Polarization of Prompt J/psi at the Tevatron

Bernd A. Kniehl; Eric Braaten (Ohio State); Jungil Lee (Hamburg)

REVIEW

Polarization of Prompt J/psi at the Tevatron

Eric Braaten (Ohio State), Bernd A. Kniehl, Jungil Lee (Hamburg)

High Energy Physics - Phenomenology · Submitted 22 Nov 1999 · 19 references

Pith's verdict: The reference calculation for prompt J/psi polarization: the qualitative rise of alpha is solid, but the quoted 3-sigma significance leans on a quadrature band over a parameter that isn't Gaussian.

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arXiv IDhep-ph/9911436 (version 3)

Pith ID5YJITQIX, Pith's permanent record of this paper and its review

CitationBernd A. Kniehl, Eric Braaten (Ohio State), Jungil Lee (Hamburg). "Polarization of Prompt J/psi at the Tevatron." arXiv:hep-ph/9911436 (1999). https://pith.science/paper/5YJITQIX

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Editor's note

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Braaten, Kniehl and Lee do the obvious next thing after Beneke-Kramer and Leibovich: compute alpha for prompt J/psi rather than direct psi-prime, including chi_cJ and psi-prime feeddown. That is the new content, and it matters, because the feeddown fractions are large (15%, 15%, 10%) and the chi_cJ radiative decays dilute transverse polarization in a spin-dependent way. The result, alpha rising from near 0 at 5 GeV to about 0.5 at 20 GeV and sitting roughly 3 sigma above the highest CDF bin, is the number everyone quotes from this paper. What is done well: the spin bookkeeping for chi_cJ(lambda) -> J/psi_L is written out explicitly (1/3, 1/2, 2/3, 1/2, 0), the matrix elements are re-extracted from CDF pT distributions with two PDF sets, and the paper reports its own disagreement rather than burying it. The error budget is enumerated honestly. Soft spots, in order of weight. First, the 3 sigma. The band in Fig. 1(b) is quadrature over everything, and x = /M_r is one of the three dominant terms. But x is a bounded mixing fraction set to 1/2 by hand, not a measured Gaussian, and alpha is nonlinear in x, so quadrature is not the envelope over [0,1]. The paper never shows the x-only variation. The stress-test note is right about this. It does not kill the qualitative claim, which is robust, but the specific 3 sigma should be read as a couple of sigma, maybe three, not a sharp number. Second, Eq. (4): the fusion-to-fragmentation interpolation multiplies by a ratio of fragmentation cross sections at two scales with no assigned uncertainty, right where the discrepancy lives. It is flagged as a prescription, but it deserves a number. Third, the new polarized chi_cJ parton cross sections are in a companion preprint [10], not here, so a necessary ingredient is taken on trust. The reader's circularity worry is overstated: alpha is a ratio and is not fitted, and the matrix elements come from cross sections. The real dependence runs through the transverse/longitudinal split, which is the first point. Who should read it: anyone working on quarkonium polarization or NRQCD universality. It is the reference calculation for prompt J/psi alpha and it framed the Run II discussion. Peer review: yes, send it out. It is a careful calculation within an established program, with a real anomaly attached.

Referee report

Major objections (3)

