pith. sign in

arxiv: 1907.03284 · v1 · pith:HD5M3VVHnew · submitted 2019-07-07 · ✦ hep-lat · nucl-th

Nπ-excited state contamination in nucleon 3-point functions using ChPT

Oliver Bar This is my paper

Pith reviewed 2026-05-25 01:20 UTC · model grok-4.3

classification ✦ hep-lat nucl-th
keywords nucleonNπ stateschiral perturbation theoryexcited state contaminationthree-point functionsaxial currentpseudoscalar densityGoldberger-Treiman relation
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The pith

Nπ excited states produce an O(M_N) enhanced contribution to nucleon axial 3-point functions with a relative sign that creates nearly linear time dependence.

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

The paper calculates the Nπ-state contributions to nucleon three-point functions involving the pseudoscalar density and the time component of the axial vector current at leading order in chiral perturbation theory. For the axial current these contributions are enhanced by a factor of the nucleon mass relative to the ground state and contain a relative sign between terms that produces an almost linear dependence on the operator insertion time. For the pseudoscalar density the Nπ contribution varies strongly with momentum transfer and distorts the extracted form factor. The same contaminations produce a violation of the generalized Goldberger-Treiman relation. These results account for specific patterns already seen in lattice data.

Core claim

At leading order in ChPT the Nπ contribution to the axial-vector time-component three-point function is O(M_N) larger than the single-nucleon term; a relative sign between two pieces of the Nπ amplitude produces an approximately linear dependence on the insertion time. The Nπ contribution to the pseudoscalar-density correlator depends strongly on momentum transfer and therefore distorts the pseudoscalar form factor. Both effects together violate the generalized Goldberger-Treiman relation.

What carries the argument

Leading-order chiral perturbation theory evaluation of Nπ excited-state contributions to nucleon three-point correlation functions for the axial current and pseudoscalar density.

If this is right

  • The axial-current three-point functions receive a mass-enhanced Nπ contamination that grows with insertion time separation.
  • Pseudoscalar-density matrix elements acquire a momentum-transfer-dependent distortion that affects extracted form factors.
  • The generalized Goldberger-Treiman relation appears violated in lattice results even when the underlying QCD relation holds.
  • Lattice analyses of nucleon matrix elements must subtract or suppress Nπ states to reach percent-level accuracy on axial and pseudoscalar observables.
  • The linear time dependence provides a diagnostic signature that can be used to identify Nπ contamination in existing data sets.

Where Pith is reading between the lines

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

  • Similar ChPT calculations could be repeated for vector currents or for transition matrix elements between different baryons.
  • The size of the effect is expected to increase as the pion mass is lowered toward the physical point.
  • Operator smearing or variational methods tuned to suppress Nπ overlap may be required for future high-precision runs.
  • The same mechanism may explain analogous linear drifts observed in other baryon three-point functions.

Load-bearing premise

Higher-order corrections in ChPT and contributions from other multi-particle states remain negligible in the kinematic regime and pion masses of present lattice simulations.

What would settle it

A lattice computation at a lighter pion mass or with explicit Nπ subtraction that shows no linear time dependence in the axial three-point functions would falsify the predicted enhancement and sign effect.

Figures

Figures reproduced from arXiv: 1907.03284 by Oliver Bar.

Figure 1
Figure 1. Figure 1: RQCD data [11] for the correlation function ratio R4(~q,t,t 0 ) (red data points) for t = 1.06 fm and the ChPT result (red line) [14]. practice, however, the data are usually excluded for large statistical errors and because of a large excited-state contamination. Examples for R4(~q,t,t 0 ) data can be found in [11, 17], and also in Y.-C. Jang’s contribution to this conference [18]. The ratio R4(~q,t,t 0 )… view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: The relative deviations εA(Q 2 ,t,t 0 ) (circles), εP˜(Q 2 ,t,t 0 ) (diamonds) and εP(Q 2 ,t,t 0 ) (triangles) as a function of Q 2 for t = 2 fm and t 0 = t/2. Discrete Q 2 values for finite spatial volumes satisfying MπL = 6. Right panel: PACS data from [10] for the normalized pseudoscalar form factor G norm P (Q 2 ,Q 2 ref,t) (black) for t = 1.3 fm and Q 2 ref = 0.072GeV2 . Red symbols show t… view at source ↗
Figure 3
Figure 3. Figure 3: Left panel: LO ChPT result for rPCAC(Q 2 ,t) for t = 2 fm (solid symbols) and t = ∞ (open symbols). Right panel: rPCAC(Q 2 ,t), ChPT result (diamonds) compared to PACS data (dots). which is independent of ZP. The right panel in figure 2 shows PACS lattice data [] for this ratio (black symbols) for Q 2 ref = 0.072(2)GeV2 . The red dashed line shows the PPD result for this ratio. Even though the statistical … view at source ↗
read the original abstract

