Compositeness of near-threshold exotic hadrons in systems with Coulomb and short-range interactions

Tetsuo Hyodo; Tomona Kinugawa

REVIEW

Compositeness of near-threshold exotic hadrons in systems with Coulomb and short-range interactions

Tomona Kinugawa, Tetsuo Hyodo

High Energy Physics - Phenomenology · Submitted 6 Oct 2026 · 19 references

Pith's verdict: A plausible regime criterion announced in a companion letter whose quantitative support all lives in the same authors' unreviewed preprint; useful and clearly framed, but not established on its own.

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arXiv ID2610.08340 (version 1)

Pith IDZSLS6AJU, Pith's permanent record of this paper and its review

CitationTetsuo Hyodo, Tomona Kinugawa. "Compositeness of near-threshold exotic hadrons in systems with Coulomb and short-range interactions." arXiv:2610.08340 (2026). https://pith.science/paper/ZSLS6AJU

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Claim paper

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Editor's note

read the letter

Quick take: this is a short companion letter whose real new element is the |r_CE|/a_B regime criterion, and nearly everything quantitative - Eq. (3), R_C, the pole trajectories, the resonance-interpretation prescription, the X to 1 limits - is delegated to the same authors' preprint [19], which is unreviewed. As a standalone manuscript it does not establish its central claim. That is a real weakness, though it is a normal genre: a letter pointing at a longer paper.

What the paper does well: the physical motivation is sharp. The 8Be and Xi-alpha examples make the case that Coulomb can qualitatively flip threshold behavior, and the criterion itself is a memorable organizing principle - effective range versus Bohr radius decides whether the standard short-range compositeness expectation survives. The writing is clear, and the provenance is honest: the authors state in b37 and b39 what the window condition is, and they do not hide that the pole analysis is in [19]. The citation pattern is fine; [13] is an accepted PTEP paper, and the self-citation to [19] is disclosed rather than buried.

The soft spots, in proportion. The abstract says "we derive a relation," but the derivation is not in this paper; the manuscript is an announcement. That alone would be a minor-to-moderate complaint for the genre. The bigger issue is the Section 3 scale separation, and I think the stress-test concern lands. The paper asserts that inside 1/a_B << k << 1/|r_CE| both the Coulomb term -2 k_C H(eta) and the effective-range term are negligible, leaving the pole governed by 1/a_CS. Two things are not shown. Near the lower end of the window, eta ~ 1 and H(eta) is order one, not small; the small-eta expansion that would justify neglecting H holds only for k >> 1/a_B. And the comparison base 1/a_CS is itself small for the near-threshold states of interest, so a Coulomb term of order 1/a_B is not obviously negligible against it inside the stated window. The existence of the window by itself does not establish scattering-length dominance. That gap is real in this manuscript; the companion paper may well fill it, but the letter doesn't.

Verdict: send it to a serious referee, but with instructions to check [19] or require the derivation in-text. The question is timely and the criterion is worth testing. For my own work I would wait for [19] before citing the letter itself.

Referee report

Significance

If established, the criterion |r_Ce|/a_B would be a genuinely useful, falsifiable rule of thumb for when Coulomb effects must be included in compositeness analyses of near-threshold exotic hadrons, with direct relevance to systems such as 8Be (αα), Ξ-α, X(3872), and T_cc. The scale-separation logic is clearly and honestly articulated, and the weak/strong-Coulomb dichotomy is physically plausible and testable. However, as it stands the manuscript is essentially a 4-page summary of the authors' unreviewed preprint [19]: every quantitative statement (pole trajectories, the expression for compositeness, the resonance prescription, the rate of approach of X to 1) is asserted rather than derived or numerically checked here. The central quantitative claim is therefore not established by this manuscript alone, and the internal window argument in Section 3 has a gap that needs to be closed before the criterion can be accepted.

Major objections (3)

