Intrinsic three-body nuclear interaction from a constituent quark model

Aaron Park; Su Houng Lee

REVIEW 3 major objections 5 minor 28 references

Intrinsic three-body nuclear interaction from a constituent quark model

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read In a constituent quark model with color-spin interaction, the intrinsic three-nucleon interaction vanishes exactly in the flavor SU(3) symmetric limit once two-baryon contributions are subtracted.

desk verdict A genuinely new calculation with a plausible zero result, but the all-channel claim rests on an explicit equal-size assumption and on tables that are stated rather than derived. read the letter →

arxiv 1908.08333 v1 pith:HARZYKXL submitted 2019-08-22 hep-ph nucl-th

Aaron Park , Su Houng Lee This is my paper · ORCID

classification hep-phnucl-th PACS 12.39.Jh21.30.-x

keywords three-bodynuclearforceconstituentquarkmodelcolor-spininteractionflavorSU(3)symmetrytribaryontransformationcoefficientsshort-distancerepulsion

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 claims that the short-distance part of the intrinsic three-nucleon interaction—the part of the three-body force that cannot be reduced to pairwise baryon interactions—vanishes exactly in the flavor SU(3) symmetric limit of a constituent quark model with color-spin interaction. It reaches this conclusion by comparing the color-spin energy of a compact nine-quark tribaryon configuration with the sum of three dibaryon and three baryon energies, using newly computed transformation coefficients that connect tribaryon states to three-baryon channels. The cancellation holds for every flavor-spin quantum number and also when the quark interaction is of flavor-spin type. If correct, the result means that at short distance in symmetric quark matter the color-spin interaction produces no genuine three-body force, and that the physical three-nucleon force in that regime is controlled by flavor-symmetry breaking and by interactions that are intrinsically three-quark in origin.

What carries the argument

The key machinery is the intrinsic three-body interaction formula $V_3 = M_T - \sum_i M_{D_i} + \sum_i M_{B_i}$, evaluated with only the color-spin part of the masses after assuming equal interquark distances in the baryon, dibaryon, and tribaryon. The calculation is carried by transformation coefficients: the dibaryon coefficients $T_2(D, B_1\otimes B_2)$ are extended to tribaryon coefficients $T_3(T, B\otimes D)$ computed in the Young–Yamanouchi basis of the $S_9$ symmetric group. These coefficients let the tribaryon color-spin energy be re-expressed as a probability-weighted sum over three-baryon channels, and the cancellation is demonstrated by explicitly summing the color-spin matrix elements given in the appendix.

What would settle it

Repeat the calculation allowing different Gaussian widths (variational parameters $a$) for the baryon, dibaryon, and tribaryon wave functions; if the color-spin part of $V_3$ becomes nonzero in the flavor SU(3) symmetric limit, the zero result is an artifact of the equal-size assumption. Alternatively, a lattice QCD determination of the three-nucleon potential in the SU(3) symmetric limit at short distance would directly test whether the intrinsic three-body force vanishes.

Watch

Extended reading notes

Core claim

The central discovery is that, after subtracting all two-baryon contributions, the intrinsic three-body interaction $V_3$ is exactly zero in the flavor SU(3) symmetric limit for all quantum numbers. The paper evaluates $V_3 = M_T - \sum_i M_{D_i} + \sum_i M_{B_i}$ using only the color-spin part of the hadron masses and shows, through explicit sums over transformation coefficients, that the tribaryon color-spin matrix element equals the probability-weighted sum of the dibaryon matrix elements, so the cancellation is complete. The same cancellation is demonstrated for a flavor-spin two-quark interaction, and the paper argues that intrinsic three-quark interactions of f-type sum to zero while d-type interactions cancel in the subtraction. The conclusion is that in the symmetric limit the short-distance color-spin interaction produces no intrinsic three-nucleon force, leaving only flavor-symmetry breaking and genuinely three-quark mechanisms as possible sources.

Load-bearing premise

The whole cancellation rests on taking the interquark distances inside the baryon, dibaryon, and tribaryon to be the same, so that every two-body spatial integral collapses to a single common constant $I_g$ (or the analogous constant for flavor-spin); if the spatial sizes differ, the kinetic and color-color terms no longer cancel and $V_3$ need not vanish.