The $N\pi$-state contribution to nucleon 3-pt functions involving the pseudoscalar density $P(x)$ and the time component $A_4(x)$ of the axial vector current are computed to LO in ChPT. In case of the latter the $N\pi$ contribution is O($M_N$) enhanced compared to the single-nucleon ground state contribution. In addition, a relative sign in two terms of the $N\pi$ contribution leads an almost linear dependence on the operator insertion time, as it is observed in lattice data. In case of the pseudoscalar density the $N\pi$ contribution is strongly dependent on the momentum transfer, leading to a distortion of the pseudoscalar nucleon form factor. Finally, the $N\pi$ state contamination in the form factors result in a violation of the generalized Goldberger-Treiman relation as observed in various lattice calculations.

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 manuscript computes the Nπ excited-state contributions to nucleon three-point functions involving the pseudoscalar density P(x) and the time component A4(x) of the axial current at leading order in chiral perturbation theory. It reports an O(M_N) enhancement of the Nπ term relative to the single-nucleon ground state for A4, a relative sign between two Nπ terms that produces nearly linear dependence on the operator insertion time, strong momentum-transfer dependence for the pseudoscalar case that distorts the form factor, and a resulting violation of the generalized Goldberger-Treiman relation.

Significance. If the leading-order results hold, the calculation supplies a parameter-free ChPT explanation for lattice-observed features such as linear t-dependence in axial matrix elements and GT-relation violations. The direct derivation from the standard LO Lagrangian without additional fitted parameters or invented entities is a clear strength and allows falsifiable comparison with existing lattice data.

major comments (2)
  1. [§3] §3 (axial-vector calculation): the O(M_N) enhancement of the Nπ contribution relative to the ground-state term is central to the main claim, yet the explicit ratio of the two contributions is not displayed after the matrix-element expressions are derived; without this comparison the enhancement statement remains qualitative.
  2. [§4] §4 (pseudoscalar case): the claimed strong momentum-transfer dependence and resulting distortion of the pseudoscalar form factor are load-bearing for the GT-relation violation; the manuscript should quantify the size of the Nπ contamination at the momentum transfers used in current lattice simulations to show it is not negligible.
minor comments (2)
  1. The abstract uses the phrase 'in case of the latter' twice; replacing it with explicit references to A4(x) and P(x) would improve readability.
  2. Figure captions should state the specific kinematic points (pion mass, momenta) at which the plotted Nπ contributions are evaluated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and the constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (axial-vector calculation): the O(M_N) enhancement of the Nπ contribution relative to the ground-state term is central to the main claim, yet the explicit ratio of the two contributions is not displayed after the matrix-element expressions are derived; without this comparison the enhancement statement remains qualitative.

    Authors: We agree that an explicit ratio would make the O(M_N) enhancement more transparent. The derived matrix-element expressions allow a direct computation of this ratio, and we will add it (as a function of the relevant kinematic variables) to the revised manuscript. revision: yes

  2. Referee: [§4] §4 (pseudoscalar case): the claimed strong momentum-transfer dependence and resulting distortion of the pseudoscalar form factor are load-bearing for the GT-relation violation; the manuscript should quantify the size of the Nπ contamination at the momentum transfers used in current lattice simulations to show it is not negligible.

    Authors: We agree that a numerical illustration at representative lattice Q² values would strengthen the discussion of the form-factor distortion and GT violation. Because the LO result is parameter-free, such an evaluation is straightforward; we will include it in the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity; direct LO ChPT computation

full rationale

The paper computes Nπ contributions to nucleon 3-point functions at leading order in standard chiral perturbation theory. The O(M_N) enhancement for the axial current and the sign-induced linear t-dependence follow directly from the LO Lagrangian, Feynman rules, and kinematics without any fitted parameters, self-definitional loops, or load-bearing self-citations. No derivation step reduces to an input by construction or to prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard leading-order ChPT Lagrangian for nucleons and pions together with the assumption that Nπ states dominate the excited-state contamination at the pion masses and volumes used in contemporary lattice simulations.

axioms (2)
  • domain assumption Leading-order ChPT is adequate to capture the dominant Nπ contamination
    The paper states it computes to LO in ChPT.
  • domain assumption Nπ states are the primary source of the observed time and momentum dependence
    The abstract attributes the lattice features to Nπ contributions.

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discussion (0)

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Reference graph

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