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REVIEW 3 major objections 4 minor 66 references

Exclusive $J/\psi$ photo-production on nuclei

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Pith's one-line read Applying a Pomeron-plus-constituent-quark model to exclusive J/psi photoproduction on nuclei, this paper predicts that near threshold the deuteron cross section is governed by the d-state of the deuteron wave function, while the standard…

desk verdict Worth engaging for the deuteron d-state result; the FSA reliability claim needs a stronger test before it is used for A>2. read the letter →

arxiv 2411.12187 v1 pith:47YKQQSS submitted 2024-11-19 nucl-th hep-ph

Sang-Ho Kim , T.-S. H. Lee , R.B. Wiringa This is my paper · ORCID
classification nucl-thhep-ph
keywords J/psiphotoproductionexclusivereactionsonnucleimultiplescatteringtheoryfixedscatterapproximationdeuterond-statePomeronconstituentquarkmodelnuclearformfactorsfinalstateinteractions
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 exclusive $J/\psi$ photoproduction cross sections on the deuteron, $^{4}$He, $^{16}$O, and $^{40}$Ca by extending a Pomeron-plus-constituent-quark model of the proton reaction to nuclear targets. For the deuteron, where the impulse amplitude can be computed exactly from realistic nucleon-nucleon wave functions, the central finding is that near threshold the cross section is strongly sensitive to the d-state, the $L=2$ component of the deuteron wave function, and the conventional fixed-scatter approximation, which factorizes the amplitude into a nucleon amplitude times a nuclear form factor, is not valid in that region but becomes reliable at higher energies. The $J/\psi$-nucleus final state interaction, built from the first-order optical potential, contributes mainly at large momentum transfer. With the fixed-scatter approximation and variational Monte-Carlo form factors, the paper provides cross-section predictions for $^{4}$He, $^{16}$O, and $^{40}$Ca intended for upcoming JLab and EIC measurements. A sympathetic reader would take this as a step toward using $J/\psi$ photoproduction to probe gluonic and short-distance structure in nuclei.

What carries the argument

The central object is the multiple-scattering decomposition of the reaction amplitude into an impulse term $T^{\rm IMP}_{J/\psi A,\gamma A}$ and a final-state-interaction term $T^{\rm FSI}_{J/\psi A,\gamma A}$. For the deuteron, the impulse amplitude is computed exactly from realistic nucleon-nucleon wave functions with relativistic boost transformations, and it is this exact treatment that exposes the d-state sensitivity. The final-state interaction is built from a first-order optical potential formed by folding the $J/\psi$-nucleon scattering amplitude from the Pom-CQM model with the nuclear form factor, with a Lippmann-Schwinger equation solved for the $J/\psi$-nucleus scattering amplitude. The fixed-scatter approximation, which sets the struck nucleon momentum to zero and factorizes the amplitude as a nucleon amplitude times a nuclear form factor, is the simplifying device used for $A > 2$ nuclei; the paper tests its validity on the deuteron and finds that it fails near threshold.

What would settle it

A measurement of $d\sigma/dt$ for $\gamma d \to J/\psi d$ near $E_\gamma = 6$ GeV in the region $-t \approx 2$ to $4$ GeV$^2$ would settle the central claim: the full calculation including the d-state is much larger than the s-wave-only result in that region, so data matching the s-wave-only shape, or failing to show the expected enhancement, would refute the claimed d-state dominance.

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Extended reading notes

Core claim

On the paper's own terms, exclusive $J/\psi$ photoproduction on the deuteron near threshold is strongly controlled by the d-state of the deuteron wave function. Using the relativistic impulse amplitude built from the Argonne-v18, NV-IIa, and CD-Bonn nucleon-nucleon potentials, the calculations show that at $E_\gamma = 6$ GeV, about 0.4 GeV above threshold, the differential cross section at large $-t$ is much larger than the s-wave-only result, tracing to the quadrupole form factor $F_2(t)$ peaking where $F_0(t)$ has its minimum. The same comparison shows that the fixed-scatter approximation, which factorizes the nuclear amplitude into an averaged nucleon amplitude times a form factor, reproduces the exact calculation only at small $-t$ and fails near threshold. The final state interaction amplitude, evaluated from a first-order optical potential using the fitted $J/\psi$-nucleon amplitude, raises the cross section significantly at large $-t$. The paper then applies the fixed-scatter approximation to spin-zero nuclei, predicting cross sections for $^{4}$He, $^{16}$O, and $^{40}$Ca with variational Monte-Carlo form factors, and notes that these near-threshold predictions are not reliable in the subthreshold region where hidden-charm bound states could appear.

Load-bearing premise

All results inherit the fitted Pom-CQM quark-nucleon potentials that were tuned to proton JLab data, so the entire nuclear calculation, especially the final-state interaction, stands on the assumption that the resulting $J/\psi$-nucleon amplitude remains correct for nucleons bound inside a nucleus.