Editorial extensions

If this is right

In flavor SU(3) symmetric quark matter, the short-distance three-nucleon force from two-quark color-spin interactions is zero, so any repulsive three-body force must come from another mechanism.
The Pauli-principle repulsion seen in the constituent quark model is fully accounted for by two-baryon interactions; three-baryon clusters gain no extra color-spin repulsion in the symmetric limit.
The vanishing holds for both color-spin and flavor-spin two-quark interactions, and the paper shows that intrinsic three-quark f-type and d-type interactions also leave $V_3$ unchanged.
In the realistic flavor-SU(3) broken case the cancellation is not exact; the paper expects the dominant contribution to still cancel, leaving a small intrinsic three-nucleon interaction.

Reading between the lines

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

Repeating the calculation with separate Gaussian widths for baryon, dibaryon, and tribaryon would show how large a color-spin three-body force appears once the equal-size assumption is relaxed.
If the vanishing survives in the broken-SU(3) calculation, then the repulsive three-body force needed for neutron-star equations of state would have to come from chiral dynamics or genuine three-quark interactions rather than the two-quark color-spin mechanism.
The transformation coefficients derived here are operator-independent and could be reused to test whether other two-quark operators, such as tensor or spin-orbit terms, produce a nonzero intrinsic three-body force in the symmetric limit.
The present calculation uses a fully symmetric spatial wave function; a natural next step is to allow orbital excitations in the Jacobi coordinates $x_7$ and $x_8$, where the kinetic terms may no longer cancel.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

Off the record: the paper does something real—extends Harvey's dibaryon transformation coefficients to tribaryons, subtracts two-body pieces, and finds a zero. The worked example is clean and the counting argument is neat. But the sweeping "vanishes for all quantum numbers" is a sketch once you leave the one channel, and the zero itself depends on an equal-size assumption that is stated but not defended. I'd send it to a referee, but with a request for the missing verification.

What's actually new: the tribaryon transformation coefficients, Eq. (11) as a definition of the intrinsic three-body force, the explicit (8,1/2) example, and the f/d-type three-quark argument. The tables are a real extension of the dibaryon coefficient literature, and the counting 36-45+9=0 is a nice consistency check, not a proof. The citation pattern is fine: [17] and [20] are genuinely prior work by the same group, and this paper extends them.

Soft spots, in order. First, the common Ig assumption: taking all interquark distances identical makes every spatial integral collapse to one constant. That is a model input, and if the 9-quark cluster has a different optimal size than the 3- and 6-quark clusters, the cancellation fails. The paper states this assumption and cites earlier work as motivation, but never quantifies the sensitivity. This is the main reason the result is conditional. Second, the all-channel proof is asserted rather than demonstrated: after Eq. (14) we get "in a similar way, we can show" and "one can show" for flavor-spin. The transformation coefficient tables are printed, but there is no derivation and no code; a referee can check one channel but not all fifteen. Third, the SU(3) breaking case is deferred, which is fine for a first paper, but it means the connection to the hyperon puzzle is indirect.

Who is this for: quark-cluster modelers and people who need to know whether a short-range intrinsic three-body force is expected in the SU(3) limit. It won't settle the hyperon puzzle, but it clears the ground. I'd bring it up in a reading group, though probably not as a main topic.

Recommendation: worth serious peer review. The referee should ask for at least one or two more channels verified explicitly, or for the coefficient tables/code, and for a short discussion of how the equal-size assumption can be relaxed. If the authors cannot produce the verification, the paper should be reframed as a one-channel result plus a conjecture.

Referee Report

3 major / 5 minor

Summary. The paper studies the short-distance part of the intrinsic three-nucleon (three-baryon) interaction in a constituent quark model with color-spin and flavor-spin two-quark interactions. The authors construct tribaryon wave functions in Jacobi coordinates, compute transformation coefficients between tribaryon configurations and three-baryon channels, and define the intrinsic three-body force by subtracting three two-body dibaryon contributions and the three free-baryon masses from the tribaryon mass (Eqs. (10)-(11)). Their central claim is that, in the flavor SU(3) symmetric limit and with all interquark distances set equal, the intrinsic three-body interaction vanishes for all fifteen flavor-spin quantum numbers, for both color-spin and flavor-spin interactions, and also for intrinsic three-quark f-type and d-type interactions. One explicit numerical example, Eq. (14) for the (8,1/2) tribaryon channel, is worked out and sums to zero.

