Effects of Multiple Scattering in Cold Nuclear Matter on J/psi Suppression and <p_T^2> in Heavy Ion Collisions

A.M. Glenn; Denes Molnar; J.L. Nagle

REVIEW

Effects of Multiple Scattering in Cold Nuclear Matter on J/psi Suppression and <p_T^2> in Heavy Ion Collisions

A.M. Glenn, Denes Molnar, J.L. Nagle

Nuclear Theory · Submitted 24 Feb 2006 · 30 references

Pith's verdict: A careful MC study that credibly rules out 2D Gaussian cold-matter rescattering as the sole source of J/psi suppression, but the stronger 'any value of <k_T^2>' claim is tied to that specific kick model.

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arXiv IDnucl-th/0602068 (version 2)

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CitationA.M. Glenn, Denes Molnar, J.L. Nagle. "Effects of Multiple Scattering in Cold Nuclear Matter on J/psi Suppression and <p_T^2> in Heavy Ion Collisions." arXiv:nucl-th/0602068 (2006). https://pith.science/paper/VGVSRSVW

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Editor's note

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I think this paper is worth engaging with. Its real contribution is the simultaneous look at J/psi suppression and in the incoherent multiple-scattering picture. The authors do not fit ; they scan it, and they show that for the 2D Gaussian random walk model the resulting RAA vs Δ curve misses both NA50 and PHENIX data for every value of the parameter. That is a clean negative result, and it sharpens Fujii's earlier point while directly undermining the QVZ coherent-shift picture.

The paper is also genuinely careful. The analytic formulas in Sec. II and the Monte Carlo agree, the shift-limit check reproduces QVZ trends, and the discretization check shows the result is not an artifact of quantizing the kicks. The color singlet/octet distinction disappearing once fluctuations are included is a clean observation, and the authors say so plainly. The comparison with d+Au data is appropriately hedged given the experimental errors.

The soft spot is that the headline claim is broader than the evidence. In Fig. 7 the scan varies only , with everything else fixed: 2D transverse Gaussian kicks, independent kicks on c and cbar, and equal initial- and final-state kick strengths. The paper itself shows in Sec. II that a 3D random walk gives a different suppression function, but it never runs the A+A scan for 3D kicks, nor does it vary the initial/final strength ratio for A+A. This is not idle nitpicking: a 3D walk would add to q^2 via longitudinal momentum transfer without adding to the transverse momentum of the J/psi, so for a given Δ it would suppress more than the 2D model. That could move the curve considerably toward the NA50 point. The statement about removing initial-state scatterings is made only for p+A, not quantified for A+A. So the abstract's 'cannot simultaneously be described ... for any value of ' is established only for this 2D kick model, not for the broader incoherent-rescattering framework.

None of this sinks the paper's core conclusion, which is that the simple 2D Gaussian picture fails. But the authors should be asked to soften the universal wording or, better, run the 3D scan and the initial/final variation. The math, data handling, and citations look solid. For anyone working on quarkonia in heavy ions—especially cold nuclear matter effects—this is a useful constraint and a good example of how to present a no-fit argument. It deserves a serious referee: a well-posed, reproducible model study with a real negative result, and the fix is mostly a matter of scope.

Referee report

Major objections (4)

