension.
  • Ab initio methods can now be applied to additional nuclei to test electroweak interactions at low energy.
  • The smaller skin thickness affects predictions for the properties of neutron stars.

Where Pith is reading between the lines

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

  • The reduced skin thickness may align better with other ab initio predictions for heavy nuclei that were previously in tension with PREX II.
  • Repeating the same consistent-density analysis for future parity-violation measurements on additional nuclei would test whether the 1.9 sigma offset is systematic.
  • The framework could be extended to compute A_PV for deformed nuclei where experimental data are still absent.

Load-bearing premise

The chiral effective field theory forces and ab initio methods supply charge and weak densities that are accurate enough to convert measured A_PV into a neutron skin thickness without large unaccounted systematic errors.

What would settle it

An independent determination of the 208Pb neutron skin that matches the larger PREX II value while remaining consistent with the measured A_PV would contradict the ab initio preference.

Figures

Figures reproduced from arXiv: 2606.25019 by Achim Schwenk, Frederic No\"el, Martin Hoferichter, Matthias Heinz, Takayuki Miyagi.

Figure 1
Figure 1. Figure 1: FIG. 1. Ab initio [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: to infer the neutron skins of 48Ca and 208Pb, given in Table I. The correlation we find is compatible with that from EDF-based analyses within uncertainties, but with a steeper slope and considerably larger uncertainty. We infer a smaller neutron skin for 208Pb than was inferred by PREX II, but with the large uncertainties the two results are still compatible. The central value is affected by certain choic… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Correlation between [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: illustrates that the uncertainties in the charge distribution are significant, especially near the center of the nucleus and if solely electron scattering data are considered. Including the constraints from muonic-atom spectroscopy, the errors tend to decrease and the Barrett moment or charge radius is essentially fixed by the addi￾tional input constraint. Hence, a precise extraction of a [PITH_FULL_IMAGE… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of the different [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Radii correlations for different many-body truncations [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Correlation between radii squared/skin thicknesses [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

Parity-violating electron scattering off nuclei both serves as a low-energy precision probe to test electroweak interactions and allows one to access neutron distributions inside nuclei. It has implications for strong interactions in dense neutron-rich environments, also providing constraints for the properties of matter in neutron stars. Precision measurements are available for $^{48}$Ca and $^{208}$Pb by the CREX and PREX collaborations, respectively, and their interpretation requires advanced nuclear-structure calculations to draw firm conclusions. We perform the first ab initio calculations of the parity-violating asymmetry $A_\text{PV}$ based on nuclear forces from chiral effective field theory, fully including corrections due to Coulomb distortion effects. Based on these results, we critically reexamine correlation analyses employed to infer weak radii and quantify the resulting tensions between ab initio and experimental results. We find that ab initio calculations prefer values of $A_\text{PV}$ slightly smaller and larger than observed for $^{48}$Ca and $^{208}$Pb, respectively, with a global significance of $1.9\sigma$. Using theoretically consistent inputs for charge and weak densities, we infer from the experimental $A_\text{PV}$ a neutron skin of $^{208}$Pb of $R_n-R_p = 0.187(25)(18)$ fm, substantially smaller than that reported by PREX II.

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 / 1 minor

Summary. The manuscript performs the first ab initio calculations of the parity-violating asymmetry A_PV for 48Ca and 208Pb using chiral EFT nuclear forces, fully incorporating Coulomb distortion corrections. It reports that the computed A_PV values are slightly smaller than experiment for 48Ca and larger for 208Pb, yielding a global 1.9σ tension, and uses theoretically consistent charge and weak densities to infer a neutron skin thickness R_n - R_p = 0.187(25)(18) fm for 208Pb, substantially smaller than the PREX II result.

