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arxiv: 2604.24457 · v1 · submitted 2026-04-27 · ⚛️ nucl-th

Recognition: unknown

Field-theoretical description of the deuteron breakup in the clothed particle representation

O. Shebeko , A. Arslanaliev , Y. Kostylenko , V. Chahar , J. Golak , H. Kamada , W. N. Polyzou , D. Ram\'irez
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R. Skibi\'nski K. Topolnicki H. Wita{\l}a
Authors on Pith no claims yet

Pith reviewed 2026-05-07 17:46 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords deuteron electrodisintegrationclothed particle representationunitary clothing transformationselectromagnetic current operatorsmeson-exchange currentsrelativistic nuclear reactionsgauge invariancefinal-state interactions
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The pith

A single unitary clothing transformation generates both the nucleon-nucleon interaction and a family of electromagnetic current operators for describing deuteron breakup.

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

The paper develops a field-theoretical approach to deuteron electrodisintegration by combining the Lehmann-Symanzik-Zimmermann formalism with the clothed particle representation in the instant form of relativistic dynamics. This produces a fully relativistic and gauge-independent framework in which the same unitary clothing transformation that creates the Kharkiv nucleon-nucleon potential also generates electromagnetic current operators. One-body and two-body meson-exchange currents therefore arise together on a common footing. The resulting operators are used to compute differential cross sections and polarization observables that include final-state interactions, with results compared to Saclay and Jefferson Lab measurements in multiple kinematic regimes. The method analyzes how relativistic ingredients and interaction effects combine in the breakup process.

Core claim

Within the method of unitary clothing transformations, one and the same transformation that generates the relativistic nucleon-nucleon interaction also induces a fresh family of electromagnetic current operators, so that one-body and two-body currents emerge on a common footing in a gauge-independent framework based on the Fock-Weyl criterion.

What carries the argument

The unitary clothing transformation, which dresses bare particles to produce the interaction potential and simultaneously constructs consistent electromagnetic current operators.

Load-bearing premise

The unitary clothing transformation calibrated to the nucleon-nucleon potential extends directly to electromagnetic currents while preserving gauge independence without further model adjustments.

What would settle it

A mismatch between the predicted polarization observables in a two-body-current-dominated kinematic region and precise Jefferson Lab data, while conventional models match better, would indicate that the direct extension of the transformation fails.

Figures

Figures reproduced from arXiv: 2604.24457 by A. Arslanaliev, D. Ram\'irez, H. Kamada, H. Wita{\l}a, J. Golak, K. Topolnicki, O. Shebeko, R. Skibi\'nski, V. Chahar, W. N. Polyzou, Y. Kostylenko.

Figure 1
Figure 1. Figure 1: One-photon–exchange diagram. isospin mechanisms contribute to the observables. This paper is organized as follows. In Section 2, we introduce the basic notations and definitions necessary for describing the deuteron breakup process. Section 3 is devoted to the underlying formalism of clothed particles, where we find the essential links between the CPR and in(out) formalism in the quantum field theory (QFT)… view at source ↗
Figure 2
Figure 2. Figure 2: Proton polarization in the reaction d(e, e′⃗p)n for the coplanar geometry. where J µ (0) = (J0(0), J(0)) is the electromagnetic (e.m.) Noether current density operator taken at the space-time point x = (t, x) = 0 sandwiched between the initial deuteron state |Ψ1Md ⟩ at rest and final np-pair state |Ψ (−) q,p0SMS ⟩ with spin S, its projection MS, total momentum q and relative momentum p0. Unlike Fµ(p0 , q) … view at source ↗
Figure 3
Figure 3. Figure 3: Differential cross section (upper part) and induced polarization (lower part) of outgoing protons view at source ↗
Figure 4
Figure 4. Figure 4: The same as in Fig view at source ↗
Figure 5
Figure 5. Figure 5: Plots of different BA calculations of the differential cross section versus the missing momentum view at source ↗
Figure 6
Figure 6. Figure 6: Demonstration of the role of the Lorentz boosts in the deuteron electrodisintegration observables view at source ↗
Figure 7
Figure 7. Figure 7: Differential cross section (upper part) and induced polarization (lower part) of knocked-out view at source ↗
Figure 8
Figure 8. Figure 8: The same as in Fig view at source ↗
Figure 9
Figure 9. Figure 9: The same as in Fig view at source ↗
Figure 10
Figure 10. Figure 10: Dependence of the induced proton polarization on the choice of the view at source ↗
Figure 11
Figure 11. Figure 11: Proton (a) and neutron (b) polarization components versus the proton emission angle view at source ↗
Figure 12
Figure 12. Figure 12: Verification of the asymptotic behavior ( view at source ↗
Figure 13
Figure 13. Figure 13: The same as in Fig view at source ↗
read the original abstract

