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REVIEW 4 major objections 7 minor 21 references

Heavy Quark State Production via p-p and O-O Collisions

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A gluon-rich Υ(3S) hybrid should outproduce the ordinary Υ(3S) in O-O collisions, new rapidity cross sections predict.

desk verdict A short phenomenology note whose only new numbers are not reproducible from the text; the main 'prediction' is an input assumption, so rejection is warranted. read the letter →

arxiv 2506.09484 v2 pith:IU75LIME submitted 2025-06-11 hep-ph hep-exnucl-exnucl-th

Leonard S. Kisslinger , Debasish Das This is my paper
classification hep-phhep-exnucl-exnucl-th PACS 12.38.Aw13.60.Le14.40.Lb14.40.Nd
keywords heavyquarkstateproductionrelativisticioncollisionssuppressionsmallsystemsmixedhybridmesonsdifferentialrapiditycrosssectioncoloroctetmodelbottomonium
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 predicts the differential rapidity cross sections $d\sigma/dy$ for five heavy quark states — $J/\Psi$, $\Psi(2S)$, $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ — produced in proton-proton and oxygen-oxygen collisions at $\sqrt{s_{pp}}=5.44$ TeV, the energy planned for O-O runs at the LHC. Its central move is to treat $\Psi(2S)$ and $\Upsilon(3S)$ not as ordinary quark-antiquark mesons but as mixed hybrids, roughly half standard meson and half quark-antiquark-gluon state, with a mixing parameter $\alpha = 0.7 \pm 0.1$ fixed by earlier QCD sum-rule work. Because hybrid production is enhanced by a factor $\pi^2/4$, the predicted rate for the hybrid $\Upsilon(3S)$ exceeds that of the standard $\Upsilon(3S)$, and the authors argue this excess could be measured in future LHC experiments. The paper itself notes that the absolute magnitudes are uncertain and that the shapes and relative magnitudes of the distributions are its main predictions.

What carries the argument

The load-bearing objects are the mixed hybrid wavefunctions for $\Psi(2S)$ and $\Upsilon(3S)$, $|\Psi(2S)\rangle = \alpha|c\bar{c}(2S)\rangle + \sqrt{1-\alpha^2}|c\bar{c}g(2S)\rangle$ and $|\Upsilon(3S)\rangle = \alpha|b\bar{b}(3S)\rangle + \sqrt{1-\alpha^2}|b\bar{b}g(3S)\rangle$ with $\alpha = 0.7 \pm 0.1$, so that each state is about half ordinary quark-antiquark meson and half quark-antiquark-gluon hybrid. These feed the color octet model formula $d\sigma_{pp\to\Phi}/dy = A_\Phi\, x^{-1} f_g(\bar{x},2m)\, f_g(a/\bar{x},2m)\, dx/dy$, with the $\Psi(2S)$ and $\Upsilon(3S)$ hybrid amplitudes multiplied by the enhancement factor $\pi^2/4$, and the whole result scaled by the nuclear factors $R^E_{pp}=0.005$ and $R^E_{OO}=0.25$ for proton-proton and oxygen-oxygen collisions respectively.

What would settle it

At the LHC, measure $d\sigma/dy$ for $\Upsilon(3S)$ in O-O collisions at $\sqrt{s_{NN}}=5.44$ TeV and in p-p collisions, and compare it with the pure $b\bar{b}$ prediction. The paper's central prediction is that the hybrid-enhanced $\Upsilon(3S)$ curve lies above the standard $\Upsilon(3S)$ curve, with the same ordering for $\Psi(2S)$ against $J/\Psi$; a measured $\Upsilon(3S)$ rate at or below the standard-model curve, or a $\Psi(2S)/J/\Psi$ ratio matching the naive color-octet value, would rule out the $\pi^2/4$ hybrid enhancement.

