Pith. sign in

REVIEW 2 major objections 3 minor 60 references

Systematic study of large-momentum distribution in nuclei with the operator product expansion

T0 review · 2 major / 3 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper shows that combining the operator product expansion with Pionless effective field theory reproduces the deuteron's high-momentum distribution to a few percent once Wilson coefficients are fixed by matching nucleon-nucleon…

desk verdict Solid OPE+Pionless-EFT matching scheme with a clean toy model, but the AV18 few-percent claim needs a D-wave accounting and sensitivity analysis before it is convincing. read the letter →

arxiv 2501.00283 v2 pith:4LKUBVZJ submitted 2024-12-31 nucl-th

Jiexin Yu , Bingwei Long This is my paper · ORCID
classification nucl-th
keywords operatorproductexpansionnucleonmomentumdistributionPionlesseffectivefieldtheoryshort-rangecorrelationsdeuteronWilsoncoefficientsAV18potentialnuclearEFT
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that the operator product expansion (OPE), combined with Pionless effective field theory, gives a systematic way to compute the large-momentum part of the single-nucleon momentum distribution in nuclei, the part governed by short-range nucleon-nucleon correlations. Its central move is to fix the OPE's Wilson coefficients not in the bound state but in low-energy nucleon-nucleon scattering states, where the matrix elements can be calculated both exactly in an underlying potential model and in the effective field theory. Matching the two at small momenta determines coefficients that are independent of the external state, so the same coefficients can later be used for other nuclei. Tested on the deuteron, the OPE/EFT expression reproduces the AV18 momentum distribution to within a few percent for $k>250$ MeV, and a separable toy model shows the expansion organizes into powers of $1/(ak)$ and $1/(aM_{\mathrm{hi}})$. A reader should care because this offers a parameter-free route from soft nuclear interactions to hard-probe observables such as short-range correlations.

What carries the argument

The load-bearing object is the OPE of the nonlocal nucleon-pair operator $\Omega(\vec{k})$ whose expectation value defines the single-nucleon momentum distribution. For short separation, the paper expands this operator into local Pionless EFT operators, the leading ones being the one-body density $N^\dagger N$ and the two-body contact operators $O_0(^3S_1)$ and $O_2(^3S_1)$, with Fourier-transformed Wilson coefficients $\widetilde W_n(k)$. The coefficients are determined by matching the exact potential-model matrix elements $A(k,p)$ to the EFT matrix elements $M_n(p)$ through Eqs. (85)-(88), using the renormalized matrix elements $M_{R0}$ and $M_{R2}$ and the deuteron expectation values of the renormalized operators. The expansion is a double series in $1/(ak)$, controlled by higher-dimension operators, and $1/(aM_{\mathrm{hi}})$, controlled by higher-order EFT corrections to the Wilson coefficients.

What would settle it

Repeat the matching while including the $^3D_1$ component of the deuteron or the $O_2(SD)$ mixing operator; if the OPE/EFT prediction for $\rho(k)$ shifts by more than the claimed few percent over $k=250$-$600$ MeV, the S-wave-only operator basis is insufficient.

Watch

Extended reading notes

Core claim

The central claim is that the large-momentum single-nucleon momentum distribution $\rho(k)$ can be written as an OPE of the nonlocal operator $\Omega(\vec{k})=\int d^3r\,e^{-i\vec{k}\cdot\vec{r}}N^\dagger(-\vec{r}/2)N(\vec{r}/2)$ into local Pionless EFT operators, with state-independent Wilson coefficients $\widetilde W_n(k)$. These coefficients are fixed by matching the exact matrix elements of $\Omega(\vec{k})$ between $^3S_1$-$^3D_1$ nucleon-nucleon scattering states computed from the underlying potential against the same matrix elements computed in Pionless EFT, at the soft momenta $p_1=4$ MeV and $p_2=5$ MeV. The resulting OPE/EFT expression reproduces the AV18 deuteron momentum distribution at the few-percent level for $k>250$ MeV, and the numerical results show that the next-to-leading-order EFT correction to the leading operator matters more than adding the next operator $O_2$ in the kinematic region studied. The same matching logic is demonstrated analytically in a separable toy model, where the OPE/EFT reproduces the exact momentum distribution term by term as a double expansion in $1/(ak)$ and $1/(aM_{\mathrm{hi}})$.

