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arxiv: 2605.05418 · v1 · submitted 2026-05-06 · ⚛️ nucl-th

Recognition: unknown

Axial-vector Current and General Unpolarized Electroweak Single-nucleon Responses

Sabine Jeschonnek, T. W. Donnelly

Authors on Pith no claims yet

Pith reviewed 2026-05-08 15:37 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords axial-vector currentelectroweak responsessingle-nucleon form factorsunpolarized nucleonvector-axial interferenceweak interactionsnuclear responses
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The pith

The axial-vector current matrix element is developed in full to yield the complete set of unpolarized electroweak VV, AA and VA response functions.

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

This work extends an earlier treatment of the electromagnetic vector current by constructing the axial-vector current for a single nucleon. The general expressions for all three classes of electroweak response functions are obtained and combined with various approximation schemes whose ranges of validity are explored numerically. The resulting framework clarifies how the individual single-nucleon form factors enter weak-interaction observables both for free nucleons and when the standard nuclear-physics prescription is applied to nucleons inside nuclei.

Core claim

The axial-vector single-nucleon current matrix element is derived in detail and joined to the vector current to produce the general forms of the VV, AA and VA response functions; approximation schemes are introduced and tested numerically to identify the kinematic domains where they remain reliable, thereby supplying the basis for understanding the roles of the various single-nucleon form factors in weak reactions on free nucleons and in nuclei.

What carries the argument

The axial-vector single-nucleon current matrix element, which together with the vector current generates the full set of electroweak response functions.

If this is right

  • The individual contributions of the weak form factors to free-nucleon reactions become transparent.
  • The standard nuclear prescription can be applied to bound-nucleon responses with quantified reliability limits.
  • Kinematic regions are identified where simpler approximations suffice for practical calculations.
  • The unpolarized baseline is established for future polarized extensions.

Where Pith is reading between the lines

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

  • The same machinery could be used to reassess neutrino-nucleus scattering models that rely on the same free-nucleon inputs.
  • Experimental tests in muon-capture or beta-decay kinematics would directly probe the axial-vector approximations.
  • Extension to polarized targets would follow the pattern already laid out for the vector case.

Load-bearing premise

The chosen approximation schemes remain valid across the kinematic regimes of interest and the standard nuclear-physics prescription maps free-nucleon responses onto bound nucleons without large uncontrolled corrections.

What would settle it

A direct numerical comparison of the approximated response functions against exact calculations or measured cross sections at momentum transfers where the approximations are expected to degrade.

Figures

Figures reproduced from arXiv: 2605.05418 by Sabine Jeschonnek, T. W. Donnelly.

Figure 1
Figure 1. Figure 1: FIG. 1. Kinematics for charge-changing neutrino or anti-neutrino reactions with single nucleons. view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The axial form factor view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The AA responses are shown as functions of view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The AA responses are shown as functions of view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The VA responses are shown as functions of view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The AA responses are shown as functions of view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The AA responses are shown as functions of view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The VA responses are shown as functions of view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The AA responses are shown as functions of view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Various dimensionless kinematic variables are shown as functions of view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The AA responses are shown as functions of view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The AA responses are shown as functions of view at source ↗
read the original abstract

The present study provides an extension to our recent work on the vector (V) electromagnetic single-nucleon current and associated response functions, both for unpolarized situations and in situations where the target nucleon is polarized. Here the axial-vector (A) single-nucleon current matrix element is developed in detail and the full set of vector and axial-vector currents used to obtain the electroweak VV, AA and VA response functions. Only the unpolarized case is studied in the present work. The general forms for all of these elements are developed together with various approximation schemes in which numerical studies are provided to indicate where these approximations may be expected to be valid. The results of this work provide the basis for a deeper understanding of the roles played by the various single-nucleon form factors in weak interaction reactions on free nucleons and when using the standard ``prescription for nuclear physics'' in reactions involving nucleons in 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 / 2 minor

Summary. The manuscript extends the authors' prior vector-current treatment to the axial-vector sector, deriving the general Lorentz-covariant matrix element of the axial-vector current for a free nucleon. This is combined with the vector current to obtain the complete set of unpolarized electroweak response functions (VV, AA, and VA). General expressions are presented together with controlled approximation schemes whose ranges of validity are explored through numerical examples; the results are intended to clarify the roles of individual single-nucleon form factors in free-nucleon weak processes and under the standard nuclear-physics prescription for bound nucleons.

Significance. If the central derivations are free of algebraic error, the work supplies a systematic, reference-grade framework for electroweak single-nucleon responses that can be directly inserted into nuclear calculations. The explicit separation of form-factor contributions, the controlled approximations, and the accompanying numerical diagnostics constitute a clear advance over piecemeal treatments in the literature and should be useful for neutrino-nucleus scattering and related electroweak observables.

major comments (1)
  1. [§4] §4 (or equivalent section containing the response-function definitions): the mapping from the free-nucleon responses to the nuclear case via the standard prescription is stated without a quantitative estimate of the size of the corrections that arise from Fermi motion, binding, or final-state interactions; because this mapping is central to the claimed utility for nuclear reactions, an explicit error budget or reference to a controlled test case would be required to support the final sentence of the abstract.
minor comments (2)
  1. The notation for the axial form factors (G_A, G_P, etc.) should be cross-referenced to the vector form-factor conventions used in the earlier vector-only paper to avoid reader confusion.
  2. Figure captions for the numerical studies should state the precise kinematic cuts and the value of the axial mass employed, rather than leaving these details only in the text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the positive overall assessment. We address the single major comment below.

read point-by-point responses

  1. Referee: [§4] §4 (or equivalent section containing the response-function definitions): the mapping from the free-nucleon responses to the nuclear case via the standard prescription is stated without a quantitative estimate of the size of the corrections that arise from Fermi motion, binding, or final-state interactions; because this mapping is central to the claimed utility for nuclear reactions, an explicit error budget or reference to a controlled test case would be required to support the final sentence of the abstract.

