The Unitarity-Limit Expansion for Two Nucleons with Perturbative Pions: Digest and Ideas

Harald W. Griesshammer (George Washington U.)

REVIEW 3 major objections 3 minor 17 references

The Unitarity-Limit Expansion for Two Nucleons with Perturbative Pions: Digest and Ideas

T0 review · 3 major / 3 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper claims that the unitarity limit's scale invariance and Wigner-SU(4) spin–isospin symmetry survive pionic corrections in two-nucleon S-waves, postponing the tensor one-pion exchange to N3LO.

desk verdict A candid, well-framed digest of a companion paper; the central hypothesis about tensor-OPE suppression is intriguing but circular as presented and needs an a priori expansion parameter. read the letter →

arxiv 2504.13353 v2 pith:YHALBHSJ submitted 2025-04-17 nucl-th hep-phphysics.atom-ph

Harald W. Griesshammer (George Washington U.) This is my paper · ORCID

classification nucl-thhep-phphysics.atom-ph

keywords unitaritylimitexpansionWigner-SU(4)symmetrychiraleffectivefieldtheoryperturbativepionsnucleon-nucleonscatteringone-pionexchangeS-wavephaseshifts

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

This paper digests a first quantitative study of what happens to the unitarity-limit expansion of two-nucleon scattering once pions are included as perturbative degrees of freedom. It claims that in the S-wave channels the symmetries of the unitarity fixed point—scale invariance and Wigner's combined spin–isospin SU(4) symmetry—persist even for momenta at and above the pion mass, where their footprint dominates over chiral-symmetry effects. The central move is to keep only the central part of one-pion exchange at next-to-next-to-leading order (N2LO) and discard the tensor part, which is the only piece that mixes the ${}^3S_1$ and ${}^3D_1$ waves and breaks Wigner-SU(4); with that truncation both S-wave phase shifts converge order by order up to about 300 MeV and agree with empirical phase-shift analyses, whereas the full N2LO amplitude fails badly in ${}^3S_1$. If right, this would mean low-energy nuclear S-wave physics is organized by the unitarity fixed point's symmetries even in the pionic regime, with chiral symmetry subdominant until higher momenta. The paper is explicit that this is a hypothesis: a systematic expansion parameter that would justify the suppression of the tensor pion before N3LO is not yet in hand.

What carries the argument

The load-bearing object is the Unitarity Expansion: an expansion of the two-nucleon amplitude about the unitarity fixed point ($\cot\delta=0$, infinite scattering lengths) in powers of $Q \sim 1/(k a) \sim (k, m_\pi)/\Lambda_{\rm NN}$, with $\Lambda_{\rm NN}\approx300$ MeV the scale where iterated one-pion exchange becomes nonperturbative. Within this expansion, the one-pion-exchange potential is split into a central part $V_C \propto (\boldsymbol{\sigma}_1\cdot\boldsymbol{\sigma}_2)(\boldsymbol{\tau}_1\cdot\boldsymbol{\tau}_2)$ that preserves Wigner-SU(4) and acts identically in ${}^1S_0$ and ${}^3S_1$, and a tensor part $V_T \propto [3\,\boldsymbol{\sigma}_1\cdot\hat{\boldsymbol{q}}\,\boldsymbol{\sigma}_2\cdot\hat{\boldsymbol{q}}-\boldsymbol{\sigma}_1\cdot\boldsymbol{\sigma}_2](\boldsymbol{\tau}_1\cdot\boldsymbol{\tau}_2)$ that mixes S and D waves and breaks the symmetry. The argument's key move is to keep $V_C$ and eliminate $V_T$ at N2LO, making the truncated amplitude Wigner-SU(4) invariant; this recovers order-by-order convergence in both S-waves. The machinery also identifies the N2LO once-iterated OPE as the first place $V_T$ can enter, since a single OPE between LO S-wave amplitudes cannot mix partial waves.