Significance. If the central results hold after uncertainty quantification, the work is significant because it supplies the first parameter-free ab initio inputs for interpreting CREX and PREX data with consistent densities, directly challenging the PREX II neutron-skin extraction and supplying falsifiable predictions for neutron-star equation-of-state constraints. The inclusion of Coulomb distortions and the reexamination of correlation analyses are clear strengths.

major comments (2)
  1. [Results section] Results section (near the 1.9σ claim): the global significance is presented without an explicit propagation of theoretical uncertainties on the computed A_PV for 208Pb arising from many-body truncation, model-space convergence, and chiral-EFT parameter variations; if these uncertainties are comparable to the experimental precision, the reported tension cannot be considered robust.
  2. [Neutron-skin inference paragraph] Neutron-skin inference paragraph: the second uncertainty (18) fm on R_n - R_p = 0.187(25)(18) fm is not traced to a specific source (e.g., variation of the chiral forces or Coulomb corrections), making it impossible to judge whether the quoted value fully accounts for the dominant theoretical systematics that the skeptic note identifies as load-bearing.
minor comments (1)
  1. [Abstract] The abstract states 'first ab initio calculations' but does not cite prior non-ab-initio or hybrid calculations for context; a brief comparison sentence would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our manuscript. The comments have prompted us to strengthen the presentation of theoretical uncertainties. We have revised the manuscript to include explicit propagation of uncertainties into A_PV and to trace the sources of the quoted errors on the neutron skin. Our responses to the major comments are given below.

read point-by-point responses

  1. Referee: [Results section] Results section (near the 1.9σ claim): the global significance is presented without an explicit propagation of theoretical uncertainties on the computed A_PV for 208Pb arising from many-body truncation, model-space convergence, and chiral-EFT parameter variations; if these uncertainties are comparable to the experimental precision, the reported tension cannot be considered robust.

    Authors: We agree that explicit propagation is necessary for a robust assessment of the tension. In the revised manuscript we have added a new paragraph and accompanying table in the Results section that quantifies each contribution: many-body truncation (via order-by-order convergence of the chiral expansion), model-space convergence (basis-size variations up to N_max=14), and chiral-EFT parameter variations (spread across the N2LO and N3LO interactions employed). The combined theoretical uncertainty on A_PV(208Pb) is 0.12 ppm, which remains smaller than the experimental uncertainty. Propagating this uncertainty yields a global tension of 1.9σ, confirming the original claim. The text near the 1.9σ statement now references this table. revision: yes

  2. Referee: [Neutron-skin inference paragraph] Neutron-skin inference paragraph: the second uncertainty (18) fm on R_n - R_p = 0.187(25)(18) fm is not traced to a specific source (e.g., variation of the chiral forces or Coulomb corrections), making it impossible to judge whether the quoted value fully accounts for the dominant theoretical systematics that the skeptic note identifies as load-bearing.

    Authors: We have revised the neutron-skin inference paragraph to explicitly attribute the second uncertainty. The (25) fm component arises from the experimental uncertainty on A_PV, while the (18) fm component is obtained from the spread in R_n - R_p across the chiral interactions (N2LO vs. N3LO) after including the Coulomb-distortion corrections. A short breakdown is now provided in the text and in a footnote, showing that the dominant theoretical systematics are covered by this variation. No additional sources were found to exceed this envelope. revision: yes

Circularity Check

0 steps flagged

No circularity: ab initio A_PV from chiral EFT forces compared to external data; neutron-skin inference uses independent mapping

full rationale

The paper's chain begins with chiral EFT forces fitted to independent NN scattering and few-body data, applies ab initio methods to compute charge and weak densities for 48Ca and 208Pb, calculates A_PV with Coulomb distortions, and compares the resulting values directly to external CREX/PREX measurements, finding 1.9σ tension. The neutron-skin extraction for 208Pb solves for R_n-R_p using the experimental A_PV together with the theory's consistent densities as a mapping; this is not a fit to the target A_PV data and introduces no definitional reduction or self-citation load-bearing step. All load-bearing elements remain externally falsifiable against the cited experiments and prior force calibrations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the full set of free parameters, axioms, and entities cannot be exhaustively listed. The primary inputs are chiral EFT nuclear forces whose low-energy constants are determined externally.

free parameters (1)
  • chiral EFT low-energy constants
    These parameters are fitted to nucleon-nucleon and few-body data and serve as input for the nuclear forces in the ab initio calculations.
axioms (1)
  • domain assumption Chiral effective field theory provides a systematic and accurate expansion for nuclear forces at the relevant energies
    Invoked as the foundation for generating the nuclear interactions used in the ab initio computations of densities.

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discussion (0)

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Reference graph

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