Load-bearing premise

The whole comparison assumes that matching $^3S_1$ scattering states at $p_1=4$ MeV and $p_2=5$ MeV, using only the $^3S_1$ operators $O_0$ and $O_2$ with no $^3D_1$ or tensor-operator contributions, captures all the short-distance dynamics that determines the deuteron momentum distribution for $k>250$ MeV.

Editorial extensions

If this is right

  • Once matched in two-body scattering, the same Wilson coefficients apply to any nucleus: computing $\rho_A(k)$ requires only the Pionless EFT matrix element $\langle A|O_n|A\rangle$.
  • At very large $k$, the one-term factorization holds and ratios such as $\rho_A(k)/\rho_d(k)$ become approximately constant; at intermediate $k$ the $O_2$ term introduces $k$-dependent corrections to those ratios.
  • For $k$ around the pion mass, including the NLO EFT interaction matters more than adding the $O_2$ operator, so the practical ordering is EFT order first, then operator dimension.
  • The matching procedure is ready to accept lattice-QCD inputs for the two-body matrix elements, replacing the phenomenological potential as the underlying theory.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same matching technology should extend to other short-range-dominated observables, such as the two-nucleon momentum distribution or generalized contact parameters, because the separation into state-independent Wilson coefficients and state-dependent EFT matrix elements is generic.
  • The S-wave-only assumption could be tested by adding the $^3D_1$ channel or the $O_2(SD)$ mixing operator; the claimed few-percent agreement would be reinforced if these extra operators barely change $\rho(k)$, and undermined if they shift it significantly.
  • A direct experimental check is possible through $y$-scaling electron-scattering data, where the extracted deuteron momentum distribution should follow the OPE prediction and deviations would locate where the one-body Wilson coefficient stops being negligible.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper develops an operator-product-expansion (OPE) framework, combined with Pionless effective field theory, for the large-momentum part of the single-nucleon momentum distribution in the deuteron. Wilson coefficients for the local Pionless operators O0 and O2 are fixed by matching exact matrix elements of the nonlocal operator Omega(k) between NN scattering states computed in an underlying nuclear potential and in the EFT. The method is checked analytically in a separable toy model and then applied numerically to the AV18 potential. The authors report that the OPE/EFT reproduces the AV18 deuteron momentum distribution to a few percent for k > 250 MeV once NLO EFT corrections and the O2 operator are included.

Significance. If the central claim holds, the paper offers a systematic, state-independent framework for short-range correlations that connects short-distance nuclear dynamics to Wilson coefficients, and it provides a concrete alternative to generalized contact formalisms. The paper has several genuine strengths: the toy-model check is analytic and exact; the renormalized operator basis in Eqs. (58)-(62) is constructed explicitly; and the matching is performed with scattering states rather than by fitting the deuteron momentum distribution itself. The AV18 comparison is a meaningful benchmark. However, the few-percent claim for AV18 currently lacks a quantitative treatment of the D-wave/tensor content of the deuteron and of the sensitivity to the matching procedure, so the soundness of the central numerical result is not yet fully established.

major comments (2)
  1. [Sec. V B, Eqs. (85)-(88)] The matching is performed at p1 = 4 MeV and p2 = 5 MeV, both much smaller than the 3S1 inverse scattering length a^{-1} ~ 36 MeV. Since M2^LO/M0^LO scales as p^2 a^2, the O2 Wilson coefficient is extracted from a very small difference between A00(k,p1) and A00(k,p2). The numerical fragility of this extraction is not discussed, and no stability test with respect to the choice of (p1,p2) is shown. Please demonstrate that fW2 and the resulting rho(k) are stable when the matching momenta are varied within the Pionless EFT range, or quantify the induced uncertainty.
  2. [Sec. V B and Figs. 6-7] The central claim of few-percent agreement is presented without uncertainty quantification. The cutoff Lambda = 800 MeV and the matching points p1 = 4 MeV, p2 = 5 MeV are single choices, and the residual cutoff dependence noted around Eq. (40) is not scanned. In addition, the numerical values of the Wilson coefficients fW0 and fW2 as functions of k are not reported, so the relative size of the O0 and O2 terms cannot be checked from the paper. Please provide numerical tables or curves for the Wilson coefficients and error bands obtained by varying Lambda and the matching momenta.
minor comments (3)
  1. [Abstract] The abstract contains the phrase “short-rang structure”; this should be “short-range structure.”
  2. [Fig. 6 caption] The caption says “The rest are the results from the OPE-Pionless EFT” without identifying which curve corresponds to which OPE order; please clarify the legend or caption.
  3. [Sec. V B] Because the same AV18 potential supplies both the scattering-state input and the deuteron benchmark, the test is not circular, but it validates state independence only within a single underlying model. Testing the matching procedure with a second potential, for example a chiral EFT potential, would strengthen the claim that the extracted Wilson coefficients are state independent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the deuteron momentum distribution is never used to fix a Wilson coefficient, and the AV18 comparison is a genuine test of the state independence of the OPE coefficients.