[Section 3, window argument] The claim that '-2 k_C H(η)' is negligible throughout the window 1/a_B << k << 1/|r_Ce| is unsupported, because H(η) is never analyzed. With k_C = 1/a_B, one has η = (1/a_B)/k, which is of order unity near the lower end of the window and only small for k >> 1/a_B; the small-η expansion H(η) ≈ ζ(3) η^2 (which the paper implicitly relies on) is valid only in that subregion. The manuscript needs an explicit bound on |H(η)| in the full window before it can assert that the Coulomb term is subleading there.
[Section 3, pole location vs. window] The pole is said to be 'mainly governed by the scattering length' in the window, but the relevant comparison is against 1/a_Cs, which is itself small for the near-threshold states of interest. The actual pole lies at k ≈ |1/a_Cs| in the scattering-length regime, and the manuscript never states the condition that this momentum falls inside the window 1/a_B << k << 1/|r_Ce| (or otherwise bounds 1/a_Cs against 1/a_B and |r_Ce|). If |1/a_Cs| is comparable to or smaller than 1/a_B, the pole sits in the Coulomb-dominated region and the composite-dominant conclusion does not follow from the mere existence of the window.
[Eq. (3) and Sections 2-4] All quantitative support for the headline claims—the compositeness formula (3), the length scale R_C, the pole trajectories for attractive and repulsive Coulomb, the resonance interpretation prescription, and the X→1 limits (including the 'faster enhancement' claim in the weak-Coulomb regime)—is delegated to the authors' own preprint [19], which is not a refereed publication. As a result, none of the central quantitative claims (sentences b41, b44, b45, b47) can be checked from this manuscript. For this letter to stand alone, the essential derivation (at minimum a sketch of the pole condition and of Eq. (3)) should be included, or [19] should be cited in a form that is verifiable.

Minor objections (5)

[Eq. (1)] The notation is not fully defined: the factor 'C 2 η e2iσ0' should be C_η^2 e^{2iσ_0}, and the sign conventions for a_Cs, r_Ce, and σ_0 are not stated in this manuscript.
[Eq. (3)] R_C is introduced by name but never characterized in this paper; even a one-sentence statement of its defining property (the length scale of the Coulomb-modified wave function) would improve self-containedness.
[Section 3, attractive Coulomb discussion] The statements that X approaches unity at the pure Coulomb ground state and does so more rapidly in the weak-Coulomb regime (sentences b45-b47) are asserted without even a qualitative argument in this manuscript; a brief explanation of why the pure Coulomb state has no bare component would help.
[References] Reference [19] is an arXiv preprint and should be marked as such (unpublished), so that the reader is aware the quantitative results it supplies are not peer-reviewed.
[Throughout] The rendered subscripts and superscripts (e.g., 'rC e', 'aC s', 'aB') are corrupted by formatting throughout the text, especially in Eqs. (1)-(3) and Section 3; these should be typeset properly.

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The paper

The paper claims

A single ratio — Coulomb effective range over Bohr radius — decides whether near-threshold hadron states stay composite-dominant despite long-range Coulomb forces.

The reading

This paper asks whether the long-range Coulomb force erases the low-energy universality that makes near-threshold states in purely short-range systems composite-dominant. Its answer is that a single dimensionless ratio controls the outcome: the Coulomb effective range $r_C^e$ relative to the Bohr radius $a_B$. When $|r_C^e|/a_B \ll 1$ the Coulomb force is weak at the relevant scales, an intermediate momentum window opens where the short-range interaction alone governs the pole, and near-threshold bound states (and, for repulsive Coulomb, nearby resonances) stay composite-dominant. When $|r_C^e|/a_B \gg 1$ that window closes, the compositeness enhancement disappears, and near-threshold states need not be composite-dominant. If correct, the criterion gives a practical flag for when Coulomb effects must be folded into structure analyses of candidates like the X(3872) and T_cc.

What carries the argument

The argument runs through the Coulomb-distorted short-range scattering amplitude $f^{CS}(k)$ of Eq. (1), whose denominator contains the Coulomb scattering length $a_C^s$, the Coulomb effective range $r_C^e$, and the Coulomb term $-2 k_C H(\eta)$, together with the compositeness formula $X = [1 - r_C^e/R_C]^{-1}$, where $R_C$ is the wave-function length scale in the presence of Coulomb interaction. The load-bearing mechanism is the scale-separation window $1/a_B \ll k \ll 1/|r_C^e|$: when such a window exists, the pole is governed primarily by the scattering length and the short-range universality leaves a remnant that pushes $X$ toward unity.

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the ratio $|r_C^e|/a_B$ of the Coulomb effective range to the Bohr radius determines whether a remnant of short-range low-energy universality survives in systems with Coulomb plus short-range interactions. In the weak-Coulomb regime $|r_C^e|/a_B \ll 1$, there is a momentum window $1/a_B \ll k \ll 1/|r_C^e|$ in which both the Coulomb term and the effective-range term in the Coulomb-distorted scattering amplitude are negligible, so the pole is set by the Coulomb scattering length; the compositeness of near-threshold bound states is then enhanced toward unity, and for repulsive Coulomb the bound state's composite-dominant nature persists into the resonance region across the threshold. In the strong-Coulomb regime $|r_C^e|/a_B \gg 1$, the Coulomb-dominant region is reached before the universal window can open, the enhancement disappears, and near-threshold states are not necessarily composite-dominant.

