Absorption of $\psi(2S)$ mesons in nuclei

E. Ya. Paryev

REVIEW 2 major objections 6 minor 77 references

Absorption of $\psi(2S)$ mesons in nuclei

T0 review · 2 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The paper claims that near-threshold ψ(2S) photoproduction on nuclei can discriminate among 7, 14, 21, and 28 mb ψ(2S)–nucleon absorption cross sections, giving a practical handle on a quantity that is otherwise poorly known.

desk verdict First real target observables for ψ(2S)-nucleon absorption at JLab 22 GeV, but the formation-time assumption undercuts the clean extraction of σψ(2S)N. read the letter →

arxiv 2502.02285 v1 pith:IX674JIT submitted 2025-02-04 nucl-th hep-phnucl-ex

E. Ya. Paryev This is my paper · ORCID

classification nucl-thhep-phnucl-ex PACS 25.20.Lj13.60.Le14.40.Pq

keywords ψ(2S)photoproductioncharmoniumabsorptiontransparencyrationuclearspectralfunctionnear-thresholdψ(2S)–nucleoncrosssectioncoldmatterquark-gluonplasmaprobe

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 argues that near-threshold photoproduction of ψ(2S) mesons off nuclei is a practical route to the poorly known ψ(2S)–nucleon absorption cross section. Using a collision model built on the nuclear spectral function, it computes excitation functions, momentum distributions, and transparency ratios for light and heavy targets, and finds that these observables shift by experimentally resolvable amounts as the assumed absorption cross section is set to 0, 7, 14, 21, or 28 mb. The result matters because the same cross section controls charmonium suppression in heavy-ion collisions and is often used in the search for the quark-gluon plasma. Measurements at an upgraded 22 GeV photon-beam facility could therefore discriminate among these scenarios and also constrain the inelastic channel ψ(2S)+N→J/ψ+N.

What carries the argument

The load-bearing object is the effective number of target nucleons, $I_V[A,\sigma_{\psi(2S)N}]$, that participate in direct γN→ψ(2S)N production after accounting for final ψ(2S) absorption through an exponential attenuation factor, together with the nuclear spectral function describing nucleon binding and Fermi motion. The elementary γp→ψ(2S)p cross section is obtained by taking the ψ(2S)/J/ψ photoproduction ratio of about 0.166 at equal excess energies and applying it to a near-threshold parametrization of J/ψ photoproduction. Transparency ratios $S_A$ and $T_A$, the latter normalized to carbon, translate measured cross sections into attenuation information and carry most of the discriminatory power claimed.

What would settle it

Measure the ψ(2S) excitation function or the A-dependence of its transparency ratio on a heavy target such as tungsten at 11.5–16.4 GeV with a precision of about 5%, and compare with the predicted curves for σψ(2S)N = 7, 14, 21, and 28 mb; if the measured ratio stays flat in A or the absolute cross sections fall outside the scenario band after accounting for binding and Fermi motion, the constant-effective-cross-section picture is ruled out.

Watch

Extended reading notes

Core claim

The central discovery claimed is that inclusive ψ(2S) photoproduction on nuclei has definite sensitivity to the effective ψ(2S)–nucleon absorption cross section σψ(2S)N. In the model, the cross sections on 12C differ by roughly 12–16% between neighboring σψ(2S)N scenarios, while on 184W the differences reach 25–50%; the transparency ratios SA and TA vary by up to about 52% for heavy nuclei, and the ψ(2S)/J/ψ transparency-ratio ratio is clearly separated under the five adopted cross-section values. From this the paper concludes that future measurements of the absolute excitation functions, momentum distributions, and A-dependences of the transparency ratios could set tight constraints on σψ(2S)N and, in particular, on the part arising from the nondiagonal transition ψ(2S)+N→J/ψ+N.

Load-bearing premise

The calculations assume that the ψ(2S) is created instantaneously as a full-sized meson and then travels through the nucleus with one constant effective absorption cross section, with negligible formation-time effects and negligible in-medium mass shift.