Significance. If fully established under stated assumptions, the result is a sharp and somewhat surprising null result: it says that at short distance the purely intrinsic three-body force generated by two-body quark-level color-spin interactions is exactly zero in the SU(3) symmetric limit, so that any three-body repulsion in dense matter would have to come from other mechanisms, such as SU(3) breaking or intrinsic three-quark forces beyond those considered. The paper makes a useful contribution by supplying explicit transformation-coefficient tables (Tables I-III) and a checkable algebraic example (Eq. (14)); I verified that the bracketed sum in Eq. (14) equals -20/3 and that the expression indeed vanishes. However, the manuscript provides no machine-checked proofs or reproducible code, and the central claim is presented as unconditional in the abstract while in fact resting on an explicitly imposed equal-size assumption that is neither derived nor tested. The significance of the result therefore depends on whether that assumption is physically justified or its sensitivity is quantified.

major comments (3)

[Section IV, paragraph after Eq. (10)] The central cancellation is conditional on the stated assumption: 'we will take the flavour SU(3) limit and further take the interquark distances inside the baryon, dibaryon and tribaryon to be the same.' This assumption is load-bearing because the pair-counting identity 36-45+9=0 in Section VI only implies cancellation when every quark pair has the same spatial integral Ig. In a variational Gaussian model, the optimal scale for a 3-quark, 6-quark, and 9-quark system will generally differ, so Ig would differ among baryon, dibaryon, and tribaryon pairs, and V3 in Eq. (11) would not vanish by the counting argument. The manuscript neither derives the equal-size condition from the model nor quantifies the sensitivity of V3 to relaxing it. The concluding caveat about flavor SU(3) breaking addresses a different issue, namely unequal strange-quark masses, not the equal-size assumption within the symmetric limit. This issue should be resolved before the abstract's unconditional statement 'the intrinsic three-body interaction vanishes' can be accepted.
[Section V, Eq. (14) and following paragraph] The paper claims that the intrinsic three-body interaction vanishes 'for all possible flavor and spin quantum numbers,' but the only explicit calculation shown is Eq. (14) for (F,S)=(8,1/2). The remaining fourteen states are covered by the sentence 'In a similar way, we can show that...' rather than by a displayed result. Since Table II and Table III are provided, the computation is in principle reproducible, but the manuscript does not present the final bracketed sums that vanish for each of the fifteen states. Given that the central claim is all-state vanishing, I ask that the authors provide a table (or a supplementary file) listing, for every (F,S) entry, the analog of Eq. (14) with the explicit numerical coefficients and matrix elements, so the reader can verify that each sum is identically zero.
[Section V, final paragraph; Section VI, Eq. (17)] The claims for the flavor-spin interaction and for intrinsic three-quark f-type and d-type interactions are also asserted rather than demonstrated. For the flavor-spin interaction, the text states 'One can show... we find that the intrinsic three-body force vanishes for all quantum numbers' without any worked example or table analogous to Eq. (14). For the three-quark interactions, Eq. (17) gives the summed operator identities, but the cancellation in Eq. (11) is only described as 'suggests that it cancels.' The d-type cancellation can be made explicit by substituting N=9 for the tribaryon, N=6 for each of three dibaryons, and N=3 for each of three baryons into the second line of Eq. (17); since the paper's abstract and conclusion both rely on these results, this step should be written out and the flavor-spin case should be backed by at least one explicit channel or a table of final sums.

minor comments (5)