Editorial extensions

If this is right

  • Near-threshold $\gamma d \to J/\psi d$ measurements can directly probe the deuteron d-state at high momentum transfer, since the s-wave-only calculation is substantially smaller in the large-$-t$ region at $E_\gamma = 6$ GeV.
  • The fixed-scatter approximation should not be trusted for threshold-region $J/\psi$ photoproduction on any nuclear target, and the paper's own $A > 2$ predictions are correspondingly approximate in that region.
  • The $J/\psi$-nucleus final state interaction significantly increases cross sections at large momentum transfer for the deuteron and for the spin-zero nuclei near threshold.
  • For $^{4}$He, $^{16}$O, and $^{40}$Ca, the predicted near-threshold cross sections are very small, while heavier targets give larger total cross sections at higher energy, so future JLab and EIC measurements are more feasible at higher energies.
  • The predicted cross sections for $^{4}$He, $^{16}$O, and $^{40}$Ca provide concrete numbers for planning exclusive measurements at JLab and the EIC.

Reading between the lines

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

  • If the d-state sensitivity holds, exclusive $J/\psi$ photoproduction on the deuteron could serve as a high-momentum filter for the deuteron quadrupole form factor $F_2(t)$, complementing electron-scattering measurements in the momentum region where $F_0(t)$ has a minimum; this use goes beyond what the paper states.
  • The failure of the fixed-scatter approximation near threshold suggests that similar fixed-scatter treatments for other heavy-quarkonium photoproduction, such as $\Upsilon$ on light nuclei, would also need exact many-body impulse calculations because the threshold momentum transfer is even larger.
  • Precise coherent deuteron data could be used to extract the $J/\psi$-nucleon scattering amplitude entering the optical potential, connecting these predictions to the hidden-charm bound-state question that the paper flags as an open direction.
  • Because the paper explicitly states its subthreshold predictions are unreliable under the fixed-scatter approximation, a natural next step is a full many-body calculation with realistic nuclear wave functions and all multiple-scattering permutations, which could be tested against the near- and sub-threshold nuclear data now being collected at JLab.
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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

3 major / 4 minor

Summary. Applying the Pom-CQM model previously fitted to γp→J/ψp JLab data, the authors compute exclusive J/ψ photoproduction on the deuteron, 4He, 16O, and 40Ca within multiple scattering theory. The deuteron impulse amplitude is calculated exactly from realistic NN wave functions with relativistic boost corrections, a fixed-scatter approximation (FSA) is introduced, and the J/ψ-nucleus final-state interaction is generated from a first-order optical potential built from the same J/ψN amplitude. Heavy-nucleus predictions use variational Monte Carlo form factors. The main claims are that near-threshold cross sections depend strongly on the deuteron d-state, that the FSA fails near threshold but is a good approximation at higher energies, that FSI effects are significant at large momentum transfer, and that the A>2 cross sections provide predictions for future JLab and EIC experiments.

Significance. If the results hold, the paper provides concrete, falsifiable predictions for a program that is experimentally active, and it identifies deuteron d-state sensitivity as a potentially observable nuclear-structure effect in J/ψ photoproduction. The strengths are the exact impulse treatment on the deuteron with realistic NN potentials, the comparison across three NN interactions, the use of VMC nuclear form factors for heavier targets, and the honest reuse of a proton-level amplitude that was previously fitted to data. The central d-state-sensitivity finding near threshold appears robust because it is obtained from the exact impulse calculation. However, the FSA-validity claim is supported only by an s-wave-only comparison, and the FSI calculation relies on that same unvalidated approximation, so the higher-energy FSA claim and the numerical FSI predictions need additional support.