Editorial extensions

If this is right

Near-threshold excitation functions in the 11.5–16.4 GeV range with percent-level precision can already separate neighboring 7/14/21/28 mb absorption scenarios on tungsten.
Momentum distributions at 13 GeV over 0°–10° give an independent constraint, with tungsten peaking at 10–40 nb/(GeV/c).
The A-dependence of $S_A$ and $T_A$ across nuclei from carbon to uranium discriminates among all five scenarios, especially for heavy targets.
The ratio of ψ(2S) to J/ψ transparency ratios near 11.5 GeV provides a probe of the nondiagonal ψ(2S)+N→J/ψ+N transition.
Estimated event numbers make such measurements feasible: hundreds to tens of thousands of ψ(2S) events per running year on carbon and tungsten.

Reading between the lines

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

If formation-time or pre-hadronic effects turn out to be non-negligible, the effective cross section extracted from transparency ratios would be systematically biased; the model's predictions could be tested against a version that lets the produced object grow from a small color dipole to a full ψ(2S).
The same ratio-symmetric parametrization could be transferred to other excited quarkonia, such as Υ(2S), whose cold-nuclear-matter absorption is even less constrained, with the carbon-normalized transparency ratio as the common diagnostic.
The ψ(2S)/J/ψ transparency-ratio ratio, being insensitive to absolute normalization, could be used to constrain relative absorption regardless of photon-flux uncertainties, provided the two states are measured in the same run.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here's the short version. This is the first paper to work out near-threshold ψ(2S) photoproduction off nuclei in the spectral-function collision model, and it gives the experimental community concrete numbers: excitation functions, momentum distributions, A-dependence of transparency ratios, and per-year event rates at a 22 GeV CEBAF. Those are genuinely useful for planning. The relative observables are also robust in one important sense: the uncertain absolute elementary cross section largely cancels in ratios like SA and TA, so the predicted sensitivity to σψ(2S)N is a real feature of the model, not an artifact of the extrapolation. I also give the author credit for showing three different parameterizations of the γp→ψ(2S)p cross section side by side; they differ by factors of 4–12 near threshold, and the paper is upfront that its choice is a guideline.

The soft spots are real, though. The load-bearing one is the instantaneous full-size meson assumption. At Eγ=13 GeV the produced ψ(2S) has lab momentum 7.5–12 GeV/c, so γ≈2.8. With a charmonium formation time of 0.5–1 fm/c, the formation length is 1.4–2.8 fm—comparable to the radius of 12C and much less than that of 184W. The paper says formation-time effects are inessential because the momenta are “relatively low,” but its own kinematics contradict that. If the pre-hadronic c-cbar pair absorbs less than the full ψ(2S), the A-dependence is flattened, and a true 28 mb cross section with formation effects could easily sit on top of the 14 mb instantaneous curve. That eats into the central claim that future data can discriminate the scenarios. The absolute cross sections carry large unquantified uncertainty from the threshold extrapolation, and the paper does not propagate the spread among parameterizations into the predictions. Also, the abstract says the observables might shed light on the nondiagonal ψ(2S)N→J/ψN transition, but the paper doesn't actually calculate that transition; it leaves it to future work. That is a limitation, not a flaw, but the wording oversells.

Methodologically, I have no complaint about the heavy self-citation. The framework comes from the author's own prior papers, and those are published derivations; substituting X(3872)/Υ(1S) by ψ(2S) is a legitimate way to transfer a nuclear model to a new channel. The channel-specific parameterization and the numerics are new.

Bottom line: this is a useful phenomenology paper for experimental planning and for anyone working on charmonium absorption in cold nuclear matter. It deserves a serious referee. The referee report should ask for (1) a quantitative estimate of formation-time effects, even a simple Glauber-style two-stage absorption test, and (2) error bands on the absolute predictions reflecting the spread in the elementary cross-section parameterizations. Without addressing the formation-time point, the claimed discrimination power is not established. My recommendation: send to peer review with major revision requested.

Referee Report

2 major / 6 minor

Summary. The paper presents calculations of inclusive ψ(2S) photoproduction from nuclei near threshold (Eγ = 8–16.4 GeV) in a collision model based on the nuclear spectral function. It computes absolute and relative excitation functions for 12C and 184W, momentum distributions at Eγ = 13 GeV, and transparency ratios S_A and T_A for nine nuclei for five assumed ψ(2S)–nucleon absorption cross sections (0, 7, 14, 21, 28 mb). It also computes the A-dependence of the ratio of ψ(2S) and J/ψ transparency ratios at 11.5 GeV and gives event-rate estimates for the upgraded CEBAF. The central claim is that these observables, particularly the relative ones, are sufficiently sensitive to σ_ψN to discriminate among the assumed scenarios.