[Title page] The header contains a broken word 'constitue nt'; this should be corrected to 'constituent'.
[Eq. (13)] Equation (13) is hard to parse because the summation index j, the probability P, and the meaning of the factor 3 are introduced only in the surrounding text. Please define all symbols in the displayed equation or in a preceding sentence.
[Table II] Table II is very wide and contains many small fractions; consider moving it to supplementary material or providing a machine-readable version so that the entries can be checked independently.
[Abstract and Section II] The abstract says 'three nucleon states,' but the classification in Section II and Table III includes all octet and decuplet three-baryon channels. Please clarify whether the vanishing result is claimed for all three-baryon flavor channels or specifically for the three-nucleon sector.
[Section VI] The closing statement that the intrinsic three-body interaction 'will be small also in the flavor SU(3) broken case' is presented as a belief supported by previous two-baryon work; since no broken-symmetry three-body calculation is shown, please mark this explicitly as an expectation rather than a model result.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: V3 = 0 is a derived group-theoretic identity under an explicitly stated equal-size assumption, not an input relabeled as a prediction.

full rationale

The paper defines the intrinsic three-body interaction as the residual after subtracting two-baryon contributions (Eq. 10), then explicitly assumes a common interquark distance so that all spatial integrals collapse to a single constant Ig. Under this stated assumption, V3 reduces to Ig times a pure group-theoretic combination of color-spin matrix elements; the vanishing of that combination is then demonstrated channel by channel (e.g., Eq. 14) using tabulated transformation coefficients and matrix elements. This is a nontrivial derived identity rather than a restatement of the definition, since the same calculation could in principle have produced a nonzero combination. The self-citations to Refs. [17] and [20] supply tribaryon/dibaryon matrix elements and the rationale for the equal-size limit, but Ref. [20] is benchmarked against lattice QCD data external to this paper, so the self-citation is not load-bearing circularity under the stated rules. The equal-size assumption is a model input whose validity is a correctness concern, not a hidden circular step: the paper states it plainly in Section IV and acknowledges that the SU(3) broken case is not calculated. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors, and no ansatz is smuggled in via citation.

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

The paper introduces no new entities and fits no data. It rests on the standard constituent quark model plus symmetry and geometry assumptions that are stated in the text. The main unproved inputs are the transformation coefficient tables and the group-theoretic identity in Eq. (17).

assumptions (4)

domain assumption Flavor SU(3) symmetric limit with degenerate u, d, s quark masses
Invoked throughout Sections II and IV; the entire classification of baryon and dibaryon flavor states and the common spatial integral Ig depend on this limit.
domain assumption Equal interquark distances, same Gaussian width a, in baryon, dibaryon, and tribaryon configurations
Stated in Section IV after Eq. (10); it makes the kinetic terms and the spatial part of the two-quark potential common to all clusters, enabling the cancellation.
domain assumption Non-relativistic constituent quark Hamiltonian with only two-body color-color and color-spin interactions
The central claim is derived within this model, Eq. (5); any three-body force from other dynamics such as pion exchange is outside the calculation.
standard math Group-theoretic identities for f-type and d-type three-quark interactions
Stated without proof in Section VI, Eq. (17); used to argue that even intrinsic three-quark interactions cancel. If the identity is incorrect, the conclusion about three-quark forces fails.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Intrinsic three-body nuclear interaction from a constituent quark model." pith.science (2026). https://pith.science/paper/HARZYKXL

@misc{pith2026190808333,
  author       = {Pith},
  title        = {Pith review of: Intrinsic three-body nuclear interaction from a constituent quark model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HARZYKXL}},
  note         = {Machine review of arXiv:1908.08333}
}

read the original abstract

We study the short distance part of the intrinsic three-nucleon interaction in a constituent quark model with color-spin interaction. For that purpose we first calculate the transformation coefficient between the tribaryon configuration and their corresponding three baryon basis. Using a formula for the intrinsic three-body interaction in terms of a tribaryon configuration, we find that after subtracting the corresponding two-baryon contributions, the intrinsic three-body interaction vanishes in flavor SU(3) symmetric limit for all quantum numbers for the three nucleon states. We further find that the intrinsic three-body interaction also vanishes for flavor-spin type of quark interaction.