[Sec. IV, Fig. 7; Conclusions] The abstract and conclusions claim that no value of <k_T^2> can simultaneously describe J/psi suppression and Delta<p_T^2> in this incoherent multiple scattering framework, but the scan in Sec. IV varies only <k_T^2> inside one model branch: 2D Gaussian kicks applied independently to c and c-bar with equal initial- and final-state strengths. The paper itself shows in Eq. (8) and Fig. 2 that the 3D random walk yields a different suppression function, and correlated quark-antiquark kicks or unequal initial/final strengths would generically produce a different R_AA versus Delta<p_T^2> locus (or a 2D region). The universal negative conclusion is therefore not established by the evidence presented; either scan these variants for A+A or reword the claim to refer specifically to the 2D independent-equal-kick model.
[Sec. III, after Eq. (9)] The assumption that the initial-state and final-state <k_T^2> are equal is load-bearing because Sec. IV states that initial-state scatterings account for roughly half of Delta<p_T^2> in p+A; unequal strengths would change the balance between suppression (final-state only) and p_T broadening (both) and would shift the Fig. 7 curve. The paper provides no sensitivity study for A+A with respect to the initial/final strength ratio. At minimum, the authors should quantify the allowed range of this ratio and show whether the no-fit conclusion survives.
[Eq. (7)] The derivation of the suppression-broadening correlation uses the nonrelativistic approximation Delta q^2 approximately Delta k_T^2 + 2 Delta k_T q cos(theta). For charm quarks with m_c = 1.25 GeV and J/psi transverse momenta of several GeV/c, relativistic corrections to this relation can be non-negligible and would alter the functional form of the R_AA versus Delta<p_T^2> curve before any variation of <k_T^2>. The manuscript does not quantify the size of these corrections in the kinematic region of NA50 and PHENIX; a numerical check comparing with the exact relativistic Delta q^2 for the same random-walk ensemble would make the central claim robust.
[Sec. IV, Fig. 7] The heavy-ion half of the no-fit claim is supported for the SPS by the single NA50 point in Fig. 7, but the RHIC half is not shown with a data point; the text relies on preliminary PHENIX results (ref. [22]) without quoting the suppression and Delta<p_T^2> values used. As written, the statement that the RHIC data are inconsistent with the curve is not quantitatively documented. Please add the RHIC point or clearly flag the RHIC conclusion as preliminary.

Minor objections (4)

[Abstract and throughout] Please clean the numerous typographical artifacts in the text, such as 'b een', 'sur vival', and 'ﬂuctuation' in the abstract and captions.
[Fig. 2 caption] The quantities Q0^2 and q0^2 are used in the caption without definition; they are defined only later in Eq. (8). A brief definition in the caption would improve readability.
[Eq. (4)] The notation in Eq. (4) is dense: the relation between dN_{c-bar}(q^2), d\bar N_{c-bar}(q^2), and the convolution variable would benefit from one explanatory sentence defining each distribution and its argument.
[Table I and Figs. 5-6] Table I gives epsilon^2 only for four <k_T^2> values, while Figs. 5 and 6 use <k_T^2> values up to 4 GeV^2; adding a conversion line or explicitly stating the linear scaling would avoid ambiguity.

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The paper

The paper claims

A Monte-Carlo study of incoherent multiple scattering of charm quark pairs in cold nuclear matter concludes that no value of the transverse-momentum fluctuation strength can simultaneously reproduce the measured J/psi suppression and…

The reading

This paper sets out to test whether the J/psi suppression seen in heavy-ion collisions can be blamed on the charm quark pair being randomly knocked around in the surrounding cold nuclear matter. In the incoherent rescattering picture examined here, the same transverse kicks that suppress J/psi formation also broaden the produced J/psi's transverse momentum, so the two measurements are locked together on a single model curve. Scanning every value of the one free parameter, the average squared momentum transfer per scattering $\langle k_T^2\rangle$, the authors find that no point on that curve matches the SPS and RHIC data for suppression and $\langle p_T^2\rangle$ at the same time. If this holds, incoherent cold-matter rescattering cannot be the whole story of the anomalous J/psi suppression, and some other mechanism, such as a hot deconfined medium, must be at work.