Significance. If the predictions are robust, the paper would provide a useful quantitative guide for future CEBAF measurements and a step toward constraining the poorly known ψ(2S)–nucleon cross section. A genuine strength is that the relative observables T_A and S_A are constructed so that the uncertain elementary γp→ψ(2S)p normalization largely cancels, making them more robust than the absolute cross sections. The paper is also transparent about what is included (Fermi motion, binding, absorption) and what is deferred (the ψ(2S)→J/ψ transition calculation). However, the quantitative usefulness of the paper depends on two issues: the assumption of instantaneous full-size ψ(2S) formation without a pre-hadronic stage, and the large uncertainty in the elementary-cross-section extrapolation that feeds the absolute observables.

major comments (2)

[Section 2, Eq. (3) and Introduction] The assumption that the ψ(2S) is produced instantaneously as a full-sized meson and then propagates with a constant absorption cross section is not quantitatively justified. At Eγ = 13 GeV, the produced ψ(2S) has laboratory momentum 7.478–12.058 GeV/c, corresponding to γ ≈ 2.0–3.3 and a formation length l_f = γβcτ of order 1–3 fm for a formation time τ ≈ 0.5–1 fm/c. This is comparable to the radius of 12C and a sizeable fraction of the path length in 184W. The statement in the Introduction that formation-time effects are inessential because the mesons are produced with 'relatively low momenta' is contradicted by these kinematics. If the pre-hadronic c-cbar pair has a smaller absorption cross section over this length, the attenuation in heavy nuclei is reduced, and the A-dependence of S_A and T_A would not follow the assumed constant-σ formulas. This can mimic a smaller effective σ_ψN and would bias the discrimination among the 7/14/21/28 mb scenarios that is the paper's central claim. The authors should estimate the size of the formation-time effect, for example by repeating the calculation with a two-component attenuation model, or provide a convincing numerical argument that the effect is negligible.
[Section 2, Eqs. (7)–(10) and Fig. 1] The elementary cross section σ_γp→ψ(2S)p at near-threshold energies is obtained by extrapolating the high-energy ratio σ(ψ(2S))/σ(J/ψ) ≈ 0.166 to equal excess energy (Eqs. (7)–(10)). This is an unvalidated assumption, and Fig. 1 shows that alternative extrapolations, Eqs. (11) and (12), differ from the adopted one by factors of 4 to 12 in the energy range of interest. Because the absolute excitation functions, momentum distributions, and event-rate estimates in Section 3 are directly proportional to this cross section, the absolute predictions carry a large model-dependent uncertainty that is not propagated into the figures. The claim in the Summary that both absolute and relative observables reveal a definite sensitivity to the σ_ψN scenarios is therefore overstrong for the absolute quantities. The authors should either quantify the sensitivity of the absolute observables to the choice of elementary-cross-section parametrization (e.g., by showing bands or comparing results with Eqs. (11) and (12)), or restrict the main conclusions to the relative observables, where the normalization cancels.

minor comments (6)