Figures

Figures reproduced from arXiv: 1908.08333 by the authors.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

28 extracted references · 13 canonical work pages

[17]

A. Park, W. Park and S. H. Lee, Phys. Rev. D 98, no. 3, 034001 (2018) doi:10.1103/PhysRevD.98.034001 [arXiv:1801.10350 [hep-ph]]

work page Pith review arXiv 2018
[20]

A. Park, S. H. Lee, T. Inoue and T. Hatsuda, arXiv:1907.06351 [hep-ph]

work page Pith review arXiv 1907
[1]

Lacombe, B

M. Lacombe, B. Loiseau, J. M. Richard, R. Vinh Mau, J. Cote, P. Pires and R. De Tourreil, Phys. Rev. C 21, 861 (1980). doi:10.1103/PhysRevC.21.861

work page doi:10.1103/physrevc.21.861 1980
[2]

Machleidt, K

R. Machleidt, K. Holinde and C. Elster, Phys. Rept. 149, 1 (1987). doi:10.1016/S0370-1573(87)80002-9

doi:10.1016/s0370-1573(87)80002-9 1987
[3]

Oka and K

M. Oka and K. Yazaki, Prog. Theor. Phys. 66, 572 (1981). doi:10.1143/PTP.66.572

work page doi:10.1143/ptp.66.572 1981
[4]

Shimizu, Rept

K. Shimizu, Rept. Prog. Phys. 52, 1 (1989). doi:10.1088/0034-4885/52/1/001

work page doi:10.1088/0034-4885/52/1/001 1989
[5]

Weinberg, Phys

S. Weinberg, Phys. Lett. B 251, 288 (1990). doi:10.1016/0370-2693(90)90938-3

doi:10.1016/0370-2693(90)90938-3 1990
[6]

Ordonez, L

C. Ordonez, L. Ray and U. van Kolck, Phys. Rev. Lett. 72, 1982 (1994). doi:10.1103/PhysRevLett.72.1982

doi:10.1103/physrevlett.72.1982 1994

Show all 28 references

[7]

P. F. Bedaque and U. van Kolck, Ann. Rev. Nucl. Part. Sci. 52, 339 (2002) doi:10.1146/annurev.nucl.52.050102.090637 [nucl-th/0203055]

2002
[8]

Polinder, J

H. Polinder, J. Haidenbauer and U.- G. Meissner, Phys. Lett. B 653, 29 (2007) doi:10.1016/j.physletb.2007.07.045 [arXiv:0705.3753 [nucl-th]]

2007 arXiv
[9]

Ishii, S

N. Ishii, S. Aoki and T. Hatsuda, Phys. Rev. Lett. 99, 022001 (2007) doi:10.1103/PhysRevLett.99.022001 [nucl-th/0611096]

2007 arXiv
[10]

Inoue et al

T. Inoue et al. [HAL QCD Collaboration], Prog. Theor. Phys. 124, 591 (2010) doi:10.1143/PTP.124.591 [arXiv:1007.3559 [hep-lat]]

2010 arXiv
[11]

Sasaki et al

K. Sasaki et al. [HAL QCD Collabora- tion], EPJ Web Conf. 175, 05010 (2018). doi:10.1051/epjconf/201817505010

2018
[12]

Fujita and H

J. Fujita and H. Miyazawa, Prog. Theor. Phys. 17, 360 (1957). doi:10.1143/PTP.17.360 8

1957 doi
[13]

Kalantar-Nayestanaki, E

N. Kalantar-Nayestanaki, E. Epelbaum, J. G. Messchen- dorp and A. Nogga, Rept. Prog. Phys. 75, 016301 (2012) doi:10.1088/0034-4885/75/1/016301 [arXiv:1108.1227 [nucl-th]]

2012 arXiv
[14]

Ohnishi, K

A. Ohnishi, K. Kashiwa and K. Morita, PTEP 2017, no. 7, 073D04 (2017) doi:10.1093/ptep/ptx095 [arXiv:1610.06306 [nucl-th]]

2017 arXiv
[15]

Doi et al

T. Doi et al. [HAL QCD Collaboration], Prog. Theor. Phys. 127, 723 (2012) doi:10.1143/PTP.127.723 [arXiv:1106.2276 [hep-lat]]

2012 arXiv
[16]

Aoki [Sinya AOKI for HAL QCD Collabora- tion], Prog

S. Aoki [Sinya AOKI for HAL QCD Collabora- tion], Prog. Part. Nucl. Phys. 66, 687 (2011) doi:10.1016/j.ppnp.2011.07.001 [arXiv:1107.1284 [hep- lat]]

2011 arXiv
[18]