major comments (3)
  1. [IV.B, Fig. 10] The conclusion that the FSA is "a good approximation at higher energies" is based on a comparison in which only the s-wave part of the deuteron is retained. Near threshold the d-state dominates the cross section (Fig. 9), and the d-state has more high-momentum content than the s-state (Fig. 14), so freezing the initial nucleon momentum to p=0 in Eq. (34) is not tested for the full amplitude. Please compare the FSA of Eqs. (38)-(40) with the exact impulse calculation of Eq. (24) using the full s+d wave function, or restrict the FSA-validity claim to the s-wave sector and re-evaluate the FSA-based FSI and A>2 predictions.
  2. [IV.C, Eqs. (41)-(51) and Fig. 11] The FSI amplitude uses the T_IMP source term evaluated in the FSA by setting the initial nucleon momentum to p=0, as stated after Eq. (48). The comparison in Fig. 11 therefore mixes the exact relativistic impulse calculation (dashed curve) with a calculation in which the FSI source term is approximated by the FSA (solid curve). Since the FSA is shown to be invalid near threshold, the displayed FSI enhancement cannot be cleanly attributed to final-state interactions alone, and the near-threshold FSI predictions are not reliable. Please use the exact impulse amplitude as the source term in Eq. (41), or quantify the FSA error in the FSI contribution.
  3. [IV.C, Eq. (45)] The J/ψ-deuteron scattering equation uses a nonrelativistic propagator E - E_V(p") - E_d(p"), while the impulse amplitude and the boost transformations use relativistic kinematics (Eqs. (28)-(33)). Given that the FSI is significant near threshold where the momentum transfer is large, the magnitude of the FSI correction may depend on this inconsistency. Please justify this choice or estimate its numerical effect, for example by comparing with a relativistic propagator.
minor comments (4)
  1. [Eq. (34)] The symbol t is used both for the Mandelstam variable and for a momentum-transfer variable in the same sentence; the displayed relation "t = (|q| − E_V(k))^2 − t^2" is self-referential and should be rewritten with distinct notation for the three-momentum transfer.
  2. [Throughout] There are several typographical errors that should be corrected: "Relatvistic" in Sec. IV.A, "calulated" near Eq. (46), "gennerated" in the Fig. 14 caption, "variaioal" in Sec. VI, "previsous" in Sec. V, and "sufficent" in the Fig. 3 caption.
  3. [Fig. 15] The legend order in panel (a) reads "2H p 16O 40Ca 4He," which does not match the plotted curves or the order in panel (b); please check that the legend and curve styles are consistent.
  4. [Eq. (51)] The text says the full FSA cross section is obtained by using Eq. (39) to evaluate T_IMP inside Eq. (41), but Eq. (39) defines the factorized FSA amplitude for the observable cross section rather than an operator to be inserted into the loop integral; clarifying the operator definition would remove ambiguity.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the nuclear predictions use externally fitted elementary amplitudes and independent nuclear wave functions; the FSA-validity concern is an approximation gap, not a circular reduction.

full rationale

The paper's derivation chain is not circular. The elementary gamma+N -> J/psi+N amplitude and the J/psi-N t-matrix are taken from the previously published Pom-CQM model [1,11], whose parameters were fitted to external JLab proton data (Eq. (8), Ref. [11]); the nuclear calculations then use those amplitudes as inputs together with deuteron wave functions from independent NN potentials [41-43] and VMC nuclear form factors [52]. The central nuclear findings, namely the d-state sensitivity near threshold and the FSI effects at large momentum transfer, are computed from these inputs rather than re-derived from the outputs. The paper does not present the proton fits as new predictions, and the fixed-scatter approximation (FSA) is introduced as an approximation, not as a derived result: Eq. (34) defines the FSA by setting the initial nucleon momentum p = 0, and Fig. 10 compares FSA with an exact s-wave-only calculation. The conclusion that FSA is reasonable at higher energies may be incompletely validated, since the comparison omits the d-state, but that is a correctness or approximation-validity concern, not a circularity: no fitted parameter is renamed as a prediction and no equation reduces to its own output by construction. The paper's own limitation statement in Sec. VI, that the A > 2 near-threshold predictions are made only within FSA and are not reliable in the sub-threshold region, further indicates that the authors do not present the approximation as a derived fact. The reliance on the authors' previous model is substantial, but that model is benchmarked against external JLab data, so the self-citations are not load-bearing in a circular sense.

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

All dynamically relevant parameters are fixed by the group's prior fits to JLab proton data, and no parameters are fitted to nuclear data in this paper. The nuclear-structure inputs (deuteron potentials, VMC form factors) are external. The main free ingredient is the Pom-CQM quark-nucleon potential, an invented effective entity whose parameters come from fitting.