[Abstract and Introduction] There are typographical errors, e.g., 'cross cross sections' in the Abstract and the garbled phrase 'the A and momentum dependences of the relative cross sections for ψ(2S) and ψ(2S) and J/ψ production' in the Introduction.
[Section 3, discussion of Fig. 1] The text says 'at photon energies around 5.0 GeV' where the abscissa of Fig. 1 is the center-of-mass energy W; this should read 'at center-of-mass energies around W = 5.0 GeV'.
[Section 2] The model relies on several formulas imported from Refs. [55] and [72] without reproduction (e.g., Eqs. (4)–(6) of Ref. [55] and Eqs. (28), (31)–(39) of Ref. [72]). Please provide these expressions or at least a concise summary in an appendix, as the treatment of Fermi motion and off-shell averaging is central to the calculation.
[Section 2, footnote 9] The assumption that σ(γp→ψ(2S)p) = σ(γn→ψ(2S)n) is stated without discussion; this should be flagged as a model assumption with possible isospin-breaking effects.
[Section 2, after Eq. (19)] The t-slope parameter b_ψ(2S) = 2.0 GeV^{-2} is borrowed from Ref. [55] at Eγ = 13 GeV and compared to LHCb high-energy data; the sensitivity of the momentum distributions to this parameter is not discussed and should be estimated.
[Section 3, event-rate estimates] For the 12C target at the lower end of the predicted cross-section range (0.3 nb) the expected yield is about 115 events, which cannot support the 6–8% precision quoted as necessary to distinguish the σ scenarios; a statistical uncertainty estimate should be included.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is a forward model with explicitly assumed absorption scenarios and externally anchored elementary cross sections.

full rationale

The derivation chain is not circular. The ψ(2S)N absorption cross section is an explicit input parameter (7, 14, 21, 28 mb) chosen from literature estimates, not an output fitted to the observables being predicted. The nuclear cross-section formalism in Eq. (3) is imported from the author's prior paper [55], but that is a published Glauber/spectral-function derivation with external comparisons, and the differential version from [72] is likewise a standard model result; these are not unverified uniqueness theorems. The elementary ψ(2S) photoproduction cross section is constructed from the H1 high-energy ratio (Eq. (6)) and the J/ψ parametrization of Ref. [61], which is anchored to GlueX data; it is not fitted to the nuclear ψ(2S) observables. Moreover, the relative observables SA and TA (Eqs. (15)–(18)) and the ψ(2S)/J/ψ transparency-ratio ratio cancel the elementary cross-section normalization to a large extent, so the central sensitivity claim does not reduce to the self-cited parametrization. The stated assumptions of instantaneous full-size ψ(2S) production and negligible medium modifications (Section 2) are physical limitations of the model, not circular steps: they are assumptions, not conclusions derived from the predicted observables. No equation defines the assumed σψ(2S)N in terms of the calculated transparency ratios, and no fitted parameter is renamed as a prediction. The paper's self-citations are to published, externally anchored derivations and do not constitute load-bearing circularity.

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

The central predictions rest on inputs carried over from the author's prior papers (Refs [55], [72], [61]) and on empirical constants (0.166, 3.5 mb, and b = 2.0 GeV^-2). No new particles or forces are introduced. The main unverified input is the near-threshold γp to ψ(2S)p cross-section normalization.

free parameters (4)

Effective ψ(2S)-nucleon absorption cross section σ_ψ(2S)N = 0, 7, 14, 21, 28 mb
Not measured; the paper scans five assumed values from theoretical estimates, and all central observables are computed as functions of this input.
ψ(2S)-to-J/ψ photon-proton cross-section ratio = 0.166
Taken from H1 high-energy data [56] and assumed valid near threshold at equal excess energy (Eqs. 6 to 8); it drives the absolute ψ(2S) elementary cross-section normalization.
J/ψ-nucleon absorption cross section σ_J/ψN = 3.5 mb
Used in the ψ(2S)/J/ψ transparency ratio calculation (Fig. 9), motivated by the SLAC J/ψ photoproduction analysis [39,40].
Exponential t-slope parameter b_ψ(2S) = 2.0 GeV^-2
Used for the c.m. angular distribution in the differential cross section; taken from an estimate in Ref [55] and consistent with an LHCb fit at high energy (Ref [73]).

assumptions (4)

domain assumption The nuclear spectral function and first-collision equations from Refs [55] and [72] correctly describe inclusive charmonium photoproduction on nuclei after the substitution ψ(2S) for X(3872) or Υ(1S).
The paper refers to these equations rather than rederiving them, explicitly in Section 2 around Eq. (3) and Eq. (19).
ad hoc to paper The high-energy ratio σ(γp to ψ(2S)p) / σ(γp to J/ψ p) of about 0.166 holds near threshold when the two cross sections are compared at equal excess energy.
This assumption is introduced in Eqs. (6) to (9) with no low-energy data; Fig. 1 shows factor of 4 to 12 differences from other parameterizations.
ad hoc to paper The ψ(2S) production cross sections in γp and γn interactions are equal.
Stated in footnote 9 of Section 2 and used to extend proton-target formulas to neutron targets.
domain assumption No significant formation-time, pre-hadronic, or in-medium mass-shift effects alter the propagation of the produced ψ(2S) inside the nucleus.
Section 2 assumes instantaneous production of the full-sized meson and ignores medium modifications, citing Ref [54] for a small expected mass shift.