Demorest, T

P. Demorest, T. Pennucci, S. Ransom, M. Roberts and J. Hessels, Nature 467, 1081 (2010) doi:10.1038/nature09466 [arXiv:1010.5788 [astro- ph.HE]]

2010 arXiv
[19]

Antoniadis et al

J. Antoniadis et al. , Science 340, 6131 (2013) doi:10.1126/science.1233232 [arXiv:1304.6875 [astro- ph.HE]]

2013 arXiv
[21]

Inoue [LATTICE-HALQCD Collaboration], PoS INPC 2016, 277 (2016) doi:10.22323/1.281.0277 [arXiv:1612.08399 [hep-lat]]

T. Inoue [LATTICE-HALQCD Collaboration], PoS INPC 2016, 277 (2016) doi:10.22323/1.281.0277 [arXiv:1612.08399 [hep-lat]]

2016 arXiv
[22]

Harvey, Nucl

M. Harvey, Nucl. Phys. A 352, 301 (1981) Erratum: [Nucl. Phys. A 481, 834 (1988)]. doi:10.1016/0375- 9474(81)90412-7

1981 doi
[23]

F. Wang, J. l. Ping and J. T. Goldman, Phys. Rev. C 51, 1648 (1995) doi:10.1103/PhysRevC.51.1648 [nucl-th/9510025]

1995 arXiv
[24]

W. Park, A. Park and S. H. Lee, Phys. Rev. D 92, no. 1, 014037 (2015) doi:10.1103/PhysRevD.92.014037 [arXiv:1506.01123 [nucl-th]]

2015 arXiv
[25]

Stancu, Oxford Stud

F. Stancu, Oxford Stud. Nucl. Phys. 19, 1 (1996)

1996
[26]

L. Y. Glozman and D. O. Riska, Phys. Rept. 268, 263 (1996) doi:10.1016/0370-1573(95)00062-3 [hep-ph/9505422]

1996 arXiv
[27]

A. T. M. Aerts, P. J. G. Mulders and J. J. de Swart, Phys. Rev. D 17, 260 (1978). doi:10.1103/PhysRevD.17.260

1978 doi
[28]

Silvestre- Brac and J

B. Silvestre- Brac and J. Leandri, Phys. Rev. D 45, 4221 (1992). doi:10.1103/PhysRevD.45.4221

1992 doi

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [17]

A. Park, W. Park and S. H. Lee, Phys. Rev. D 98, no. 3, 034001 (2018) doi:10.1103/PhysRevD.98.034001 [arXiv:1801.10350 [hep-ph]]

work page Pith review arXiv 2018

[2] [20]

A. Park, S. H. Lee, T. Inoue and T. Hatsuda, arXiv:1907.06351 [hep-ph]

work page Pith review arXiv 1907

[3] [1]

Lacombe, B

M. Lacombe, B. Loiseau, J. M. Richard, R. Vinh Mau, J. Cote, P. Pires and R. De Tourreil, Phys. Rev. C 21, 861 (1980). doi:10.1103/PhysRevC.21.861

work page doi:10.1103/physrevc.21.861 1980

[4] [2]

Machleidt, K

R. Machleidt, K. Holinde and C. Elster, Phys. Rept. 149, 1 (1987). doi:10.1016/S0370-1573(87)80002-9

doi:10.1016/s0370-1573(87)80002-9 1987

[5] [3]

Oka and K

M. Oka and K. Yazaki, Prog. Theor. Phys. 66, 572 (1981). doi:10.1143/PTP.66.572

work page doi:10.1143/ptp.66.572 1981

[6] [4]

Shimizu, Rept

K. Shimizu, Rept. Prog. Phys. 52, 1 (1989). doi:10.1088/0034-4885/52/1/001

work page doi:10.1088/0034-4885/52/1/001 1989

[7] [5]

Weinberg, Phys

S. Weinberg, Phys. Lett. B 251, 288 (1990). doi:10.1016/0370-2693(90)90938-3

doi:10.1016/0370-2693(90)90938-3 1990

[8] [6]

Ordonez, L

C. Ordonez, L. Ray and U. van Kolck, Phys. Rev. Lett. 72, 1982 (1994). doi:10.1103/PhysRevLett.72.1982

doi:10.1103/physrevlett.72.1982 1994