What carries the argument

The load-bearing mechanism is a momentum-space random walk: each charm quark and antiquark receives a set of independent, small transverse momentum kicks whose total is Gaussian-distributed (Eq. 6), with the strength per unit pathlength set by $\langle k_T^2\rangle$. The accumulated change in the c-cbar relative momentum is driven by the nonrelativistic approximation $\Delta q^2 \approx \Delta k_T^2 + 2 \Delta k_T q \cos\theta$ (Eq. 7), which couples the suppression mechanism (growth of $q^2$ reduces the J/psi formation probability $F(q^2)$) to the observable broadening $\Delta\langle p_T^2\rangle$. The effective formation probabilities in Eq. (8) show how including fluctuations in the magnitude and direction of the kicks converts exponential suppression into a milder power-law behavior. A Monte-Carlo model of the nuclear collision geometry provides the pathlengths, and the event generator for proton-proton collisions provides the initial $q^2$ distribution of the pairs.

Extended reading notes

Core claim

The central claim is that in the incoherent multiple-scattering framework, with independent two-dimensional Gaussian transverse momentum kicks on the charm quark and the charm antiquark, the experimentally measured J/psi suppression and transverse momentum broadening from nucleus-nucleus collisions at the SPS and at RHIC cannot be described simultaneously for any value of the fluctuation strength parameter $\langle k_T^2\rangle$. The argument runs through the nonrelativistic relation between the change in the pair's relative momentum and the transverse momentum broadening (Eq. 7), which forces increasing suppression to come with increasing $\langle p_T^2\rangle$. In the $(R_{AA}, \Delta\langle p_T^2\rangle)$ plane, the model traces a one-parameter curve; the measured points from central SPS and RHIC collisions lie away from that curve. The same conclusion holds for both color-singlet and color-octet J/psi formation, and the paper stresses that fluctuations make suppression much weaker than the earlier constant-shift treatment, for a given rescattering strength.

Load-bearing premise

The conclusion rests on the assumption that the charm quark and antiquark are kicked independently with Gaussian-distributed transverse momenta, and that only the transverse relative momentum determines J/psi formation; if the kicks are correlated, or longitudinal momentum transfer matters, or the kick distribution is not Gaussian, the curve linking suppression and <$p_T^{2}$> could be different.

Editorial extensions

If this is right

Any incoherent rescattering model of this type predicts a one-parameter family of (suppression, <p_T^2>) pairs, so measuring both observables in the same system tightly constrains or excludes the model.
The earlier coherent-scattering conclusion that cold matter alone explains Pb+Pb suppression is shown to depend on ignoring fluctuations, since fluctuations dramatically weaken the suppression at a fixed rescattering strength.
With fluctuations included, color-singlet and color-octet formation probabilities become nearly indistinguishable, so J/psi suppression data alone cannot discriminate the production mechanism in this framework.
Since cold-matter rescattering cannot account for the data, additional suppression from a hot deconfined medium, or some other mechanism, is required to explain the observed J/psi yields in nucleus-nucleus collisions.
The same suppression-broadening correlation can be computed for other quarkonium states, such as the Upsilon, and compared with future data as a test of the incoherent multiple-scattering picture.

Reading between the lines

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

A testable extension is to model correlated kicks, where the quark and antiquark receive equal-and-opposite transverse momenta so the pair's total p_T is unchanged; this would break the tight relation between suppression and <p_T^2> and could in principle rescue this class of models.
The paper's no-fit statement is for the 2D Gaussian case; since the 3D random walk gives stronger suppression at moderate pathlengths, a full 3D analysis might shift the curve, although the mismatch for central events would likely survive.
The (R_AA, Delta<p_T^2>) curve could serve as a reference line for future p+Pb or Pb+Pb measurements at the LHC, offering a quick way to decide whether incoherent rescattering contributes significantly to quarkonium suppression.