What would settle it

Compute or measure the N3LO correction to the ${}^3S_1$ phase shift and the ${}^3S_1$--${}^3D_1$ mixing angle with the full tensor OPE included: if at $k\approx m_\pi$ the correction is comparable to the NLO-to-N2LO shift rather than suppressed to about $(m_\pi/\Lambda_{\rm NN})^3\times90^\circ\approx10^\circ$, the tensor pion enters before N3LO and the persistence hypothesis fails.

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Extended reading notes

Core claim

On its own terms, the paper's claim is a persistence hypothesis for the unitarity fixed point in the two-nucleon system. In the unitarity limit the S-wave scattering lengths are infinite, binding energies are zero, and the low-energy amplitudes are universal and symmetric under scale transformations and under Wigner's SU(4) spin–isospin rotations, with ${}^1S_0$ and ${}^3S_1$ sitting in the same multiplet. When perturbative pions are added, the pion mass and decay constant break scale invariance explicitly, and the tensor part of one-pion exchange breaks Wigner-SU(4) by allowing ${}^3S_1 o{}^3D_1$ transitions. The paper reports that the once-iterated tensor OPE at N2LO destroys order-by-order convergence in ${}^3S_1$, while dropping that tensor part leaves a theory that is Wigner-SU(4) symmetric, converges smoothly in both S waves up to $k\approx250$--$300$ MeV $\approx\Lambda_{\rm NN}$, and matches empirical phase shifts within Bayesian truncation uncertainties. The author therefore proposes that the symmetry-breaking tensor OPE is super-perturbative and should be postponed to N3LO or beyond, with chiral symmetry subdominant in the immediate neighbourhood of the fixed point.

Load-bearing premise

The hypothesis rests on treating the tensor part of one-pion exchange as negligible through next-to-next-to-leading order; the author imposes the unitarity limit's combined spin–isospin (Wigner-SU(4)) symmetry by hand because no systematic expansion parameter has yet been shown to justify that suppression.

Editorial extensions

If this is right

If the hypothesis holds, a chiral EFT with perturbative pions can describe both S-wave NN channels up to the breakdown scale $\Lambda_{\rm NN}\approx300$ MeV using a Wigner-SU(4)-symmetric pion interaction, with the tensor OPE entering only at N3LO.
The unitarity fixed point would protect Wigner-SU(4) symmetry: near the fixed point, chiral-symmetry breaking is subdominant, so an EFT without explicit pions and a chiral EFT with pions belong to the same universality class for S-wave observables.
The ${}^3S_1$--${}^3D_1$ mixing angle and ${}^3D_1$ phase shift, poorly described by the full N2LO amplitude, become naturally small under the Wigner-SU(4)-symmetric truncation, with an estimated size of order $(m_\pi/\Lambda_{\rm NN})^3\times 90^\circ\approx10^\circ$ at $k\approx m_\pi$.
One would be able to demote certain pion contributions in the chiral counting: a contribution that breaks a symmetry of the unitarity fixed point can be postponed to higher orders rather than promoted by renormalisation-group arguments.

Reading between the lines

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

A testable diagnostic the paper does not run is to extract the effective strength of the tensor OPE from the ${}^3S_1$--${}^3D_1$ mixing data and check whether it is numerically of order $(m_\pi/\Lambda_{\rm NN})^3$, as the persistence hypothesis requires.
If persistence holds, the same Wigner-SU(4)-symmetric truncation should also organize higher-body forces: the leading three-nucleon interaction in the unitarity window should be SU(4)-symmetric, with tensor-pion-dependent three-body terms postponed to higher orders.
The hypothesis implies a specific pion-mass dependence of S-wave observables; varying $m_\pi$ in a lattice or effective-field-theory calculation and watching how ${}^1S_0$ and ${}^3S_1$ track the unitarity-limit prediction would test whether scale-invariance breaking is as weak as claimed.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This is a conference proceedings digest of Teng & Grießhammer [1], plus a speculative hypothesis. The concrete numerical story is not self-contained: the amplitude calculations, Bayesian uncertainties, and most of the analysis live in the companion paper. What is new here is the hypothesis that the tensor part of one-pion exchange is suppressed to N3LO because Wigner-SU(4) symmetry persists near the unitarity fixed point.