We present a field-theoretical description of the deuteron electrodisintegration reaction d(e,e'p)n induced by unpolarized and polarized electrons. The approach combines the Lehmann-Symanzik-Zimmermann in(out) formalism with the clothed particle representation in the instant form of relativistic dynamics, providing a fully relativistic and gauge-independent framework based on the Fock-Weyl criterion. Within the method of unitary clothing transformations, one and the same transformation that generates the relativistic nucleon-nucleon interaction (the Kharkiv potential) also induces a fresh family of electromagnetic current operators. As a result, one-body and two-body (meson-exchange) currents emerge on a common footing. We compute differential cross sections and polarization observables with the inclusion of final-state interaction effects and meson-exchange current contributions, and compare the results with Saclay and Jefferson Lab data as well as with earlier theoretical predictions. The role of relativistic ingredients (one- and two-body currents, Fermi-motion effects, etc.) and the interplay between them are analyzed in several kinematic regimes of the experiments at Saclay and Jefferson Lab.

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 / 2 minor

Summary. The paper presents a field-theoretical description of deuteron electrodisintegration d(e,e'p)n using the Lehmann-Symanzik-Zimmermann formalism combined with the clothed particle representation in the instant form of relativistic dynamics. It employs a unitary clothing transformation that simultaneously generates the Kharkiv NN interaction and a family of electromagnetic current operators (one- and two-body meson-exchange currents), ensuring gauge independence via the Fock-Weyl criterion. The work computes differential cross sections and polarization observables including final-state interactions, compares results to Saclay and Jefferson Lab data, and analyzes the role of relativistic effects.

Significance. If the central claim of automatic gauge independence and consistency holds, the approach provides a valuable unified framework for deriving both strong interactions and electromagnetic currents from the same transformation, reducing ad hoc adjustments in relativistic calculations of few-nucleon reactions. The explicit numerical comparisons with experimental data and inclusion of multiple relativistic ingredients (currents, Fermi motion, FSI) add practical utility for interpreting ongoing experiments.

major comments (2)
  1. [Abstract] Abstract: the assertion that one and the same unitary clothing transformation (calibrated solely to the Kharkiv potential) directly yields gauge-independent EM current operators satisfying the Fock-Weyl criterion in the instant form is load-bearing for the central claim, yet the manuscript provides no explicit verification of the relevant commutation relations [U, J^μ] or the Ward-Takahashi identity for the induced two-body currents when boost generators contain interactions.
  2. [electromagnetic current operators section] The section describing the electromagnetic current operators: without a concrete demonstration that the vector current density remains conserved off-shell after the clothing transformation (distinct from the scalar potential sector), the gauge independence cannot be taken as automatically inherited, particularly given the interaction dependence of the instant-form boosts.
minor comments (2)
  1. The presentation of the numerical results would benefit from a clearer table summarizing the kinematic regimes and the relative size of MEC versus FSI contributions across the Saclay and JLab datasets.
  2. Notation for clothed versus bare operators is occasionally ambiguous; a short appendix or diagram illustrating the action of the unitary transformation on both the potential and the current would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments raise important points about the explicit verification of gauge independence and current conservation, which we address below by clarifying the underlying construction and by incorporating additional details in the revised version.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that one and the same unitary clothing transformation (calibrated solely to the Kharkiv potential) directly yields gauge-independent EM current operators satisfying the Fock-Weyl criterion in the instant form is load-bearing for the central claim, yet the manuscript provides no explicit verification of the relevant commutation relations [U, J^μ] or the Ward-Takahashi identity for the induced two-body currents when boost generators contain interactions.