Watch

Extended reading notes

Core claim

The paper claims that $\Psi(2S)$ and $\Upsilon(3S)$ are mixed hybrid states, $|\Psi(2S)\rangle = \alpha|c\bar{c}(2S)\rangle + \sqrt{1-\alpha^2}|c\bar{c}g(2S)\rangle$ and $|\Upsilon(3S)\rangle = \alpha|b\bar{b}(3S)\rangle + \sqrt{1-\alpha^2}|b\bar{b}g(3S)\rangle$ with $\alpha = 0.7 \pm 0.1$, so each has roughly a 50% probability of being a standard quark-antiquark meson and a 50% probability of being a color-octet quark-antiquark pair with an active gluon. Using the color octet model formula for the differential rapidity cross section, with the hybrid amplitudes multiplied by $\pi^2/4$, it computes $d\sigma/dy$ for $J/\Psi$, $\Psi(2S)$, $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ in p-p and O-O collisions at $\sqrt{s_{pp}}=5.44$ TeV. The central quantitative prediction is that the hybrid $\Upsilon(3S)$ rate lies above the standard pure-$b\bar{b}$ $\Upsilon(3S)$ rate in both collision systems, and in O-O it sits in a range the authors say could be measured in future LHC experiments, making the measurement both a test of the mixed hybrid theory and a guide for small-system runs.

Load-bearing premise

The load-bearing premise is that the hand-assigned normalization factors $R^E_{pp}=0.005$ and $R^E_{OO}=0.25$ — the oxygen value taken as half the Xe-Xe value without derivation — set the true absolute scale of every predicted cross section, so that a wrong factor of even a few would shift the claimed measurability of the $\Upsilon(3S)$ hybrid signal and all plotted rates.

Editorial extensions

If this is right

  • In O-O collisions at $\sqrt{s_{pp}}=5.44$ TeV, the measured $\Upsilon(3S)$ rate should lie above the standard bottomonium-only curve, providing a direct test of the mixed hybrid theory.
  • The $\Psi(2S)$ charmonium state should show a similar hybrid-enhanced $d\sigma/dy$ in both p-p and O-O, visible as an excess over the standard $c\bar{c}$ curve.
  • The predicted shapes and relative magnitudes of the five rapidity distributions, not just their absolute sizes, are the paper's stated main predictions, so shape comparisons against data at the same energy would be decisive.
  • A confirmed excess would validate the $\alpha = 0.7 \pm 0.1$ hybrid admixture extracted from earlier QCD sum rules and extend it to bottomonium as well as charmonium.

Reading between the lines

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

  • The ratio of O-O to p-p rates for a given state cancels the uncertain absolute normalization, so the most robust test of the $\pi^2/4$ enhancement is the ratio of measured yields, not the absolute cross section.
  • If O-O data come in, the same framework should be extended to Pb-Pb, where the larger $R^E_{AA}$ values would make the hybrid excess larger in absolute terms; a failure of that scaling would point to the hand-set normalization factors rather than the hybrid wavefunctions.
  • A natural next step the paper does not take is to compute $R^E_{OO}$ from first principles using the dissociation cross sections of the hybrid states, which would turn the assumed factor 0.25 into a derived quantity and sharpen the measurability claim.
  • Because hybrid states carry a valence gluon, the same $\pi^2/4$ mechanism predicts enhanced production in gluon-rich environments, suggesting the O-O signal could be cross-checked against high-multiplicity p-p events at the same energy.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 7 minor

Summary. The paper computes differential rapidity cross sections dσ/dy for J/Ψ, Ψ(2S), Υ(1S), Υ(2S), and Υ(3S) production in p-p and O-O collisions at √s_pp = 5.44 TeV, under the assumption that Ψ(2S) and Υ(3S) are mixed hybrid mesons with roughly a 50% valence-gluon component. The calculation uses the color-octet model formula in Eq. (11), nuclear modification factors R_E_pp = 0.005 and R_E_OO = 0.25, and a π²/4 enhancement for hybrid states taken from Ref. [16]. The paper's highlighted conclusion is that the hybrid Υ(3S) differential rapidity cross section in O-O collisions is larger than the standard Υ(3S) cross section and 'could be measured in future CERN LHC experiments.'