Load-bearing premise

The load-bearing premise is that a genuinely empty intermediate momentum window $1/a_B \ll k \ll 1/|r_C^e|$ exists in which the Coulomb form factor $-2 k_C H(\eta)$ is negligible; the paper infers this from the Bohr-radius scale but does not analyze $H(\eta)$ or verify that the Coulomb-modified effective-range expansion remains accurate there.

Editorial extensions

If this is right

The ratio $|r_C^e|/a_B$ becomes a quantitative screening criterion: candidates with $|r_C^e|/a_B \ll 1$ can be treated under short-range universality, while those with the ratio of order one or larger require Coulomb-corrected structure analyses.
For repulsive Coulomb systems in the weak-Coulomb regime, near-threshold resonances inherit the composite-dominant nature of the connected bound state across the threshold, extending the universal expectation into the resonance region.
For attractive Coulomb systems, the compositeness approaches unity at the pure Coulomb ground state regardless of the effective range, and does so faster in the weak-Coulomb regime.
Systems of the 8Be type, where switching off Coulomb repulsion turns a near-threshold resonance into a bound state, illustrate the qualitative sensitivity of the pole structure to the long-range force that this scheme aims to characterize.

Reading between the lines

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

The criterion could serve as a red flag in experimental searches: a narrow near-threshold candidate with $|r_C^e|/a_B$ of order one or larger should not be assumed composite-dominant without explicitly accounting for Coulomb distortions.
The composite-dominant conclusion for repulsive-Coulomb resonances depends on the specific interpretation prescription applied to the complex compositeness; a different prescription could shift that reading.
The same scale-separation logic may extend to other long-range power-law forces, such as dipole or van der Waals interactions, with an analogous dimensionless ratio controlling the surviving remnant of universality.

Original abstract

We study the universal properties of near-threshold $s$-wave eigenstates in systems with Coulomb plus short-range interactions by analyzing their compositeness. Using a nonrelativistic effective field theory, we derive a relation between the compositeness of near-threshold states and the Coulomb scattering length, the Coulomb effective range, and the Bohr radius. We find that the long-range Coulomb interaction modifies the threshold behavior expected from the low-energy universality of purely short-range systems. When the Coulomb interaction is relatively weak compared with the short-range interaction, a remnant of the low-energy universality associated with the short-range interaction survives, leading to composite-dominant near-threshold eigenstates. In contrast, in the strong-Coulomb regime, this remnant disappears.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-07: 1 request, 4,326 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.25 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.58 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We study the universal properties of near-threshold $s$-wave eigenstates in systems with Coulomb plus short-range interactions by analyzing their compositeness. Using a nonrelativistic effective field theory, we derive a relation between the compositeness of near-threshold states and the Coulomb scattering length, the Coulomb effective range, and the Bohr radius. We find that the long-range Coulomb interaction modifies the threshold behavior expected from the low-energy universality of purely short-range systems. When the Coulomb interaction is relatively weak compared with the short-range interaction, a remnant of the low-energy universality associated with the short-range interaction survives, leading to composite-dominant near-threshold eigenstates. In contrast, in the strong-Coulomb regime, this remnant disappears.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the universal properties of near-threshold $s$-wave eigenstates in systems with Coulomb plus short-range interactions by analyzing their compositeness.	contribution 0.99	0.94	0.07	asserted 0.81
s1	Using a nonrelativistic effective field theory, we derive a relation between the compositeness of near-threshold states and the Coulomb scattering length, the Coulomb effective range, and the Bohr radius.	method 0.66	0.96	0.13	asserted 1.00
s2	We find that the long-range Coulomb interaction modifies the threshold behavior expected from the low-energy universality of purely short-range systems.	result 0.97	0.94	0.31	asserted 1.00
s3	When the Coulomb interaction is relatively weak compared with the short-range interaction, a remnant of the low-energy universality associated with the short-range interaction survives, leading to composite-dominant near-threshold eigenstates.	result 0.88	0.89	0.35	asserted 0.99
s4	In contrast, in the strong-Coulomb regime, this remnant disappears.	result 0.98	0.86	0.16	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (19)

[19]

T. Kinugawa, T. Hyodo, Compositeness of near-threshold eigenstates with Coulomb plus short-range interactions (2026),2604.17813

View on Pith Pith review arXiv 2026
[13]

T. Kinugawa, T. Hyodo, Compositeness of near-thresholds-wave resonances (2024), 2403.12635, accepted in Prog. Theor. Exp. Phys. 10.1093/ptep/ptag173

View on Pith Pith review arXiv 2024
[1]

S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D110, 030001 (2024). 10.1103/PhysRevD.110.030001