full rationale

The Wilson coefficients in the AV18 calculation are fixed exclusively by matching the scattering-state matrix element A00(k,p) at the low momenta p1 = 4 MeV and p2 = 5 MeV through Eqs. (85)-(88); the deuteron momentum distribution rho18(k) is not an input to that matching. The deuteron matrix elements used on the OPE side, Eqs. (69)-(70), are computed in Pionless EFT from the scattering length a and effective range r0, not from rho(k). The comparison of the resulting OPE/EFT expression with the directly computed AV18 deuteron momentum distribution in Figs. 6-7 is therefore a test of the advertised state independence of the Wilson coefficients, not a fit renamed as a prediction. The toy-model comparison is likewise a term-by-term consistency check in which the EFT inputs are a and r0 derived from the effective-range expansion of the model, while the deuteron distribution itself is the predicted quantity. The paper's self-citations, including Refs. [53], [56], [58], and [60], are used for standard Pionless EFT matching techniques and a separable toy model; none is load-bearing for the central factorization claim. The omission of the O2(SD) operator from the AV18 matching basis is a completeness and power-counting concern about tensor and D-wave contributions, but it is not circularity: no equation in the derivation defines the predicted deuteron distribution in terms of itself.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particles or forces. Its burden rests on the OPE factorization premise, the Pionless-EFT power counting, and the choice to treat AV18 as the underlying theory; the only hand-chosen numerical inputs are the matching momenta and the regulator cutoff.

free parameters (2)
  • Matching momenta p1 and p2 = 4 MeV, 5 MeV
    Chosen by hand as soft kinematics for extracting Wilson coefficients from AV18; no sensitivity study reported.
  • Pionless EFT cutoff Lambda = 800 MeV
    Numerical regulator scale used in the AV18 matching; residual cutoff dependence is acknowledged but not quantified in the final distributions.
assumptions (4)
  • domain assumption The nonlocal operator N^dagger(-r/2)N(r/2) has an OPE expansion Eq. (11) with state-independent Wilson coefficients for r -> 0.
    This is the central factorization premise inherited from OPE; the paper does not derive it.
  • domain assumption Pionless EFT perturbative expansion in Q/Mhi applies to the soft scattering states and the deuteron, with a and r0 as inputs.
    Used throughout Sec. IV to compute T_LO, T_NLO, and the deuteron matrix elements.
  • domain assumption AV18 may serve as the underlying 'true' theory with only nucleon degrees of freedom, so Eq. (6) with Gamma from the Lippmann-Schwinger equation gives the exact momentum distribution.
    Stated in Sec. I; this defines the benchmark against which the OPE is tested.
  • ad hoc to paper Renormalization of the Pionless EFT operators removes the UV cutoff dependence, leaving only small residual dependence at Lambda = 800 MeV.
    The paper constructs renormalized operators in Sec. IV and numerically chooses Lambda = 800 MeV, relying on residual cutoff effects being small.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Systematic study of large-momentum distribution in nuclei with the operator product expansion." pith.science (2026). https://pith.science/paper/4LKUBVZJ

@misc{pith2026250100283,
  author       = {Pith},
  title        = {Pith review of: Systematic study of large-momentum distribution in nuclei with the operator product expansion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4LKUBVZJ}},
  note         = {Machine review of arXiv:2501.00283}
}
read the original abstract

The operator product expansion (OPE) is applied in conjunction with Pionless effective field theory to study the short-rang structure of nuclei. By matching the OPE with the selected nuclear potentials for nucleon-nucleon scattering states, we obtain the Wilson coefficients. The nucleon momentum distribution in the deuteron is then used to test the OPE against the predictions of these nuclear potentials. In order to achieve a systematic separation of short-range and long-range interactions, we discuss how the OPE approximation can be improved by including higher-order EFT potentials and higher-dimension local operators.