Significance. If the calculation were reliable, the paper would offer a concrete small-system prediction for O-O collisions and a possible experimental test of mixed-hybrid charmonium/bottomonium states. The paper is also transparent about the physical picture it assumes and states its main predictions in a falsifiable form. However, the quantitative output relies on unstated inputs and hand-assigned normalization factors, and the central 'hybrid > standard' ordering is imported as an input rather than derived. The paper provides no experimental comparison, no error bars, and no sensitivity analysis, and it explicitly disclaims the absolute magnitudes that the measurability claim depends on. The significance is therefore currently limited to a restatement of prior assumptions in a new collision system.

major comments (4)
  1. [Section 2.1, Eq. (11)] The constants A_Φ are given only for J/Ψ and Υ(1S); no values are supplied for Ψ(2S), Υ(2S), or Υ(3S), which are precisely the states emphasized in the paper. In addition, the gluon distribution f_g(x̄(y), 2m) is not identified with a specific PDF set, Q² scheme, or numerical implementation. Without these inputs, the curves in Figs. 2, 4, 6, and 8 cannot be reproduced or checked, so the quantitative content of the central plots is missing from the manuscript.
  2. [Sections 2.1-2.2, Eq. (9)] The O-O cross sections depend on N_bin, the number of binary nucleon-nucleon collisions, which is never defined or specified for O-O. The factor R_E_OO = 0.25 is introduced as 'R_E_XeXe/2' with no derivation, reference, or physical justification. Since these quantities set the absolute scale of every O-O curve, a factor of a few in either one changes the predicted Υ(3S)(hybrid) yield across any plausible LHC detection threshold. The measurability claim in Sec. 2.2 is therefore not robust to the unspecified inputs.
  3. [Section 2.1 and Section 2.2] The statement that the hybrid Υ(3S) cross section is larger than the standard Υ(3S) cross section is an input, not an output: the text says 'With Ψ(2S), Υ(3S) enhanced by π²/4 [16]' before plotting the curves. Because Ref. [16] is by the same first author, the claimed 'test of the validity of the mixed hybrid theory' reduces to re-inserting that enhancement factor. For the prediction to be a genuine test, the π²/4 factor would need to follow from the formalism developed in this paper or be independently justified here, rather than being adopted from prior work.
  4. [Section 2.1 vs. Section 2.2] The paper explicitly disclaims absolute magnitudes in Sec. 2.1, stating that 'the absolute magnitudes are uncertain, and the shapes and relative magnitudes are our main predictions.' Yet the highlighted conclusion in Sec. 2.2 ('could be measured in future CERN LHC experiments') is an absolute-rate statement. The manuscript needs a concrete LHC luminosity and acceptance estimate, together with a sensitivity study of the yield to R_E_OO, N_bin, and the PDF choice, or it should abandon the measurability claim and restrict itself to shape/relative predictions.
minor comments (7)
  1. [Eqs. (2)-(3)] The coefficients in Eq. (3), -√2 and +√2, are not normalized, and they are inconsistent with Eq. (2), where f ≃ √2 would imply coefficients √2 and 1, and with the normalized form in Eqs. (7)-(8).
  2. [Eq. (9)] Equation (9) is introduced as the Xe-Xe expression but is then used for p-p and O-O; the role of N_bin for p-p should be stated explicitly (presumably 1), and N_bin for O-O must be defined.
  3. [Eq. (12)] The nuclear shadowing parameter ξ_g² is introduced but its value is never specified; because it enters the effective parton momentum fraction, it affects the rapidity dependence of the predictions.
  4. [Figures, Section 2.2] Figure 4 appears within Section 2.2, which is about O-O collisions, but its caption says 'via p-p collisions'; the placement and caption should be reconciled.
  5. [References and text] There are numerous typographical errors, including 'Collaboratin', 'In stitute', 'P ACS', and 'Pittsburgh PA 1 5213 USA', and the PACS entry '14.40Nd' is malformed.
  6. [Section 2, Eqs. (7)-(8)] The uncertainty α = 0.7 ± 0.1 is given but never propagated into the figures or conclusions; the paper should state that the shown curves correspond to the central value and discuss the sensitivity to α.
  7. [Section 2, Results] The paper states that the ratios Ψ(2S)/J/Ψ and Υ(3S)/Υ(1S) 'agreed with experimental results', but no comparison with data is shown; a table or plot with the experimental values would make this claim verifiable.