What the paper does well is frame a real puzzle. Full KSW N2LO gives a catastrophic 3S1 phase shift, while truncating the pion to its central (Wigner-SU(4) symmetric) part restores order-by-order convergence and matches the Nijmegen PWA. The 1S0 channel converges fine with the full OPE, and the contrast is cleanly displayed. The author is unusually candid: he labels the central claim a hypothesis, says a systematic expansion parameter "must be found," and lists two candidates that are "somewhat problematic." That honesty is real credit.

The soft spot is exactly where the stress-test lands. If the tensor piece were genuinely N3LO-suppressed, including it at N2LO should move the phase shift by only a small amount. Instead, Fig. 4 shows an order-one, sudden failure. That is evidence that V_T is not a small perturbation at this order, not evidence of suppression. The author's response is to drop V_T and then fit better; the improvement then serves as confirmation of the hypothesis. That is partly circular. He explicitly acknowledges this by calling for an a priori expansion parameter, but the paper does not supply one. The nonperturbative-pion LO results in Fig. 7 are preliminary and the uncertainty bands are self-admittedly underestimates (cutoff variation, not Bayesian DoB). So the quantitative support for the central hypothesis is not in this paper.

Bottom line: this is a useful digest and a thought-provoking speculation, not a demonstration. If you work on chiral EFT power counting, it is worth reading alongside [1] to see whether the persistence idea can be made systematic. I would not cite the digest itself; I would cite [1] for the numbers. For a proceedings volume it is fine; for a refereed journal the central claim would need much stronger support, but the paper is honest about that, so it deserves a serious referee rather than a desk rejection. If you referee it, ask the author to clarify the status of the hypothesis and to either provide the a priori counting or explicitly leave it open. The current draft is a good "ideas" paper, not a resolution.

Referee Report

3 major / 3 minor

Summary. This proceedings paper summarizes a study (Teng and Grießhammer, arXiv:2410.09653) of the Unitarity Expansion in chiral EFT with perturbative (KSW) pions at N2LO. The author shows that the 1S0 phase shift converges order by order and agrees with the Nijmegen PWA up to about 300 MeV, while the full N2LO 3S1 result is catastrophic. The paper then proposes to eliminate the tensor part V_T of one-pion exchange at N2LO to restore Wigner-SU(4) symmetry, which greatly improves the 3S1 phase shift. This leads to the central hypothesis that scale invariance and Wigner-SU(4) symmetry show persistence at k ≳ m_pi, with the tensor/Wigner-SU(4)-breaking part of OPE suppressed until N3LO. The final sections discuss possible mechanisms, candidates for an expansion parameter, and LO results with nonperturbative pions.

Significance. If the hypothesis is correct, it would constitute a significant reorganization of the few-nucleon power counting, identifying the Unitarity fixed point as the organizing principle that protects Wigner-SU(4) symmetry and demotes tensor pion exchange. The paper's strengths include its clear presentation of the 1S0 convergence, the direct comparison to the PWA, the honest admission that no systematic expansion parameter has yet been found, and the inclusion of LO nonperturbative-pion results. The central claim is explicitly labeled a hypothesis, and the paper offers concrete next steps. The evidence, however, is currently a post hoc truncation rather than a derivation, so the significance is prospective rather than established.

major comments (3)

[Section 2, Fig. 4] The central evidence for the hypothesis is the improvement of the 3S1 phase shift after "eliminating the V_T part," but this is a post hoc truncation. In the KSW counting used here, V_T first enters at N2LO; if V_T were truly N3LO-suppressed, adding it to the N2LO calculation should change the phase shift by only an N3LO-sized amount. Instead, the left panel of Fig. 4 shows that the full N2LO amplitude deviates dramatically from the PWA, i.e. the effect of V_T is order-one. The observed sensitivity is therefore evidence against the claimed suppression under the present counting, unless a renormalization-scale artifact is identified and shown to be the cause.
[Section 3] The paper itself concedes that "a small, dimensionless (systematic) expansion parameter rooted in Wigner-SU(4) symmetry must be found" and that the candidates discussed are "somewhat problematic." Without such a parameter, the demotion of V_T to N3LO is a phenomenological choice rather than a systematic expansion, and the persistence hypothesis remains unsupported by the calculation. The manuscript should either supply an a priori counting argument or explicitly frame the statement as an open conjecture with falsifiable predictions, rather than presenting the fit improvement as evidence for the conjecture.
[Section 2, Eq. (2.3)] The operation "impose Wigner-SU(4) symmetry on the pion" by eliminating V_T is not a symmetry transformation of the pion-nucleon interaction: V_C and V_T arise from the same vertex with a fixed spin-isospin structure, so dropping V_T modifies the interaction rather than implementing a symmetry of the Lagrangian. This matters because the central hypothesis is phrased as a symmetry-based suppression; the manuscript should clarify whether the suppression is a dynamical consequence of the fixed point or an imposed truncation.