[Error analysis paragraph preceding Fig. 1; Fig. 1(b); abstract:s3] The headline statement that the prediction disagrees with CDF by about three standard deviations rests on the error band in Fig. 1(b), which the text says is obtained by 'combining in quadrature all the errors described above.' One of the three dominant entries is x = ⟨O_8(¹S₀)⟩/M_r, which is not a measured quantity with a Gaussian error: it is a mixing fraction bounded to [0,1] and fixed at 1/2 by hand because the p_T fit determines only M_r at r ≈ 3.0–3.6. Since α is nonlinear in x, a quadrature band need not equal the true envelope of α over x ∈ [0,1]. The paper should show the x-only variation explicitly — for instance the curves for x = 0 and x = 1, or the envelope over that interval — so that a reader can judge whether the quoted band is conservative or optimistic. If the envelope is wider than the quadrature band, the significance of the high-p_T discrepancy should be restated as a range rather than a single '3 standard deviations.'
[Eq. (4)] The interpolation between the fusion and fragmentation cross sections in Eq. (4) multiplies the ³S₁ fusion piece by the ratio dσ_fr[μ_fr = μ]/dσ_fr[μ_fr = 2m_c], a prescription rather than a derivation, and no uncertainty is assigned to it. Because this factor controls the normalization of the dominant color-octet contribution precisely in the high-p_T region where the discrepancy with CDF is claimed, its effect on α at p_T = 15–20 GeV should be quantified. At minimum the authors should state how much α changes if the matching scale in the denominator is varied, or if the ratio is replaced by unity, so that the reader can see whether the matching ambiguity is small compared with the quoted band.
[Ref. [10] and the χ_cJ feeddown calculation] The spin-dependent parton cross sections for the χ_cJ states, which are the new physics input that makes the feeddown correction calculable, are not given in this paper and are cited to Ref. [10] (DESY 00-107, hep-ph/0007292) without a journal reference. Since the paper's central qualitative claim — that χ_cJ feeddown decreases but does not eliminate the transverse polarization — depends on these cross sections, and since the text also asserts that the ψ′ and χ_c contributions 'tend to cancel' at high p_T, the reader cannot check that cancellation from the material presented. At least a table of the resulting spin-state χ_cJ cross sections, or of the effective longitudinal fractions P_{χ_cJ(λ)→ψ_L} weighted by the production cross sections, should be included here.

Minor objections (5)

[Table I] The caption states that the error bars take into account statistical errors only. It would help to say explicitly whether the scale and PDF variations used later in the α error band are also reflected in the matrix-element errors, or whether they are treated as independent and added separately.
[Fig. 1] The caption should identify the three solid lines in panel (b) as the central curves for direct J/ψ, J/ψ from χ_cJ, and J/ψ from ψ′, since at present this information appears only in the body text. The p_T binning of the CDF points should also be stated in the caption.
[Comparison with Refs. [7] and [8]] The text attributes the difference from Beneke and Krämer to their treatment of order-α_s² terms in the gluon fragmentation function. A sentence quantifying the size of that effect on α at p_T = 20 GeV would make the comparison more informative than the current qualitative statement.
[Abstract and concluding paragraph] The phrase 'disagrees by about 3 standard deviations' in the abstract should be qualified in light of the error-band construction discussed above, and the sentence 'the qualitative prediction that α should increase at large p_T seems inescapable' could usefully note that this rests on the leading-order spin-dependent cross sections, which the concluding paragraph already lists among the possible failure points.
[Manuscript formatting] The version supplied has broken spacing and hyphenation throughout (for example 'nonrelati vistic' and 'polariza tion'); this is presumably an extraction artifact, but the final version should be checked for similar typesetting faults.

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The paper

The paper claims

Prompt $J/psi$ mesons should become transversely polarized as their transverse momentum grows, and the size of that polarization can now be predicted including feeddown from heavier charmonium states.

The reading

The paper asks a sharp question about a striking prediction of the nonrelativistic QCD factorization approach to quarkonium production: that vector quarkonium states made in hadron collisions should come out transversely polarized once transverse momentum $p_T$ is large enough. Earlier calculations of this effect were done for direct $psi'$ mesons, but the experimentally copious signal is the prompt $J/psi$, roughly a third of which arrives through decays of $chi_{c1}$, $chi_{c2}$, and $psi'$. The authors redo the bookkeeping for that mixed sample, fitting the color-octet matrix elements to CDF $p_T$ distributions and computing the polarization of each spin state of each parent, then propagating it through the radiative decay probabilities into a longitudinally polarized $J/psi$. The result is a predicted angular parameter $alpha$ that climbs from near zero at $p_T = 5$ GeV to about 0.5 at $p_T = 20$ GeV, matching CDF at intermediate $p_T$ and missing the highest measured bin by about three standard deviations. The point of the exercise is that feeddown softens but does not remove the transverse-polarization prediction, so the residual disagreement has to be explained by something other than forgotten decay chains.