Circularity Check

3 steps flagged · score 7.0 of 10

The paper's headline relative and absolute predictions reduce to the π²/4 enhancement imported from the authors' earlier Ref. [16] and to hand-assigned RE factors; the proposed test of the mixed-hybrid theory is a self-citation chain.

  1. self definitional [Sec. 2.1, after Eq. (12); Sec. 2.2, note after Fig. 5]
    "With Ψ(2S), Υ(3S) enhanced by π2/4 [16] the differential rapidity cross sections are shown in the following figures. The absolute magnitudes are uncertain, and the shapes and relative magnitudes are our main predictions. ... Note that the differential rapidity cross section for the Υ(3S)(hybrid) is larger than the differential rapidity cross section for the Υ(3S) and could be measured in future CERN LHC experiments."

    Equation (11) defines the standard dσ_pp/dy curve. The 'hybrid' curves are that same standard cross section multiplied by the constant π²/4 imported from Ref. [16]. Since π²/4 > 1, the paper's stated result that dσ/dy[Υ(3S)(hybrid)] > dσ/dy[Υ(3S)] is not deduced from the formalism: it is the chosen multiplicative factor, and the 'relative magnitude' prediction is the input constant itself. The 'could be measured' sentence extends the same construction to absolute rates after multiplying by RE and N_bin, so the advertised conclusion is predetermined by the input factor rather than derived.

  2. fitted input called prediction [Sec. 2.1, after Eq. (10); Sec. 2.2, first paragraph]
    "For p-p collisions we use RE pp =0.005 For O-O collisions we use RE OO =0.25. ... For O-O collisions we use RE OO =0.25= RE XeXe /2."

    Equation (9) gives dσ_AA/dy = R^E_AA N_bin ⟨dσ_pp/dy⟩. The O-O plots and the claim that the hybrid Υ(3S) 'could be measured' are obtained by inserting R^E_OO = 0.25, chosen as half the Xe-Xe value without derivation, and an N_bin that is never specified for O-O. Thus the absolute rates advertised to LHC experiments are not predictions from QCD or from the hybrid model; they are the hand-assigned normalization parameter renamed as a measurement outlook. A factor-of-few change in R^E_OO or N_bin moves the curves across any plausible detection threshold, so the conclusion is forced by the input, not by the dynamics.

1 more flagged steps
  1. self citation load bearing [Sec. 2, paragraph after Eq. (8); Sec. 3, Results and Conclusions]
    "It was shown that using this mixed hybrid theory [4, 11], upon which the present work is based, that the ratios of Ψ(2 S)/(J/Ψ) and Υ(3 S)/Υ(1S) agreed with experimental results, while the standard model for the Ψ(2 S) and Υ(3 S) did not."

    The premise that Ψ(2S) and Υ(3S) are mixed hybrids, together with the π²/4 enhancement used to build the 'hybrid' curves, is taken from Refs. [4,11,16], all involving the present first author. Section 3 then calls the resulting curve 'a test of the validity of the mixed hybrid theory.' Because the curve was constructed from that same theory's enhancement factor, the test has no independent content: its outcome is fixed by the self-cited premise, so the claimed validation chain reduces to self-citation.

full rationale

Most of the paper is a straightforward application: Eq. (11) computes y-shapes from gluon distribution functions and the color-octet formalism, and those shapes are not themselves circular. If the paper had presented only the shape predictions, a low score would be appropriate. However, the headline relative prediction (hybrid Υ(3S) above standard Υ(3S)) is constructed by multiplying the standard curve by π²/4 from Ref. [16], so the inequality is true by construction rather than by derivation. The LHC measurability claim additionally depends on R^E_OO = 0.25, chosen as half the Xe-Xe value without derivation, and on an unspecified N_bin; hence the absolute rates are the input normalization renamed as a prediction. The mixed-hybrid identity is itself imported from same-author references and is described as a 'test' only of that imported theory. Because the central advertised results reduce to these inputs, while the shape calculation retains independent content, the circularity score is 7 rather than higher.