Figures

Figures reproduced from arXiv: 2501.00283 by the authors.

Figure 1
Figure 1. FIG. 1. Feynman-diagram representation of the deuteron [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Diagrams for the matrix elements of the nonlocal [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Diagrams for the matrix elements of the one-body [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Diagram for the matrix elements of two-body local [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Diagrams for matrix elements of two-body local [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The deuteron single-nucleon momentum distribu [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The relative difference between [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

60 extracted references · 26 canonical work pages

  1. [1]

    Ordonez, L

    C. Ordonez, L. Ray, and U. van Kolck, Phys. Rev. C 53, 2086 (1996), arXiv:hep-ph/9511380

    arXiv 1996

  2. [2]

    van Kolck, Phys

    U. van Kolck, Phys. Rev. C 49, 2932 (1994)

    work page 1994

  3. [3]

    Epelbaum, A

    E. Epelbaum, A. Nogga, W. Gloeckle, H. Kamada, U. G. Meissner, and H. Witala, Phys. Rev. C 66, 064001 (2002), arXiv:nucl-th/0208023

    arXiv 2002

  4. [4]

    D. R. Entem and R. Machleidt, Phys. Rev. C 68, 041001 (2003), arXiv:nucl-th/0304018

    arXiv 2003

  5. [5]

    Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory

    P. Navratil, V. G. Gueorguiev, J. P. Vary, W. E. Or- mand, and A. Nogga, Phys. Rev. Lett. 99, 042501 (2007), arXiv:nucl-th/0701038

    work page Pith review arXiv 2007

  6. [6]

    Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions

    G. Hagen, T. Papenbrock, D. J. Dean, and M. Hjorth- Jensen, Phys. Rev. C 82, 034330 (2010), arXiv:1005.2627 [nucl-th]

    work page Pith review arXiv 2010

  7. [7]

    R. Roth, J. Langhammer, A. Calci, S. Binder, and P. Navratil, Phys. Rev. Lett. 107, 072501 (2011), arXiv:1105.3173 [nucl-th]

    arXiv 2011

  8. [8]

    Ekstr¨ om, G

    A. Ekstr¨ om, G. R. Jansen, K. A. Wendt, G. Hagen, T. Papenbrock, B. D. Carlsson, C. Forss´ en, M. Hjorth- Jensen, P. Navr´ atil, and W. Nazarewicz, Phys. Rev. C 91, 051301 (2015), [Erratum: Phys.Rev.C 109, 059901 (2024)], arXiv:1502.04682 [nucl-th]

    arXiv 2015

Show all 60 references
  1. [9]

    P. F. Bedaque, H. W. Hammer, and U. van Kolck, Nucl. Phys. A 676, 357 (2000), arXiv:nucl-th/9906032

    2000 arXiv

  2. [10]

    Platter, H

    L. Platter, H. W. Hammer, and U.-G. Meissner, Phys. Lett. B 607, 254 (2005), arXiv:nucl-th/0409040

    2005 arXiv

  3. [11]

    K¨ onig, H

    S. K¨ onig, H. W. Grießhammer, H. W. Hammer, and U. van Kolck, Phys. Rev. Lett. 118, 202501 (2017), arXiv:1607.04623 [nucl-th]

    2017 arXiv

  4. [12]

    B.-N. Lu, N. Li, S. Elhatisari, D. Lee, E. Epelbaum, and U.-G. Meißner, Phys. Lett. B 797, 134863 (2019), arXiv:1812.10928 [nucl-th]

    2019 arXiv

  5. [13]

    K¨ onig, Eur

    S. K¨ onig, Eur. Phys. J. A 56, 113 (2020), arXiv:1910.12627 [nucl-th]. 13

    2020 arXiv

  6. [14]

    Deltuva, M

    A. Deltuva, M. Gattobigio, A. Kievsky, and M. Viviani, (2020), arXiv:2011.06828 [nucl-th]

    2020 arXiv

  7. [15]

    E. D. Jurgenson, P. Navratil, and R. J. Furnstahl, Phys. Rev. C 83, 034301 (2011), arXiv:1011.4085 [nucl-th]

    2011 arXiv

  8. [16]