minor comments (3)

[Section 2, text near Fig. 4] The sentence "see left graph of fig. 4" should read "right graph," since the left panel is the full N2LO result and the right panel is the Wigner-SU(4)-symmetric result.
[Section 2] "on-Bayesian estimates" should read "non-Bayesian estimates."
[Fig. 5] The legend entry "LO=N2LO Wigner" is potentially confusing; clarifying that, in the absence of V_T, the N2LO mixing angle is identical to LO would help the reader.

Circularity Check

1 steps flagged · score 6.0 of 10

The N3LO suppression claim for the tensor OPE is the dropped-V_T truncation restated, with no independent expansion parameter supplied.

self definitional [Sec. 2 (3S1 discussion, Fig. 4) and Sec. 3 (Ideas/Hypothesis), echoed in the Abstract.]
"This led to the idea to simply impose Wigner-SU(4) symmetry on the pion at N2LO: eliminate the V_T part! ... In particular, the tensor/Wigner-SU(4) symmetry-breaking part of one-pion exchange in the NN 3S1 channel of χEFT with Perturbative (KSW) Pions is super-perturbative, i.e. suppressed and does not enter before N3LO."

In the paper's own KSW counting, once-iterated OPE is an N2LO effect and its V_T part is present ('At N2LO, however, sandwiching once-iterated OPE between the LO 3S1 waves does allow for an 3S1→3D1→3S1 transition'). The improved N2LO amplitude is then defined by imposing Wigner-SU(4) symmetry, i.e. by deleting V_T. The resulting agreement with the PWA is therefore a property of the truncated amplitude and cannot by itself establish that V_T 'does not enter before N3LO'; that claim is the truncation choice restated in power-counting language. The full-N2LO amplitude including V_T is described as 'catastrophic,' so V_T is not shown to be a small perturbation at N2LO.

full rationale

Most of the paper's quantitative content is a digest of [1]; the 1S0 order-by-order convergence and the Wigner-SU(4)-symmetric 3S1 amplitude are self-contained comparisons to the Nijmegen PWA and are not circular. However, the abstract/Sec. 3 Hypothesis that the tensor part of OPE 'does not enter before N3LO' is reached by first deleting V_T from the N2LO amplitude because the full N2LO result is 'catastrophic,' and then taking the improved fit as evidence for the suppression. That is a truncation restated as a prediction: the N2LO amplitude used as evidence contains no V_T by construction. Section 3 candidly concedes that no systematic expansion parameter has been found, which confirms that the demotion is imposed rather than derived. This candor lowers the severity, but the central claim still reduces by construction to the imposed truncation. The 1S0 results, the EFT(pi/) comparison, and the nonperturbative-pion LO results are independent of this step, so the circularity is partial. The self-citation of [1] is normal for a conference digest and is not itself the circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The analysis rests on standard EFT machinery: KSW power counting with perturbative pions, input from the Nijmegen phase-shift analysis, and the unitarity expansion itself. The novel load-bearing element is the ad hoc truncation that deletes the tensor part of one-pion exchange at N2LO to enforce Wigner-SU(4) symmetry; the paper freely admits this is an idea rather than a derived suppression, and calls for a systematic expansion parameter to make it rigorous.