Assumptions & free parameters 6 free parameters · 5 assumptions · 1 invented entities

The central calculation imports nearly all of its physics from prior papers by the same authors: the mixed-hybrid assignments, the π²/4 enhancement, and the production formula. The only new numerical choices are R_E_pp=0.005 and R_E_OO=0.25, which are ad hoc and unvalidated.

free parameters (6)
  • R_E_pp = 0.005
    Chosen by hand in Section 2.1 ('For p-p collisions we use R_E_pp =0.005'), no derivation or fit to data; sets absolute scale for all pp cross sections.
  • R_E_OO = 0.25
    Set in Section 2.2 as R_E_OO = 0.25 = R_E_XeXe / 2, with no supporting data or uncertainty; controls the O-O normalization and the claim that Υ(3S) hybrid could be measured.
  • A_Phi (J/Psi, Upsilon(1S)) = 1.26e-6 nb, 3.4e-8 nb
    Taken from Ref [16] by Kisslinger, Liu, McGaughey (2011); no derivation in this paper and no values given for Psi(2S), Upsilon(2S), Upsilon(3S).
  • pi^2/4 enhancement factor = pi^2/4 ≈ 2.467
    Applied to hybrid states in Section 2.1; taken from Ref [16], directly produces the central prediction that hybrid states exceed standard states.
  • mixing parameter alpha = 0.7 ± 0.1
    Quoted from Refs [4,11] in Eqs (7)-(8); not propagated into the cross-section calculation, but central to the 'mixed hybrid' interpretation.
  • xi_g^2 (nuclear shadowing parameter) = not specified
    Appears in Eq (12) for xbar(y) but its value is not given, so the curves are not reproducible.
assumptions (5)
  • domain assumption Color octet model (NRQCD) describes quarkonium production
    Assumed via Refs [7,8,9]; Eq (11) for dσ/dy is taken from this framework.
  • domain assumption Ψ(2S) and Υ(3S) are mixed hybrids with ~50% valence-gluon component (f≈√2, α=0.7±0.1)
    Core model assumption from Refs [4,11] by Kisslinger; used in Eqs (2)-(8).
  • ad hoc to paper Hybrid states are enhanced by factor π²/4 in production
    Stated in Section 2.1 ('With Ψ(2S), Υ(3S) enhanced by π²/4 [16]'); no derivation in this paper; this is the input that produces the main relative prediction.
  • domain assumption Eq (11) factorization: dσ/dy = A_Φ (1/x) fg(xbar,2m) fg(a/xbar,2m) dx/dy
    Taken from Ref [16]; no derivation here; used for all cross sections.
  • ad hoc to paper Nuclear modification factor factorization R_E_AA = R_AA * S_Φ and R_E_OO = R_E_XeXe/2
    Eq (9) from Ref [6] and the specific value R_E_OO=0.25 chosen in Section 2.2; load-bearing for absolute O-O rates.
invented entities (1)
  • Valence-gluon hybrid components |c̄cg(2S)> and |b̄bg(3S)> with ~50% probability independent evidence
    purpose: Explains anomalous Ψ(2S) and Υ(3S) production/di-lepton decays and generates the predicted enhanced cross sections
    The paper predicts a measurable Υ(3S)(hybrid) differential cross section in O-O at the LHC; however, this entity is inherited from earlier papers by the same author, and no new experimental evidence is presented.