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Pith. "Pith review of Absorption of $\psi(2S)$ mesons in nuclei." pith.science (2026). https://pith.science/paper/IX674JIT

@misc{pith2026250202285,
  author       = {Pith},
  title        = {Pith review of: Absorption of $\psi(2S)$ mesons in nuclei},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IX674JIT}},
  note         = {Machine review of arXiv:2502.02285}
}

abstract

In the present work we explore the inclusive $\psi(2S)$ meson photoproduction from nuclei near the kinematic threshold within the collision model, based on the nuclear spectral function, for incoherent direct photon--nucleon charmonium creation processes. The model takes into account the final $\psi(2S)$ absorption, target nucleon binding and Fermi motion. We calculate the absolute and relative excitation functions for production of $\psi(2S)$ mesons on $^{12}$C and $^{184}$W target nuclei at near-threshold photon beam energies of 8.0--16.4 GeV, the absolute momentum differential cross sections for their production off these target nuclei at laboratory polar angles of 0$^{\circ}$--10$^{\circ}$, the momentum dependence of the ratio of these cross sections as well as the A-dependences of the ratios (transparency ratios) of the total cross cross sections for $\psi(2S)$ production at photon energy of 13 GeV within the different scenarios for the $\psi(2S)N$ absorption cross section. We also calculate the A-dependence of the ratio of $\psi(2S)$ and $J/\psi$ photoproduction transparency ratios at photon energies around of 11.5 GeV within the adopted scenarios for this cross section. We demonstrate that both the absolute and relative observables considered reveal a definite sensitivity to these scenarios. Therefore, the measurement of such observables in future experiments at the upgraded up to 22 GeV CEBAF facility in the near-threshold energy region might shed light both on the $\psi(2S)N$ absorption cross section and on its part associated with the nondiagonal process $\psi(2S)+N \to J/\psi+N$ at finite momenta, which are of crucial importance in understanding of charmonium production and suppression in high-energy nucleus--nucleus collisions in a search for the quark-gluon plasma.

Figures

Figures reproduced from arXiv: 2502.02285 by the authors.

**Figure 2.** (Color online.) Excitation function for production of [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** (Color online.) The same as in Fig. 2, but for the [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: (Color online.) Momentum differential cross sections for the production of [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: (Color online.) Transparency ratio SA for the ψ(2S) mesons from direct γp(n) → ψ(2S)p(n) processes proceeding on an off-shell target nucleons and on a free ones being at rest at incident photon energy of 13 GeV in the laboratory system as a function of the nuclear mass…

**Figure 6.** Figure 6: (Color online.) Transparency ratio TA for the ψ(2S) mesons from direct γp(n) → ψ(2S)p(n) processes proceeding on an off-shell target nucleons and on a free ones being at rest at incident photon energy of 13 GeV in the laboratory system as a function of the nuclear mass…

**Figure 7.** Figure 7: (Color online.) Transparency ratio TA for the ψ(2S) mesons from direct γp(n) → ψ(2S)p(n) processes proceeding on an off-shell and free target nucleons as a function of the incident photon energy for combination 184W/12C, calculated for different values of the ψ(2S) abs…

**Figure 8.** Figure 8: (Color online.) Transparency ratio TA for the ψ(2S) mesons from direct γp(n) → ψ(2S)p(n) processes proceeding on an off-shell target nucleons as a function of the ψ(2S) laboratory momentum for incident photon energy of 13 GeV for combination 184W/12C, calculated in th…

**Figure 9.** Figure 9: (Color online.) Nuclear mass number A-dependence of the ratio of ψ(2S) and J/ψ photoproduction transparency ratios for incident photon energies around of 11.5 GeV, calculated for different values of the ψ(2S) absorption cross section σψ(2S)N in nuclei indicated in the …

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