free parameters (3)

scattering lengths a in 1S0 and 3S1 = physical values, about -23 fm and 5.4 fm
Set to physical values at NLO in the KSW unitarity expansion (Section 2).
effective ranges r in 1S0 and 3S1 = physical values, about 2.7 fm and 1.7 fm
Enter at NLO together with a and are fitted to low-energy phase shifts (Section 2).
N2LO contact counterterms Delta a and Delta r = chosen to keep a and r unchanged from NLO
Fixed to cancel N2LO contributions to a and r, as shown in fig. 2.

assumptions (4)

domain assumption KSW power counting with perturbative pions is renormalizable and convergent order by order in the unitarity window.
Section 2 cites refs. [12,13,14]; this is a foundational assumption for the whole analysis.
domain assumption The expansion parameter Q = 1/((k,m_pi) a) ~ (k,m_pi)/Lambda_NN is small in the unitarity window.
Eq. (2.2) defines the regime of applicability of the unitarity expansion.
ad hoc to paper Wigner-SU(4) symmetry can be imposed on the N2LO pion by dropping the tensor part V_T.
Section 2, 'This led to the idea to simply impose Wigner-SU(4) symmetry on the pion at N2LO: eliminate the V_T part!'; motivated by the failure of the full N2LO amplitude, not derived.
domain assumption The Nijmegen phase-shift analysis is a reliable benchmark for comparison.
Used throughout as the reference data (figs. 3-5 and 7).

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Pith. "Pith review of The Unitarity-Limit Expansion for Two Nucleons with Perturbative Pions: Digest and Ideas." pith.science (2026). https://pith.science/paper/YHALBHSJ

@misc{pith2026250413353,
  author       = {Pith},
  title        = {Pith review of: The Unitarity-Limit Expansion for Two Nucleons with Perturbative Pions: Digest and Ideas},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YHALBHSJ}},
  note         = {Machine review of arXiv:2504.13353}
}

abstract

In the Unitarity Limit, the NN S-wave binding energies are zero, the scattering lengths infinite, Physics is universal, i.e. insensitive to details of the interactions, and observables display richer symmetries, namely invariance under both scaling and Wigner's combined SU(4) transformation of spin and isospin. This presentation is a digest of the first quantitative exploration of corrections to this picture when pions are included [1] (see there for a more comprehensive list of references). Since the pion mass and decay constant introduce dimensionful scales in the NN system, they explicitly break the symmetries of the Unitarity fixed point. In $\chi$EFT, these symmetries must therefore be classified as emergent. This text focuses on the $\chi$EFT variant with Perturbative ("KSW") Pions at next-to-next-to leading order (N2LO). This leads to the Hypothesis that both scale invariance and Wigner-SU(4) symmetry in the Unitarity Expansion show persistence, i.e. the footprint of both combined dominates even for $k\gtrsim m_\pi$ and is more relevant than chiral symmetry, so that the tensor/Wigner-SU(4) symmetry-breaking part of OPE is suppressed and does not enter before N3LO. Included are also ideas about underlying mechanisms and LO results of $\chi$EFT with Nonperturbative Pions in the expansion about Unitarity.

Figures

Figures reproduced from arXiv: 2504.13353 by the authors.

**Figure 1.** (Colour on-line) Born Corridor (shaded) and Unitarity Window (white) of NN phase shifts for the 𝐽 ≤ 3 channels in the Nĳmegen PWA [11] (Stapp-Ypsilanti-Metropolis (SYM/”bar”) parametrisation). 2. The Unitarity Expansion with Perturbative Pions How is the Unitarity Window accommodated in χEFT? Let us investigate the transition between “pionless” and “pionic” EFT by employing χEFT “with Perturbative/KSW Pions”, propos… view at source ↗

**Figure 2.** (Colour on-line) χEFT with Perturbative Pions in the Unitarity Expansion at LO (top); NLO (middle) with CTs (red circle) fixed to scattering length 𝑎 and effective range 𝑟; N2LO with CTs (blue diamonds) so that 𝑎 and 𝑟 do not change from the respective NLO values. The last term in square brackets at N2LO is once-iterated OPE, with intermediate orbital angular momentum as indicated. 4 [PITH_FULL_IMAGE:figures/full_f… view at source ↗