Original abstract

Coherent multiple scatterings of c and cbar quark pairs in the environment of heavy ion collisions have been used in a previous work by Qiu et al. [Qiu:1998rz] to study J/psi suppression. That model suggests that heavy quark re-scatterings in a cold nuclear medium can completely explain the centrality dependence of the observed J/psi suppression in Pb+Pb collisions at the SPS [Abreu:2001kd]. Their calculations also revealed significant differences under the assumptions of a color singlet or color octet production mechanism. A more recent analytic calculation [Fujii:2003fq], which includes incoherent final-state re-scatterings with explicit momentum transfer fluctuations in three dimensions, indicates much less suppression and little sensitivity to the production mechanism. In this article, we study simultaneously both the J/psi suppression and p_T modifications, at SPS and RHIC energies. We mainly focus on incoherent momentum transfer fluctuations in two dimensions, which is more appropriate for the heavy-ion collision kinematics. Our analytic and Monte-Carlo calculations reinforce the analytic results in [Fujii:2003fq]. Additionally, we find that the experimental J/psi suppression and <p_T^2> from nucleus-nucleus collisions at the SPS or RHIC cannot simultaneously be described in this incoherent multiple scattering framework for any value of the fluctuation strength parameter <k_T^2>.

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, 2026-09-23: 1 request, 6,456 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Coherent multiple scatterings of c and cbar quark pairs in the environment of heavy ion collisions have been used in a previous work by Qiu et al. [Qiu:1998rz] to study J/psi suppression. That model suggests that heavy quark re-scatterings in a cold nuclear medium can completely explain the centrality dependence of the observed J/psi suppression in Pb+Pb collisions at the SPS [Abreu:2001kd]. Their calculations also revealed significant differences under the assumptions of a color singlet or color octet production mechanism. A more recent analytic calculation [Fujii:2003fq], which includes incoherent final-state re-scatterings with explicit momentum transfer fluctuations in three dimensions, indicates much less suppression and little sensitivity to the production mechanism. In this article, we study simultaneously both the J/psi suppression and p_T modifications, at SPS and RHIC energies. We mainly focus on incoherent momentum transfer fluctuations in two dimensions, which is more appropriate for the heavy-ion collision kinematics. Our analytic and Monte-Carlo calculations reinforce the analytic results in [Fujii:2003fq]. Additionally, we find that the experimental J/psi suppression and <p_T^2> from nucleus-nucleus collisions at the SPS or RHIC cannot simultaneously be described in this incoherent multiple scattering framework for any value of the fluctuation strength parameter <k_T^2>.

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	Coherent multiple scatterings of c and cbar quark pairs in the environment of heavy ion collisions have been used in a previous work by Qiu et al. [Qiu:1998rz] to study J/psi suppression.	background 1.00	0.03	0.01	asserted 1.00
s1	That model suggests that heavy quark re-scatterings in a cold nuclear medium can completely explain the centrality dependence of the observed J/psi suppression in Pb+Pb collisions at the SPS [Abreu:2001kd].	background 0.99	0.04	0.04	hedged possibility 0.89
s2	Their calculations also revealed significant differences under the assumptions of a color singlet or color octet production mechanism.	background 0.96	0.04	0.02	asserted 1.00
s3	A more recent analytic calculation [Fujii:2003fq], which includes incoherent final-state re-scatterings with explicit momentum transfer fluctuations in three dimensions, indicates much less suppression and little sensitivity to the production mechanism.	background 1.00	0.04	0.04	hedged possibility 0.88
s4	In this article, we study simultaneously both the J/psi suppression and p_T modifications, at SPS and RHIC energies.	contribution 1.00	0.77	0.03	asserted 0.97
s5	We mainly focus on incoherent momentum transfer fluctuations in two dimensions, which is more appropriate for the heavy-ion collision kinematics.	method 0.89	0.54	0.03	asserted 0.87
s6	Our analytic and Monte-Carlo calculations reinforce the analytic results in [Fujii:2003fq].	result 0.89	0.90	0.07	asserted 1.00
s7	Additionally, we find that the experimental J/psi suppression and <p_T^2> from nucleus-nucleus collisions at the SPS or RHIC cannot simultaneously be described in this incoherent multiple scattering framework for any value of the fluctuation strength parameter <k_T^2>.	result 0.98	0.96	0.89	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.82 · evidence from simulation or computation 0.87.

