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arxiv: 2606.07829 · v1 · pith:WVBKFHYYnew · submitted 2026-06-05 · ⚛️ nucl-th · hep-ph

Clustering in hadrons and light nuclei from Lorentz boosted form factors

F.E. Rodr\'iguez Barrera , N. G. Kelkar This is my paper

Pith reviewed 2026-06-27 20:05 UTC · model grok-4.3

classification ⚛️ nucl-th hep-ph
keywords nuclear charge radiiLorentz boosted form factorscluster structureelectron scatteringmuonic spectroscopylight nucleiBreit framerelativistic formalisms
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The pith

Lorentz boosting form factors from the Breit to the rest frame reconciles charge radius discrepancies in light nuclei and reveals quark and nucleon cluster configurations.

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

The paper addresses the persistent mismatch between nuclear charge radii measured via electron scattering and those obtained from muonic spectroscopy in light nuclei and the proton. It applies Lorentz boosts to the form factors using the Licht-Pagnamenta and Mitra-Kumari relativistic formalisms to transform results from the Breit frame into the nuclear rest frame. This transformation corrects the moments of the charge density distributions. The boosted form factors reduce the observed discrepancy and simultaneously indicate the presence of quark clusters in hadrons and nucleon clusters in nuclei. A sympathetic reader cares because accurate radii constrain models of nuclear structure and because clustering insights affect how internal configurations of matter are pictured.

Core claim

By applying two distinct relativistic formalisms, namely the Licht-Pagnamenta and Mitra-Kumari approaches, boosting the form factors from the Breit to the rest frame of the nucleus not only assists in reconciling the spectroscopic and scattering measurements but also provides a method to infer on the quark and nucleon cluster configurations within nuclei.

What carries the argument

Lorentz boost of nuclear form factors from Breit frame to rest frame, which corrects moments of density distributions.

If this is right

  • The boosted form factors bring electron scattering radii closer to muonic spectroscopy values for light nuclei.
  • The same boosting procedure can be used to extract information on quark clustering inside hadrons.
  • Nucleon cluster configurations inside light nuclei become accessible through analysis of the corrected density moments.
  • Consistent results from the two relativistic formalisms support the reliability of the frame transformation for clustering studies.

Where Pith is reading between the lines

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

  • The method might be extended to test whether similar frame corrections affect radius extractions in medium-mass nuclei.
  • If clustering signatures appear consistently, models that treat nuclei as collections of nucleons could be refined to include explicit quark substructure.
  • The approach could connect to other frame-dependent observables such as momentum distributions measured in scattering experiments.

Load-bearing premise

The discrepancy between electron-scattering and muonic-spectroscopy radii is dominantly caused by the Breit-to-rest-frame difference in the form factor rather than by other effects such as higher-order corrections or experimental systematics.

What would settle it

A calculation of boosted radii in a light nucleus that leaves a large residual mismatch with the spectroscopic value after applying either formalism would show the boost does not resolve the discrepancy.

Figures

Figures reproduced from arXiv: 2606.07829 by F.E. Rodr\'iguez Barrera, N. G. Kelkar.

Figure 1
Figure 1. Figure 1: Graph of the expected correction for several nuclei as a function of the number of nucleons [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
read the original abstract

The determination of nuclear charge radii is crucial for understanding the internal structure of nuclei and their fundamental interactions. A persistent discrepancy, not only in the measured proton charge radius but also in the light nucleus charge radius, between electron scattering and muonic spectroscopy has fueled ongoing debates in nuclear and particle physics. Using this discrepancy, we revisit the role of one of the proposed solutions, namely the use of Lorentz-boosted nuclear form factors to find a subtle connection between the boost and the cluster structure of nuclei. By applying two distinct relativistic formalisms, namely the Licht-Pagnamenta and Mitra-Kumari approaches, we systematically analyze corrections to the moments of the density distributions in hadrons and nuclei. Our results demonstrate that boosting the form factors from the Breit to the rest frame of the nucleus not only assists in reconciling the spectroscopic and scattering measurements but also provides a method to infer on the quark and nucleon cluster configurations within nuclei.

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

1 major / 0 minor

Summary. The manuscript claims that Lorentz boosting of nuclear form factors from the Breit frame to the rest frame, implemented via the Licht-Pagnamenta and Mitra-Kumari relativistic formalisms, produces corrections to the moments of the charge density distributions. These corrections are argued to assist in reconciling the discrepancy between electron-scattering and muonic-spectroscopy determinations of charge radii in the proton and light nuclei, while simultaneously providing a diagnostic for quark and nucleon cluster configurations inside nuclei.

Significance. If the boost corrections are shown to be of the correct magnitude to account for the observed radius discrepancies and the formalism is demonstrated to distinguish cluster structures in a falsifiable manner, the work would offer a potential kinematic resolution to a persistent experimental tension in nuclear physics and supply a new interpretive link between form-factor data and internal nuclear structure.

major comments (1)
  1. [Abstract] Abstract: the central claim that boosting 'assists in reconciling the spectroscopic and scattering measurements' is not supported by a quantitative size comparison. The analysis shows that the Breit-to-rest-frame transformation produces some correction to the moments, but the manuscript does not report the magnitude of this correction relative to the experimental radius discrepancy (several percent in light systems) or demonstrate that it dominates over higher-order QED, two-photon exchange, or experimental systematics.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive feedback. We address the single major comment below and will incorporate revisions to strengthen the quantitative support for our claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that boosting 'assists in reconciling the spectroscopic and scattering measurements' is not supported by a quantitative size comparison. The analysis shows that the Breit-to-rest-frame transformation produces some correction to the moments, but the manuscript does not report the magnitude of this correction relative to the experimental radius discrepancy (several percent in light systems) or demonstrate that it dominates over higher-order QED, two-photon exchange, or experimental systematics.

    Authors: We agree that the abstract would benefit from explicit numerical context. The manuscript calculates boost corrections to moments via the Licht-Pagnamenta and Mitra-Kumari formalisms and links them to cluster structure, but does not tabulate the percentage size of those corrections against the known electron-scattering versus muonic-atom radius differences. In revision we will add a short quantitative subsection (and update the abstract) that reports the fractional corrections for the proton and selected light nuclei, directly comparing them to the several-percent experimental tension. We will also clarify that the work presents the kinematic boost as one contributing mechanism rather than asserting dominance over two-photon exchange or higher-order QED effects; those remain separate systematic considerations outside the scope of the present kinematic analysis. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies external relativistic formalisms to data discrepancies without self-referential reduction.

full rationale

The paper motivates its analysis from an observed experimental discrepancy between electron scattering and muonic spectroscopy radii, then applies the Licht-Pagnamenta and Mitra-Kumari relativistic formalisms (cited as prior independent work) to compute boost corrections to form-factor moments. No equations or steps in the abstract or described method reduce a claimed prediction or cluster inference to a fitted parameter or self-citation by construction; the boost effect is computed from the formalisms and compared to data. The central claim is an interpretive conclusion from those computations rather than a definitional or fitted tautology. This is the normal case of an independent analysis grounded in external methods and observables.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no specific free parameters, axioms, or invented entities can be extracted. The work appears to rest on the standard assumptions of the two named relativistic formalisms and on the premise that frame boosting is the dominant source of the radius discrepancy.

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discussion (0)

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Reference graph

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