View on Pith doi:10.1103/physrevd.110.030001 2024
[2]

A. Hosaka, Y . Kanada-En’yo, Y . Yamaguchi, Clustering in nuclei and hadrons, Eur. Phys. J. A61, 103 (2025). 10.1140/epja/s10050-025-01530-8

View on Pith doi:10.1140/epja/s10050-025-01530-8 2025
[3]

S. Weinberg, Evidence That the Deuteron Is Not an Elementary Particle, Phys. Rev. 137, B672 (1965). 10.1103/PhysRev.137.B672

View on Pith doi:10.1103/physrev.137.b672 1965
[4]

T. Hyodo, Structure and compositeness of hadron resonances, Int. J. Mod. Phys. A28, 1330045 (2013),1310.1176. 10.1142/S0217751X13300457

View on Pith Pith review arXiv 2013
[5]

J.A. Oller, New results from a number operator interpretation of the composite- ness of bound and resonant states, Annals Phys.396, 429 (2018),1710.00991. 10.1016/j.aop.2018.07.023

View on Pith Pith review arXiv 2018
[6]

U. van Kolck, Weinberg’s Compositeness, Symmetry14, 1884 (2022),2209.08432. 10.3390/sym14091884

View on Pith Pith review arXiv 2022
[7]

T. Kinugawa, T. Hyodo, Compositeness of hadrons, nuclei, and atomic systems, Eur. Phys. J. A61, 154 (2025),2411.12285. 10.1140/epja/s10050-025-01548-y

View on Pith arXiv 2025
[8]

T. Kinugawa, T. Hyodo, Structure of exotic hadrons by a weak-binding relation with finite-range correction, Phys. Rev. C106, 015205 (2022),2205.08470. 10.1103/Phys- RevC.106.015205

View on Pith Pith review arXiv 2022
[9]

E. Braaten, H.W. Hammer, Universality in few-body systems with large scattering length, Phys. Rept.428, 259 (2006),cond-mat/0410417. 10.1016/j.physrep.2006.03.001

View on Pith Pith review arXiv 2006
[10]

P. Naidon, S. Endo, Efimov Physics: a review, Rept. Prog. Phys.80, 056001 (2017), 1610.09805. 10.1088/1361-6633/aa50e8

View on Pith Pith review arXiv 2017
[11]

T. Hyodo, Hadron mass scaling near the s-wave threshold, Phys. Rev. C90, 055208 (2014),1407.2372. 10.1103/PhysRevC.90.055208

View on Pith Pith review arXiv 2014
[12]

T. Kinugawa, T. Hyodo, Compositeness of Tcc and X(3872) by considering de- cay and coupled-channels effects, Phys. Rev. C109, 045205 (2024),2303.07038. 10.1103/PhysRevC.109.045205

View on Pith Pith review arXiv 2024
[14]

R. Higa, H.W. Hammer, U. van Kolck, alpha alpha Scattering in Halo Effective Field Theory, Nucl. Phys. A809, 171 (2008),0802.3426. 10.1016/j.nuclphysa.2008.06.003

View on Pith Pith review arXiv 2008
[15]

E. Hiyama, M. Isaka, T. Doi, T. Hatsuda, Probing theΞN interaction through inver- sion of spin-doublets inΞNααnuclei, Phys. Rev. C106, 064318 (2022),2209.06711. 10.1103/PhysRevC.106.064318

View on Pith Pith review arXiv 2022
[16]

X. Kong, F. Ravndal, Proton proton scattering lengths from effective field the- ory, Phys. Lett. B450, 320 (1999), [Erratum: Phys.Lett.B 458, 565–565 (1999)], nucl-th/9811076. 10.1016/S0370-2693(99)00144-6

View on Pith Pith review arXiv 1999
[17]

X. Kong, F. Ravndal, Coulomb effects in low-energy proton proton scattering, Nucl. Phys. A665, 137 (2000),hep-ph/9903523. 10.1016/S0375-9474(99)00406-6

View on Pith Pith review arXiv 2000
[18]

S.i. Ando, J.W. Shin, C.H. Hyun, S.W. Hong, Low energy proton-proton scattering in effective field theory, Phys. Rev. C76, 064001 (2007),0704.2312. 10.1103/Phys- RevC.76.064001

View on Pith Pith review arXiv 2007

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [19]

T. Kinugawa, T. Hyodo, Compositeness of near-threshold eigenstates with Coulomb plus short-range interactions (2026),2604.17813

View on Pith Pith review arXiv 2026

[2] [13]

T. Kinugawa, T. Hyodo, Compositeness of near-thresholds-wave resonances (2024), 2403.12635, accepted in Prog. Theor. Exp. Phys. 10.1093/ptep/ptag173