What was examined, and what was not

sources read

arXiv listing abstract v2

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

Figures

**Figure 1.** FIG. 1: Diagram of a nucleus-nucleus collision. Arrows at th

**Figure 3.** also shows a comparison of J/ψ suppression in the shifted q 2 model and the fluctuation model. Just like for the analytic study in Section II, we keep the average q 2 shift the same in both cases and therefore use hk 2 T i = 0.3

**Figure 5.** FIG. 5: The nuclear modification factor and ∆

**Figure 6.** FIG. 6: The nuclear modification factor and ∆

**Figure 7.** We show that for any parameter values of

Showing 5 of the paper's 7 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:nucl-th/0602068 by the authors.

References

Works cited (30)

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J. Qiu, J. P. Vary and X. Zhang, Phys. Rev. Lett. 88, 232301 (2002). J. w. Qiu, J. P. Vary and X. f. Zhang, Nucl. Phys. A 698, 571 (2002) [arXiv:nucl-th/0106040]

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M. C. Abreu et al. [NA50 Collaboration], Phys. Lett. B 521, 195 (2001)

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H. Fujii, Phys. Rev. C 67, 031901 (2003)

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R. L. Thews and M. L. Mangano, arXiv:nucl-th/0505055

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J. L. Nagle and M. J. Bennett, Phys. Lett. B 465, 21 (1999) [arXiv:nucl-th/9907004]

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We used PYTHIA 6.154 with CTEQ5M1 parton distribution f unctions, a c quark mass of 1.25 GeV PMAS(PYCOMP(4),

View on Pith
[12]

= 1.25 , ⟨kT ⟩ = 1.5 GeV PARP(91) = 1.5 , and a kT cutoﬀ of 5.0 GeV PARP(93) = 5.0

View on Pith
[13]

The average Q2 0 =q2 z −q2 0 is largely independent of the J/ψ rapidityy. However, the average q2 0 grows with |y|

View on Pith
[14]

This is roughly consistent with a comparison of results by Qiu et al. [1] and Fujii [3]. They use similar numerical values forε2, however, in [3], ε2 is multiplied by an additional factor of 3. We need to scale by a larger factor of 5 because, unlike Fujii, we consider a nonzero q2 0 (cf. Eq. (8))

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R. Vogt, arXiv:nucl-th/0507027

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This assumption is also made by studies of radiative par ton energy loss [28, 29]

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M. C. Abreu et al. [NA50 Collaboration], Phys. Lett. B 499, 85 (2001)

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R. Vogt, Phys. Rev. C 71, 054902 (2005) [arXiv:hep-ph/0411378]

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[25]

S. S. Adler et al. [PHENIX Collaboration], arXiv:nucl-ex/0510047

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[26]

J. Bielcik [STAR Collaboration], arXiv:nucl-ex/0511 005

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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] [22]

N. S. Topilskaya et al. [NA50 Collaboration], Nucl. Phys. A 715, 675 (2003); B. Alessandro et al. [NA50 Collaboration], Eur. Phys. J. C 33, 31 (2004)

View on Pith 2003

[2] [1]

J. Qiu, J. P. Vary and X. Zhang, Phys. Rev. Lett. 88, 232301 (2002). J. w. Qiu, J. P. Vary and X. f. Zhang, Nucl. Phys. A 698, 571 (2002) [arXiv:nucl-th/0106040]

View on Pith Pith review arXiv 2002

[3] [2]

M. C. Abreu et al. [NA50 Collaboration], Phys. Lett. B 521, 195 (2001)

View on Pith 2001

[4] [3]

H. Fujii, Phys. Rev. C 67, 031901 (2003)

View on Pith 2003

[5] [4]

T. Matsui and H. Satz, Phys. Lett. B 178, 416 (1986)

View on Pith 1986

[6] [5]

R. L. Thews and M. L. Mangano, arXiv:nucl-th/0505055

View on Pith Pith review arXiv

[7] [6]

C.J. Benesh, J. Qiu, J. P. Vary, Phys. Rev. C 50, 1015 (1994)

View on Pith 1994

[8] [7]