free parameters (5)
  • alpha_B (Born quark-nucleon potential strength) = -0.145
    Adjusted in Ref. [11] to fit JLab gamma-p data; reused here as fixed input. Eq. (8).
  • alpha_FSI (J/psi-N potential strength) = -0.1
    Fitted to JLab data in Ref. [11]; determines t_{VN,VN} used for the nuclear FSI. Eq. (8).
  • mu_B and mu_FSI (Yukawa ranges) = 0.3 GeV
    Fitted in Ref. [11]; fixed here. Eq. (8).
  • N_B and N_FSI (Yukawa shape ratios) = N_B=5, N_FSI=2
    Fitted in Ref. [11]; fixed here. Eq. (8).
  • Pomeron parameters (mu0, beta_u/d, beta_c, alpha0) = mu0=1.1 GeV^2, beta_u/d=2.07 GeV^-1, beta_c=0.32 GeV^-1, alpha0=1.25
    Fixed by earlier fits to high-energy photoproduction data, as stated in the Appendix. These are inputs to this paper.
assumptions (5)
  • domain assumption The first-order optical potential U = <Phi_A| sum_i t_{VN,VN}(i) |Phi_A> with t_{VN,VN} from the fitted Pom-CQM model is a valid basis for the J/psi-nucleus FSI.
    The reliability of the FSI calculation directly depends on t_{VN,VN} and the first-order approximation. Described in Secs. III and V, Eqs. (14)-(15) and (41)-(53).
  • domain assumption The fixed-scatter approximation, validated against the exact deuteron calculation, remains sufficiently accurate for the heavier-nucleus predictions.
    The FSA is calibrated only for the deuteron, and the authors state that the heavier-nucleus threshold predictions are not reliable in the sub-threshold region. Introduced in Sec. IV.B and applied in Sec. V.
  • domain assumption The relativistic treatment of the deuteron wave function includes the boost but ignores spin rotations, which are argued to be negligible.
    The authors cite Refs. [44,45,48] for the claim that spin rotations have negligible effects on spin-averaged observables. Sec. IV.A, after Eq. (33).
  • standard math The nuclear form factors for 4He, 16O, 40Ca from the VMC calculations of Lonardoni et al. [52] are used as the nuclear-structure input.
    The VMC wave functions are an external input, not derived here. Eq. (54).
  • domain assumption Non-relativistic multiple-scattering theory is valid for the deuteron FSI at the energies considered.
    The FSI equation is solved with nonrelativistic propagators in the V-d c.m. frame, Eq. (45), while the impulse term receives a relativistic treatment. The consistency of this mixed treatment is not discussed.
invented entities (1)
  • Phenomenological quark-nucleon potentials v_cN^B(r) and v_cN^{FSI}(r)
    purpose: Effective interactions used to generate the J/psi-N production amplitude and the J/psi-N scattering amplitude within the Pom-CQM model.
    These potentials are the model's mechanism. Their parameters are fitted to the proton JLab data, and they appear only inside the model. No independent prediction outside the fit is provided.

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Pith. "Pith review of Exclusive $J/\psi$ photo-production on nuclei." pith.science (2026). https://pith.science/paper/47YKQQSS

@misc{pith2026241112187,
  author       = {Pith},
  title        = {Pith review of: Exclusive $J/\psi$ photo-production on nuclei},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/47YKQQSS}},
  note         = {Machine review of arXiv:2411.12187}
}
abstract

Motivated by the recent experimental developments, the Pom-CQM model of the $\gamma + N \to J/\psi + N$ reaction of Lee et al. [Eur. Phys. J. A. 58, 252 (2022)] and Sakinah et al. [Phys. Rev. C. 109, 065204 (2024)] has been applied to predict the exclusive $J/\psi$ photo-production on nuclei ($A$). Within the multiple scattering theory, the calculations have been performed by including the impulse amplitude $T^{\rm IMP}_{J/\psi A,\gamma A}$ and the $J/\psi$-nucleus final state interaction (FSI) amplitude $T^{\rm FSI}_{J/\psi A,\gamma A}$. For the deuteron target, $T^{\rm IMP}_{J/\psi d,\gamma d}$ is calculated exactly using the wave function generated from the realistic nucleon-nucleon potentials. It is found that, near the threshold region, the $J/\psi$ photo-production cross sections depend sensitively on the $d$-state of the deuteron wave function. The FSI amplitude $T^{\rm FSI}_{J/\psi A,\gamma A}$ is calculated using the first-order optical potential constructed from the $J/\psi$-$N$ scattering amplitude generated from the employed Pom-CQM model. It turns out that the FSI has significant effects in the large momentum-transfer region. By using the conventional fixed scatter approximation (FSA) and the nuclear form factors from the variational Monte-Carlo (VMC) calculations of Lonardoni et al. [Phys. Rev.C. 96, 024326 (2017)], the cross sections of the $J/\psi$ photo-production on ${^4\rm He}$, ${^{16}\rm O}$, and ${^{40}\rm Ca}$ are also predicted for future experimental investigations at JLab and EIC.

Figures

Figures reproduced from arXiv: 2411.12187 by the authors.

Figure 1
Figure 1. FIG. 1. Born term of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Differential cross sections of [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figures from the paper (11 more)
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Total cross section of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Diagrammatic representation of [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Total cross section of [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Differential cross sections of [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Differential cross sections of [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Differential cross sections of [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. FSI effects on the total cross section of [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. FSI effects on the differential cross sections of [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Deuteron form factors (a) [PITH_FULL_IMAGE:figures/full_fig_p010_14.png]
Figure 16
Figure 16. Figure 16: FIG. 16. The top panels show the nuclear form factors of nuclei [PITH_FULL_IMAGE:figures/full_fig_p011_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17 [PITH_FULL_IMAGE:figures/full_fig_p013_17.png]

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Reference graph

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