    R. J. Furnstahl and K. Hebeler, Rept. Prog. Phys. 76, 126301 (2013), arXiv:1305.3800 [nucl-th]

    2013 arXiv

  9. [17]

    Ciofi degli Atti, Phys

    C. Ciofi degli Atti, Phys. Rept. 590, 1 (2015)

    2015

  10. [18]

    O. Hen, G. A. Miller, E. Piasetzky, and L. B. Weinstein, Rev. Mod. Phys. 89, 045002 (2017), arXiv:1611.09748 [nucl-ex]

    2017 arXiv

  11. [19]

    Tang et al., Phys

    A. Tang et al., Phys. Rev. Lett. 90, 042301 (2003), arXiv:nucl-ex/0206003

    2003 arXiv

  12. [20]

    Piasetzky, M

    E. Piasetzky, M. Sargsian, L. Frankfurt, M. Strikman, and J. W. Watson, Phys. Rev. Lett. 97, 162504 (2006), arXiv:nucl-th/0604012

    2006 arXiv

  13. [21]

    K. S. Egiyan et al. (CLAS), Phys. Rev. C 68, 014313 (2003), arXiv:nucl-ex/0301008

    2003 arXiv

  14. [22]

    K. S. Egiyan et al. (CLAS), Phys. Rev. Lett. 96, 082501 (2006), arXiv:nucl-ex/0508026

    2006 arXiv

  15. [23]

    Shneor et al

    R. Shneor et al. (Jefferson Lab Hall A), Phys. Rev. Lett. 99, 072501 (2007), arXiv:nucl-ex/0703023

    2007 arXiv

  16. [24]

    Fomin et al., Phys

    N. Fomin et al., Phys. Rev. Lett. 108, 092502 (2012), arXiv:1107.3583 [nucl-ex]

    2012 arXiv

  17. [25]

    Hen et al., Science 346, 614 (2014), arXiv:1412.0138 [nucl-ex]

    O. Hen et al., Science 346, 614 (2014), arXiv:1412.0138 [nucl-ex]

    2014 arXiv

  18. [26]

    Korover et al

    I. Korover et al. (Lab Hall A), Phys. Rev. Lett. 113, 022501 (2014), arXiv:1401.6138 [nucl-ex]

    2014 arXiv

  19. [27]

    Ye et al

    Z. Ye et al. (Hall A), Phys. Rev. C 97, 065204 (2018), arXiv:1712.07009 [nucl-ex]

    2018 arXiv

  20. [28]

    D. B. Day, L. L. Frankfurt, M. M. Sargsian, and M. I. Strikman, Phys. Rev. C 107, 014319 (2023)

    2023

  21. [29]

    Fomin, Nadia, Arrington, John, and Li, Shujie, Eur. Phys. J. A 59, 205 (2023)

    2023

  22. [30]

    A. J. Tropiano, S. K. Bogner, and R. J. Furnstahl, Phys. Rev. C 104, 034311 (2021), arXiv:2105.13936 [nucl-th]

    2021 arXiv

  23. [31]

    A. J. Tropiano, S. K. Bogner, R. J. Furnstahl, M. A. Hisham, A. Lovato, and R. B. Wiringa, Phys. Lett. B 852, 138591 (2024), arXiv:2402.00634 [nucl-th]

    2024 arXiv

  24. [32]

    Weiss, B

    R. Weiss, B. Bazak, and N. Barnea, Phys. Rev. Lett. 114, 012501 (2015), arXiv:1405.2734 [nucl-th]

    2015 arXiv

  25. [33]

    Weiss, B

    R. Weiss, B. Bazak, and N. Barnea, Phys. Rev. C 92, 054311 (2015), arXiv:1503.07047 [nucl-th]

    2015 arXiv

  26. [34]

    Weiss, R

    R. Weiss, R. Cruz-Torres, N. Barnea, E. Piasetzky, and O. Hen, Phys. Lett. B 780, 211 (2018), arXiv:1612.00923 [nucl-th]

    2018 arXiv

  27. [35]

    Weiss, D

    R. Weiss, D. Lonardoni, and S. Gandolfi, Phys. Lett. B 857, 138974 (2024), arXiv:2307.05910 [nucl-th]

    2024 arXiv

  28. [36]

    R. B. Wiringa, R. Schiavilla, S. C. Pieper, and J. Carl- son, Phys. Rev. C 89, 024305 (2014)

    2014

  29. [37]