    Authors: We agree that the abstract's reference to the standard nuclear-physics prescription would be strengthened by explicit context on its limitations. The central aim of the present work is the derivation of the general unpolarized VV, AA, and VA response functions together with controlled approximations at the free-nucleon level; the nuclear prescription is invoked only as the conventional bridge to bound-nucleon applications. To address the concern, we will revise the manuscript by adding a concise paragraph (in the conclusions or a dedicated subsection) that references existing literature quantifying the typical sizes of Fermi-motion, binding, and final-state-interaction corrections in electroweak nuclear processes. This addition will support the abstract without changing the core single-nucleon results or requiring new calculations. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to prior vector-current work; axial derivation independent

full rationale

The paper extends the authors' recent vector-current treatment by deriving the axial-vector single-nucleon current matrix element from standard Lorentz-covariant decomposition and electroweak form-factor parametrizations. VV, AA, and VA responses are then assembled from the combined currents, with approximation schemes whose validity is checked numerically. The self-citation is confined to the vector sector and is not load-bearing for the axial results or the claimed basis for understanding form-factor roles. No step reduces by construction to a fitted input, self-definition, or unverified self-citation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard electroweak current structure and on the authors' earlier vector-current derivation. No new particles or forces are postulated. The single-nucleon form factors are treated as external inputs taken from prior literature rather than fitted here.

free parameters (1)
  • single-nucleon form factors
    These are external inputs from experiment or prior parametrizations; the present work does not determine or refit their values.
axioms (2)
  • standard math Standard Lorentz-covariant decomposition of nucleon currents into vector and axial-vector form factors
    Invoked when constructing the general matrix elements for the axial-vector current.
  • domain assumption Validity of the impulse approximation when embedding free-nucleon responses into nuclei
    Underlying the use of the standard nuclear-physics prescription mentioned in the abstract.

pith-pipeline@v0.9.0 · 5456 in / 1473 out tokens · 78715 ms · 2026-05-08T15:37:19.930060+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

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    The functionsν 0,etc.are all real and have been derived previously in [1]

    (u′ 2 ·σ)u ′ 1},(18) and accordingly V 0 =ν 0 +iν ′ 0σ2′ (19) V 1′ =ν 1 +iν ′ 1σ2′ (20) V 2′ =−i h ν′ 2σ1′ +ν ′′ 2 σ3′ i (21) V 3′ = λ κ V 0,(22) the last arising from the continuity equation. The functionsν 0,etc.are all real and have been derived previously in [1]. They are ν0 = κ√τ GE + µ1µ2 2(1 +τ) τ GM δ2 ν′ 0 = κ√1 +τ µ1GM − 1 2 µ2GE δ ν1 = 1√1 +τ µ...

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    = 2 κ2 τ λ κ G′2 A +G 2 Aδ2 W T AA =f 2 0 [(γ2 2 +γ ′2 2 ) + (γ′2 1 +γ ′2 3 )] = [2(1 +τ) +δ 2]G2 A W T T AA =f 2 0 [(γ2 2 +γ ′2 2 )−(γ ′2 1 +γ ′2 3 )] cos 2ϕ=−δ 2G2 A cos 2ϕ W T C AA ≡2 √ 2W 01 AA = 2 √ 2f 2 0 (β′ 1γ′ 1 +β ′ 3γ′

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    In this sense the choice ofG ′ A made above is analogous to the definition of the Sachs form factors

    cosϕ= 2 √ 2 λ κ ¯ϵG2 Aδcosϕ.(55) Note that only the combinationsG 2 A andG ′2 A occur here with no interference terms pro- portional toG AG′ A; a similar situation was found in discussing the purely vector current 17 operators (see above), where in that case only contributions proportional toG 2 E andG 2 M enter with no interference terms proportional toG...

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    sinϕ = 2 √ 2κGM GAδsinϕ W T L′ V A ≡ −2 √ 2Im(W 32 V A) sinϕ= λ κ W T C′ V A = 2 √ 2Im(W 23 V A) sinϕ= 2 √ 2f 2 0 (ν′ 2β′′ 1 +ν ′′ 2 β′′

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    sinϕ = 2 √ 2λGM GAδsinϕ .(56) The other terms,W T ′ AV ,W T C′ AV andW T L′ AV are easily obtained either directly or using the sym- metry in the tensors. Here only the combinationG M GA occurs, with no terms proportional toG M G′ A,G EGA orG EG′ A. All other responses are zero (see [11, 12] for some discussions of TRE/TRO responses; here only TRE respons...

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    The responsesW CC AA , W LL AA andW CL AA now have a distinct difference between theG A-only and full result. This difference is particularly pronounced for the two latter responses. In the expression forW LL AA ,G ′2 A appears by itself, whereasG A is multiplied not just byδ 2, but also by the factor (λ/κ)2, which is less than one for spacelike kinematic...

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