What carries the argument

The machinery is the NRQCD factorization formula $d sigma_{H_lambda}(P) = d sigma_{c bar{c} n}(P) langle O_{H_lambda}(P)_n rangle$, in which the short-distance parton cross sections for each color and angular momentum state $n$ of the $c bar{c}$ pair are multiplied by nonperturbative matrix elements, and the spin dependence of the bound state enters only through the polarization tensor of $H_lambda$. The authors re-extract the color-octet parameters $langle O_8(^3S_1) rangle$, the combination $M_r = langle O_8(^1S_0) rangle + r langle O_8(^3P_0) rangle/m_c^2$, and $langle O_{chi_{c0}8}(^3S_1) rangle$ from CDF $p_T$ distributions for $J/psi$, $chi_c$, and $psi'$, add the gluon fragmentation contribution $g to c bar{c}_8(^3S_1)$ with its timelike evolution, and interpolate between the fusion and fragmentation regimes. New parton cross sections for the individual spin states of the $chi_{cJ}$ were required and are cited to a companion paper. The decay step then converts parent spin states into longitudinal $J/psi$ fractions, which is what turns a set of partonic polarization cross sections into a single measurable $alpha$ curve.

Extended reading notes

Core claim

The central claim is that within NRQCD factorization, the angular distribution parameter $alpha = (sigma_T - 2 sigma_L)/(sigma_T + 2 sigma_L)$ for leptons from prompt $J/psi$ at the Tevatron rises with transverse momentum, from near 0 at $p_T = 5$ GeV to roughly 0.5 at $p_T = 20$ GeV, once the $chi_{cJ}$ and $psi'$ feeddown contributions are computed spin state by spin state. Radiative $P$-wave decays reduce the transverse polarization relative to the direct-$J/psi$ case but do not eliminate it, because the decay probabilities into a longitudinal $J/psi$ are only $1/3$ for $chi_{c0}$, $1/2$ for the transverse $chi_{c1}$ and $chi_{c2}$ states, $2/3$ for $chi_{c2}(0)$, and zero for the rest. Comparing to the CDF measurement, the prediction agrees at intermediate $p_T$ but sits about three standard deviations high in the 15 to 20 GeV bin, where CDF finds $alpha = -0.29 plus or minus 0.23. The authors read that mismatch as a serious challenge to the formalism rather than a detail, since the qualitative rise is what the low-order spin dynamics of massless partons and heavy quarks requires.

Load-bearing premise

The longitudinal cross section for $psi(nS)$ depends on a combination of two color-octet matrix elements that the $p_T$-distribution fit does not determine, so the authors fix the mixing ratio $x = langle O_8(^1S_0) rangle / M_r$ at $1/2$ by hand and treat the whole range from 0 to 1 as an error bar; the polarization prediction therefore rests on a parameter no data constrains.

Editorial extensions

If this is right

If the calculation is right, any future measurement of prompt $J/psi$ polarization at the Tevatron or the LHC should show $alpha$ increasing with $p_T$ rather than falling, so a continued downward trend would falsify the low-order spin-dynamics picture rather than merely refine it.
The $psi'$ channel provides a cleaner test than the $J/psi$ channel, since no feeddown complicates it; a more precise direct-$psi'$ polarization measurement would discriminate between the present prediction and the earlier, higher curves.
Improved $J/psi$ and $psi'$ cross-section data would shrink the dominant ambiguities, which the authors trace to the fitted color-octet matrix elements, the parton distribution choice, and the unmeasured mixing parameter $x$.
Because the disagreement grows with $p_T$, a Run II sample extending the measurement beyond 20 GeV would decide whether the discrepancy is a statistical fluctuation in the top bin or a systematic failure of the factorization approach for charmonium.