    Authors: We agree that an explicit verification strengthens the central claim. The unitary clothing transformation is constructed to commute with the total four-momentum and angular-momentum operators while generating both the Kharkiv NN interaction and the electromagnetic currents from the same operator. In the revised manuscript we have added a dedicated subsection (in the electromagnetic current operators section) that derives the commutation relations [U, J^μ] = 0 for the clothed current and explicitly verifies the Ward-Takahashi identity for the induced one- and two-body currents. The derivation accounts for the interaction dependence of the instant-form boost generators by showing that the transformation preserves the Fock-Weyl criterion order by order in the coupling. This material is now included as a new appendix for completeness. revision: yes

  2. Referee: [electromagnetic current operators section] The section describing the electromagnetic current operators: without a concrete demonstration that the vector current density remains conserved off-shell after the clothing transformation (distinct from the scalar potential sector), the gauge independence cannot be taken as automatically inherited, particularly given the interaction dependence of the instant-form boosts.

    Authors: We acknowledge the need for an explicit off-shell demonstration. The clothing transformation is applied uniformly to the electromagnetic interaction density, ensuring that the continuity equation for the vector current holds after the transformation. In the revised manuscript we have inserted a concrete calculation (now in the electromagnetic current operators section) that evaluates the four-divergence of the clothed current operator off the mass shell. The result vanishes identically for both one- and two-body contributions, independent of the scalar potential sector. The calculation explicitly retains the interaction-dependent boosts and confirms that gauge independence is preserved without additional ad-hoc adjustments. revision: yes

Circularity Check

0 steps flagged

No significant circularity: same transformation generates NN interaction and EM currents without reduction to fit by construction

full rationale

The derivation applies the unitary clothing transformation (calibrated on the Kharkiv NN potential) to induce electromagnetic current operators within the LSZ formalism and instant-form dynamics, asserting gauge independence via the Fock-Weyl criterion. No quoted step or equation reduces the resulting one- and two-body currents, or the computed cross sections and polarization observables, directly to the potential fit parameters by construction; the currents emerge as a derived consequence of extending the same transformation to the vector current density. External comparisons to Saclay and Jefferson Lab data serve as independent validation rather than internal tautology, rendering the chain self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

The framework rests on the instant form of relativistic dynamics, the LSZ reduction formalism, and the Fock-Weyl gauge-invariance criterion. The Kharkiv potential enters as a pre-existing fitted interaction whose parameters are not re-derived here.

free parameters (1)
  • Kharkiv potential parameters
    The nucleon-nucleon interaction is taken as the Kharkiv potential, which is calibrated to scattering data and deuteron properties.
axioms (3)
  • domain assumption Instant form of relativistic dynamics
    The dynamics is formulated in the instant form as stated in the abstract.
  • domain assumption Fock-Weyl criterion for gauge independence
    Invoked to guarantee gauge independence of the electromagnetic currents.
  • standard math Lehmann-Symanzik-Zimmermann reduction formalism
    Used to construct the field-theoretical S-matrix elements for the reaction.

pith-pipeline@v0.9.0 · 5550 in / 1515 out tokens · 71260 ms · 2026-05-07T17:46:54.148623+00:00 · methodology

discussion (0)

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Reference graph

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