M. Luo, J. w. Qiu and G. Sterman, Phys. Rev. D 49, 4493 (1994)

View on Pith 1994

[9] [8]

R. J. Fries, Phys. Rev. D 68, 074013 (2003)

View on Pith 2003

[10] [9]

D. Kharzeev, M. Nardi and H. Satz, Phys. Lett. B 405, 14 (1997) [arXiv:hep-ph/9702273]

View on Pith Pith review arXiv 1997

[11] [10]

J. L. Nagle and M. J. Bennett, Phys. Lett. B 465, 21 (1999) [arXiv:nucl-th/9907004]

View on Pith Pith review arXiv 1999

[12] [11]

We used PYTHIA 6.154 with CTEQ5M1 parton distribution f unctions, a c quark mass of 1.25 GeV PMAS(PYCOMP(4),

View on Pith

[13] [12]

= 1.25 , ⟨kT ⟩ = 1.5 GeV PARP(91) = 1.5 , and a kT cutoﬀ of 5.0 GeV PARP(93) = 5.0

View on Pith

[14] [13]

The average Q2 0 =q2 z −q2 0 is largely independent of the J/ψ rapidityy. However, the average q2 0 grows with |y|

View on Pith

[15] [14]

This is roughly consistent with a comparison of results by Qiu et al. [1] and Fujii [3]. They use similar numerical values forε2, however, in [3], ε2 is multiplied by an additional factor of 3. We need to scale by a larger factor of 5 because, unlike Fujii, we consider a nonzero q2 0 (cf. Eq. (8))

View on Pith

[16] [15]

R. J. Glauber and G. Matthiae, Nucl. Phys. B 21, 135 (1970)

View on Pith 1970

[17] [16]

B. B. Back et al. [PHOBOS Collaboration], Phys. Rev. C 65, 031901 (2002) [arXiv:nucl-ex/0105011]

View on Pith Pith review arXiv 2002

[18] [17]

K. Adcox et al. [PHENIX Collaboration], Phys. Rev. Lett. 88, 022301 (2002) [arXiv:nucl-ex/0109003]

View on Pith Pith review arXiv 2002

[19] [18]

S. S. Adler et al. , Phys. Rev. Lett. 96, 012304 (2006) [arXiv:nucl-ex/0507032]

View on Pith Pith review arXiv 2006

[20] [19]

R. Vogt, arXiv:nucl-th/0507027

View on Pith Pith review arXiv

[21] [20]

This assumption is also made by studies of radiative par ton energy loss [28, 29]

View on Pith

[22] [21]

M. C. Abreu et al. [NA50 Collaboration], Phys. Lett. B 499, 85 (2001)

View on Pith 2001

[23] [23]

H. Pereira Da Costa et al. [PHENIX Collaboration], [arXiv:nucl-ex/0510051]

View on Pith Pith review arXiv

[24] [24]

R. Vogt, Phys. Rev. C 71, 054902 (2005) [arXiv:hep-ph/0411378]

View on Pith Pith review arXiv 2005

[25] [25]

S. S. Adler et al. [PHENIX Collaboration], arXiv:nucl-ex/0510047

View on Pith Pith review arXiv

[26] [26]

J. Bielcik [STAR Collaboration], arXiv:nucl-ex/0511 005

View on Pith

[27] [27]

S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. C 72, 024901 (2005) [arXiv:nucl-ex/0502009]

View on Pith Pith review arXiv 2005

[28] [28]

D. Molnar and M. Gyulassy, Nucl. Phys. A 697, 495 (2002) [Erratum-ibid. A 703, 893 (2002)] [arXiv:nucl-th/0104073]

View on Pith Pith review arXiv 2002

[29] [29]

R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne and D . Schiﬀ, Nucl. Phys. B 483, 291 (1997)

View on Pith 1997

[30] [30]

M. Gyulassy, P. Levai and I. Vitev, Phys. Rev. Lett. 85, 5535 (2000)

View on Pith 2000