**Figure 3.** (Colour on-line) 1S0 phase shift compared to the Nĳmegen PWA [11] (thick green dashed). Green dotted: LO; blue dashed: NLO; red solid: N2LO with 68% degree-of-belief (DoB) interval (Bayesian truncation uncertainty); red dash-dotted: NLO=N 2LO in EFT(π/ ). Shaded: “Born Corridors” of fig. 1. In contradistinction, the result for the 3S1 channel is catastrophic, as FMS already noticed; see left of fig. 4. While NLO loo… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: (Colour on-line) Phase shift in the 3S1 channel compared to the Nĳmegen PWA [11]. Left: full N 2LO amplitude. Right: Wigner-SU(4) symmetric part only. Details as in fig. 3. What is the origin of the stark discrepancy between the 1S0 and 3S1 channels in both convergence…

**Figure 5.** Figure 5: (Colour on-line) Mixing angle (left) and 3D1 phase shift (right) in the 3SD1 channel, compared to the Nĳmegen PWA [11] (thick green dashed). Details as in fig. 3. 𝑘 ≳ 50 MeV, i.e. order-by-order convergence is extremely poor. It is even worse in 3D1. On the other hand,…

**Figure 6.** Figure 6: (Colour on-line) Sketch of an idea of symmetries around the Unitarity fixed point. If this Hypothesis is to be more than a hunch, then a small, dimensionless (systematic) expansion parameter rooted in Wigner-SU(4) symmetry must be found to decide both a priori and semi…

**Figure 7.** Figure 7: (Colour on-line) Phase shifts with nonperturbative pions at LO in the Unitarity Limit ( 1 𝑎 = 0), compared to the Nĳmegen PWA [11]. Left: 1S0 (top) and 3S1 (bottom) channels. Right: 3SD1 mixing angle (top right) and 3D1 phase shift (bottom right), compared to the Nĳmeg…

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Works this paper leans on

17 extracted references · 7 canonical work pages

[1]

Y. P. Teng and H. W. Grießhammer, [arXiv:2410.09653 [nucl-th]]

work page Pith review arXiv
[2]

Fleming, T

S. Fleming, T. Mehen and I. W. Stewart, Phys. Rev. C 61 (2000), 044005 doi:10.1103/PhysRevC.61.044005 [arXiv:nucl-th/9906056 [nucl-th]]

arXiv 2000
[3]

Fleming, T

S. Fleming, T. Mehen and I. W. Stewart, Nucl. Phys. A 677 (2000), 313-366 doi:10.1016/S0375-9474(00)00221-9 [arXiv:nucl-th/9911001 [nucl-th]]

arXiv 2000
[4]

Mehen, I

T. Mehen, I. W. Stewart and M. B. Wise, Phys. Rev. Lett. 83 (1999), 931-934 doi:10.1103/PhysRevLett.83.931 [arXiv:hep-ph/9902370 [hep-ph]]

arXiv 1999
[5]

Low and T

I. Low and T. Mehen, Phys. Rev. D 104 (2021) no.7, 074014 doi:10.1103/PhysRevD.104.074014 [arXiv:2104.10835 [hep-th]]

arXiv 2021
[6]

Q. Liu, I. Low and T. Mehen, Phys. Rev. C 107 (2023) no.2, 025204 doi:10.1103/PhysRevC.107.025204 [arXiv:2210.12085 [quant-ph]]

arXiv 2023
[7]

118(2017), no

S.König,H.W.Grießhammer,H.-W.HammerandU.vanKolck,Phys.Rev.Lett. 118(2017), no. 20, 202501 doi:10.1103/PhysRevLett.118.202501 [arXiv:1607.04623 [nucl-th]]

arXiv 2017
[8]

Naturalness in Nuclear Effective Field Theories

U. van Kolck, Eur. Phys. J. A56 (2020), no. 3, 97 doi:10.1140/epja/s10050-020-00092-1 [arXiv:2003.09974 [nucl-th]]

work page Pith review arXiv 2020

Show all 17 references

[9]