View on Pith Pith review arXiv 2024

[3] [1]

S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D110, 030001 (2024). 10.1103/PhysRevD.110.030001

View on Pith doi:10.1103/physrevd.110.030001 2024

[4] [2]

A. Hosaka, Y . Kanada-En’yo, Y . Yamaguchi, Clustering in nuclei and hadrons, Eur. Phys. J. A61, 103 (2025). 10.1140/epja/s10050-025-01530-8

View on Pith doi:10.1140/epja/s10050-025-01530-8 2025

[5] [3]

S. Weinberg, Evidence That the Deuteron Is Not an Elementary Particle, Phys. Rev. 137, B672 (1965). 10.1103/PhysRev.137.B672

View on Pith doi:10.1103/physrev.137.b672 1965

[6] [4]

T. Hyodo, Structure and compositeness of hadron resonances, Int. J. Mod. Phys. A28, 1330045 (2013),1310.1176. 10.1142/S0217751X13300457

View on Pith Pith review arXiv 2013

[7] [5]

J.A. Oller, New results from a number operator interpretation of the composite- ness of bound and resonant states, Annals Phys.396, 429 (2018),1710.00991. 10.1016/j.aop.2018.07.023

View on Pith Pith review arXiv 2018

[8] [6]

U. van Kolck, Weinberg’s Compositeness, Symmetry14, 1884 (2022),2209.08432. 10.3390/sym14091884

View on Pith Pith review arXiv 2022

[9] [7]

T. Kinugawa, T. Hyodo, Compositeness of hadrons, nuclei, and atomic systems, Eur. Phys. J. A61, 154 (2025),2411.12285. 10.1140/epja/s10050-025-01548-y

View on Pith arXiv 2025

[10] [8]

T. Kinugawa, T. Hyodo, Structure of exotic hadrons by a weak-binding relation with finite-range correction, Phys. Rev. C106, 015205 (2022),2205.08470. 10.1103/Phys- RevC.106.015205

View on Pith Pith review arXiv 2022

[11] [9]

E. Braaten, H.W. Hammer, Universality in few-body systems with large scattering length, Phys. Rept.428, 259 (2006),cond-mat/0410417. 10.1016/j.physrep.2006.03.001

View on Pith Pith review arXiv 2006

[12] [10]

P. Naidon, S. Endo, Efimov Physics: a review, Rept. Prog. Phys.80, 056001 (2017), 1610.09805. 10.1088/1361-6633/aa50e8

View on Pith Pith review arXiv 2017

[13] [11]

T. Hyodo, Hadron mass scaling near the s-wave threshold, Phys. Rev. C90, 055208 (2014),1407.2372. 10.1103/PhysRevC.90.055208

View on Pith Pith review arXiv 2014

[14] [12]

T. Kinugawa, T. Hyodo, Compositeness of Tcc and X(3872) by considering de- cay and coupled-channels effects, Phys. Rev. C109, 045205 (2024),2303.07038. 10.1103/PhysRevC.109.045205

View on Pith Pith review arXiv 2024

[15] [14]

R. Higa, H.W. Hammer, U. van Kolck, alpha alpha Scattering in Halo Effective Field Theory, Nucl. Phys. A809, 171 (2008),0802.3426. 10.1016/j.nuclphysa.2008.06.003

View on Pith Pith review arXiv 2008

[16] [15]

E. Hiyama, M. Isaka, T. Doi, T. Hatsuda, Probing theΞN interaction through inver- sion of spin-doublets inΞNααnuclei, Phys. Rev. C106, 064318 (2022),2209.06711. 10.1103/PhysRevC.106.064318

View on Pith Pith review arXiv 2022

[17] [16]

X. Kong, F. Ravndal, Proton proton scattering lengths from effective field the- ory, Phys. Lett. B450, 320 (1999), [Erratum: Phys.Lett.B 458, 565–565 (1999)], nucl-th/9811076. 10.1016/S0370-2693(99)00144-6

View on Pith Pith review arXiv 1999

[18] [17]

X. Kong, F. Ravndal, Coulomb effects in low-energy proton proton scattering, Nucl. Phys. A665, 137 (2000),hep-ph/9903523. 10.1016/S0375-9474(99)00406-6

View on Pith Pith review arXiv 2000

[19] [18]

S.i. Ando, J.W. Shin, C.H. Hyun, S.W. Hong, Low energy proton-proton scattering in effective field theory, Phys. Rev. C76, 064001 (2007),0704.2312. 10.1103/Phys- RevC.76.064001

View on Pith Pith review arXiv 2007