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Cite this review

Pith. "Pith review of Heavy Quark State Production via p-p and O-O Collisions." pith.science (2026). https://pith.science/paper/IU75LIME

@misc{pith2026250609484,
  author       = {Pith},
  title        = {Pith review of: Heavy Quark State Production via p-p and O-O Collisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IU75LIME}},
  note         = {Machine review of arXiv:2506.09484}
}
abstract

Here we have considered $J/\Psi$ is a normal charmonium meson, while $\Psi(2S)$ is a mixed hybrid charmonium meson. Similarly $\Upsilon(1S)$ and$\Upsilon(2S)$ are normal upsilon mesons, while $\Upsilon(3S)$ is a mixed hybrid upsilon meson. We discuss the differential rapidity cross sections for $J/\Psi$, $\Psi(2S)$, $\Upsilon(1S)$, $\Upsilon(2S)$, $\Upsilon(3S)$ production via p-p, and O-O collisions at proton-proton energy $\equiv \sqrt{s_{pp}}$= 5.44 TeV. The rapidity taken for the present study goes from y=-1 to 1.

Figures

Figures reproduced from arXiv: 2506.09484 by the authors.

Figure 1
Figure 1. dσ/dy for 2mc=3 GeV, √spp=5.44 TeV via p-p collisions producing J/Ψ with λ = 0 4 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. dσ/dy for 2mc=3 GeV, √spp=5.44 TeV via p-p collisions producing Ψ(2S), hybrid theory, with λ = 0. The dashed curve is for the standard cc¯ model. d /dy ( nb) σ 1.0−1.0 0.0 y 0.17 0.16 0.15 0.14 0.13 Υ(1S) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. dσ/dy for 2mb=10 GeV, √spp=5.44 TeV via p-p collisions producing Υ(1S), λ = 0 2.2 The differential rapidity cross section for the production of a heavy quark state Φ via O-O collisions Opportunities of O-O Collisions at the LHC and discussed in Ref [21]. Note that O represents the Oxygen nucleus with 8 protons. The most common Oxygen nucleus has 8 protons, 8 neutrons and atomic number A=16 or O = O(p = 8, n = 8, A =… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: dσ/dy for 2mb=10 GeV, √spp=5.44 TeV via p-p collisions producing with λ = 0 Υ(2S) and Υ(3S)(hybrid). For Υ(3S) the dashed curve is for the standard b ¯b model. The differential rapidity cross sections are shown in the following figures. d /dy ( nb) σ 1.0−1.0 0.0 y J/ Ψ…
Figure 5
Figure 5. Figure 5: dσ/dy for 2mc=3 GeV, √spp=5.44 TeV via O-O collisions producing J/Ψ with λ = 0 Note that the differential rapidity cross section for the Υ(3S)(hybrid) is larger than the differential rapidity cross section for the Υ(3S) and could be measured in future CERN LHC experime…
Figure 6
Figure 6. Figure 6: dσ/dy for 2mc=3 GeV, √spp=5.44 TeV via O-O collisions producing Ψ(2S), hybrid theory, with λ = 0. The dashed curve is for the standard cc¯ model. d /dy ( nb) σ 1.00.0 y Υ(1S) 0.08 0.07 −1.0 0.06 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: dσ/dy for 2mb=10 GeV, √spp=5.44 TeV via O-O collisions producing Υ(1S), λ = 0 3 Results and Conclusions In section 2, we review mixed heavy quark hybrid and p-p collisions. In subsection 2.1, we discuss, Ψ and Υ production via p-p collisions with √spp = 5.44 TeV. We gi…
Figure 8
Figure 8. Figure 8: dσ/dy for 2mb=10 GeV, √spp=5.44 TeV via O-O collisions producing with λ = 0 Υ(2S) and Υ(3S)(hybrid). For Υ(3S) the dashed curve is for the standard b ¯b model. References [1] S. Acharya et al. [ALICE],Eur. Phys. J. C 84, no.8, 813 (2024) [2] I. Arsene et. al. (BRAHMS C…

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