Kievsky, L

A. Kievsky, L. Girlanda, M. Gattobigio and M. Viviani, Ann. Rev. Nucl. Part. Sci.71(2021), 465-490 doi:10.1146/annurev-nucl-102419-032845 [arXiv:2102.13504 [nucl-th]]

2021 arXiv
[10]

Brown,Universality, Faber & Faber (London) 2025

N. Brown,Universality, Faber & Faber (London) 2025

2025
[11]

V. G. J. Stoks, R. A. M. Klomp, M. C. M. Rentmeester and J. J. de Swart, Phys. Rev. C48 (1993), 792-815 doi:10.1103/PhysRevC.48.792, nn-online.org accessed August 2024

1993 doi
[12]

D. B. Kaplan, M. J. Savage and M. B. Wise, Phys. Lett. B 424 (1998), 390-396 doi:10.1016/S0370-2693(98)00210-X [arXiv:nucl-th/9801034 [nucl-th]]

1998 arXiv
[13]

D. B. Kaplan, M. J. Savage and M. B. Wise, Nucl. Phys. B 534 (1998), 329-355 doi:10.1016/S0550-3213(98)00440-4 [arXiv:nucl-th/9802075 [nucl-th]]

1998 arXiv
[14]

S.R.Beane,P.F.Bedaque,M.J.SavageandU.vanKolck,Nucl.Phys.A 700(2002),377-402 doi:10.1016/S0375-9474(01)01324-0 [arXiv:nucl-th/0104030 [nucl-th]]

2002 arXiv
[15]

G.RupakandN.Shoresh,Phys.Rev.C 60(1999),054004doi:10.1103/PhysRevC.60.054004 [arXiv:nucl-th/9902077 [nucl-th]]

1999 arXiv
[16]

Wigner, Phys

E. Wigner, Phys. Rev.51(1937), 106;ibid. 56(1939), 519

1937
[17]

Hund, Zeitschrift für Physik105 (1937) 202

F. Hund, Zeitschrift für Physik105 (1937) 202. 10

1937

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

Y. P. Teng and H. W. Grießhammer, [arXiv:2410.09653 [nucl-th]]

work page Pith review arXiv

[2] [2]

Fleming, T

S. Fleming, T. Mehen and I. W. Stewart, Phys. Rev. C 61 (2000), 044005 doi:10.1103/PhysRevC.61.044005 [arXiv:nucl-th/9906056 [nucl-th]]

arXiv 2000

[3] [3]

Fleming, T

S. Fleming, T. Mehen and I. W. Stewart, Nucl. Phys. A 677 (2000), 313-366 doi:10.1016/S0375-9474(00)00221-9 [arXiv:nucl-th/9911001 [nucl-th]]

arXiv 2000

[4] [4]

Mehen, I

T. Mehen, I. W. Stewart and M. B. Wise, Phys. Rev. Lett. 83 (1999), 931-934 doi:10.1103/PhysRevLett.83.931 [arXiv:hep-ph/9902370 [hep-ph]]

arXiv 1999

[5] [5]

Low and T

I. Low and T. Mehen, Phys. Rev. D 104 (2021) no.7, 074014 doi:10.1103/PhysRevD.104.074014 [arXiv:2104.10835 [hep-th]]

arXiv 2021

[6] [6]

Q. Liu, I. Low and T. Mehen, Phys. Rev. C 107 (2023) no.2, 025204 doi:10.1103/PhysRevC.107.025204 [arXiv:2210.12085 [quant-ph]]

arXiv 2023

[7] [7]

118(2017), no

S.König,H.W.Grießhammer,H.-W.HammerandU.vanKolck,Phys.Rev.Lett. 118(2017), no. 20, 202501 doi:10.1103/PhysRevLett.118.202501 [arXiv:1607.04623 [nucl-th]]

arXiv 2017

[8] [8]

Naturalness in Nuclear Effective Field Theories

U. van Kolck, Eur. Phys. J. A56 (2020), no. 3, 97 doi:10.1140/epja/s10050-020-00092-1 [arXiv:2003.09974 [nucl-th]]

work page Pith review arXiv 2020