    Piarulli, S

    M. Piarulli, S. Pastore, R. B. Wiringa, S. Brusilow, and R. Lim, Phys. Rev. C 107, 014314 (2023)

    2023

  30. [38]

    R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C 51, 38 (1995), arXiv:nucl-th/9408016

    1995 arXiv

  31. [39]

    Braaten and L

    E. Braaten and L. Platter, Phys. Rev. Lett. 100, 205301 (2008), arXiv:0803.1125 [cond-mat.other]

    2008 arXiv

  32. [40]

    S. B. Emmons, D. Kang, and L. Platter, Phys. Rev. A 94, 043615 (2016)

    2016

  33. [41]

    Tan, Annals Phys

    S. Tan, Annals Phys. 323, 2952 (2008)

    2008

  34. [42]

    J.-W. Chen, W. Detmold, J. E. Lynn, and A. Schwenk, Phys. Rev. Lett. 119, 262502 (2017), arXiv:1607.03065 [hep-ph]

    2017 arXiv

  35. [43]

    Huang, Y

    Y. Huang, Y. Jia, and R. Yu, (2018), arXiv:1809.09023 [hep-ph]

    2018 arXiv

  36. [44]

    D. B. Kaplan, M. J. Savage, and M. B. Wise, Phys. Rev. C 59, 617 (1999)

    1999

  37. [45]

    D. B. Day, J. S. McCarthy, T. W. Donnelly, and I. Sick, Ann. Rev. Nucl. Part. Sci. 40, 357 (1990)

    1990

  38. [46]

    D. B. Day et al., Phys. Rev. Lett. 59, 427 (1987)

    1987

  39. [47]

    Ciofi degli Atti, E

    C. Ciofi degli Atti, E. Pace, and G. Salme, Phys. Rev. C 43, 1155 (1991)

    1991

  40. [48]

    C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, Phys. Rev. D 63, 114020 (2001), arXiv:hep-ph/0011336

    2001 arXiv

  41. [49]

    Eichten and B

    E. Eichten and B. R. Hill, Phys. Lett. B 234, 511 (1990)

    1990

  42. [50]

    H. W. Hammer, S. K¨ onig, and U. van Kolck, Rev. Mod. Phys. 92, 025004 (2020), arXiv:1906.12122 [nucl-th]

    2020 arXiv

  43. [51]

    Fleming, T

    S. Fleming, T. Mehen, and I. W. Stewart, Nucl. Phys. A 677, 313 (2000), arXiv:nucl-th/9911001

    2000 arXiv

  44. [52]

    D. B. Kaplan, M. J. Savage, and M. B. Wise, Nucl. Phys. B 478, 629 (1996), arXiv:nucl-th/9605002

    1996 arXiv

  45. [53]

    Long and U

    B. Long and U. van Kolck, Annals Phys. 323, 1304 (2008), arXiv:0707.4325 [quant-ph]

    2008 arXiv

  46. [54]

    E. J. Moniz, I. Sick, R. R. Whitney, J. R. Ficenec, R. D. Kephart, and W. P. Trower, Phys. Rev. Lett. 26, 445 (1971)

    1971

  47. [55]

    Z. X. Yang, X. L. Shang, G. C. Yong, W. Zuo, and Y. Gao, Phys. Rev. C 100, 054325 (2019), arXiv:1907.10977 [nucl-th]

    2019 arXiv

  48. [56]

    R. Peng, S. Lyu, S. K¨ onig, and B. Long, Phys. Rev. C 105, 054002 (2022)

    2022

  49. [57]

    S. R. Beane and R. C. Farrell, Few Body Syst. 63, 45 (2022), arXiv:2112.05800 [nucl-th]

    2022 arXiv

  50. [58]

    Long and C

    B. Long and C. J. Yang, Phys. Rev. C 85, 034002 (2012), arXiv:1111.3993 [nucl-th]

    2012 arXiv

  51. [59]

    A. M. Gasparyan and E. Epelbaum, Phys. Rev. C 107, 034001 (2023), arXiv:2210.16225 [nucl-th]

    2023 arXiv

  52. [60]

    R. Peng, B. Long, and F.-R. Xu, Phys. Rev. C 110, 054001 (2024), arXiv:2407.08342 [nucl-th]

    2024 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.