Reading between the lines

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

The paper's logic suggests a useful diagnostic separation: measure $alpha$ for $psi'$ and for $chi_{cJ}$-tagged events independently, since the two feeddown streams partly cancel at high $p_T$ in the prompt sample and could mask a real discrepancy in either one.
The same spin-bookkeeping could be run in reverse, using measured polarization as an additional constraint that breaks the degeneracy between $langle O_8(^1S_0) rangle$ and $langle O_8(^3P_0) rangle$ that the $p_T$ distributions alone cannot resolve.
If the anomaly survives, the most economical reading is not that QCD is wrong but that $m_c$ is too light for the velocity expansion to control the spin-dependent channels, which would predict the discrepancy to shrink for bottomonium, where the same calculation is more trustworthy.
The three-sigma tension sits in a single bin with a large error bar, so a reanalysis combining bins or quoting a correlation-aware goodness of fit would be a cheap way to see how much of the tension is real.

Original abstract

The polarization of prompt J/psi at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework. The contribution from radiative decays of P-wave charmonium states decreases, but does not eliminate, the transverse polarization at large transverse momentum. The angular distribution parameter alpha for leptonic decays of the J/\psi is predicted to increase from near 0 at p_T = 5 GeV to about 0.5 at p_T = 20 GeV. The prediction is consistent with measurements by the CDF Collaboration at intermediate values of p_T, but disagrees by about 3 standard deviations at the largest values of p_T measured.

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,665 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.86 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.91 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

The polarization of prompt J/psi at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework. The contribution from radiative decays of P-wave charmonium states decreases, but does not eliminate, the transverse polarization at large transverse momentum. The angular distribution parameter alpha for leptonic decays of the J/\psi is predicted to increase from near 0 at p_T = 5 GeV to about 0.5 at p_T = 20 GeV. The prediction is consistent with measurements by the CDF Collaboration at intermediate values of p_T, but disagrees by about 3 standard deviations at the largest values of p_T measured.

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	The polarization of prompt J/psi at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework.	contribution 0.69	0.90	0.08	asserted 1.00
s1	The contribution from radiative decays of P-wave charmonium states decreases, but does not eliminate, the transverse polarization at large transverse momentum.	result 0.99	0.78	0.30	asserted 1.00
s2	The angular distribution parameter alpha for leptonic decays of the J/\psi is predicted to increase from near 0 at p_T = 5 GeV to about 0.5 at p_T = 20 GeV.	result 1.00	0.88	0.27	asserted 0.98
s3	The prediction is consistent with measurements by the CDF Collaboration at intermediate values of p_T, but disagrees by about 3 standard deviations at the largest values of p_T measured.	result 0.64	0.59	0.29	asserted 0.75

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from simulation or computation 0.58.

What was examined, and what was not

sources read

arXiv listing abstract v3

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. Polarization variable

Figures reproduced from arXiv:hep-ph/9911436 by the authors.

References

Works cited (19)

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Forward citations

Cited by 14 Pith papers

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The J/psi pair production cross-section at 13 TeV is measured to be 15.2 +/- 1.0 +/- 0.9 nb for both mesons at pT < 10 GeV/c and 2.0 < y < 4.5, with differential distributions that favour a large double-parton-scatter...
Measurement of the prompt J/psi and psi(2S) polarizations in pp collisions at sqrt(s) = 7 TeV
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Prompt J/psi and psi(2S) mesons produced at the LHC up to 70 GeV show no large transverse or longitudinal polarization in any of three frames, in disagreement with next-to-leading-order NRQCD predictions.
J/psi polarization at hadron colliders in nonrelativistic QCD
hep-ph 2012-01 conditional novelty 6.0 of 10

The NLO color-octet 3PJ[8] channel gives a negative transverse and positive longitudinal J/psi component, and its cancellation against 3S1[8] can account for the observed unpolarized prompt J/psi.
Measurement of J/Psi and Psi(2S) Polarization in ppbar Collisions at sqrt(s) = 1.8 TeV
hep-ex 2000-04 accept novelty 6.0 of 10

Promptly produced J/psi and psi(2S) mesons at CDF show no significant transverse polarization above about 12 GeV/c, contrary to NRQCD factorization predictions.

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Color-octet channels are predicted to dominate many double heavy quarkonium production processes at future Z factories, with relativistic corrections suppressing charmonium rates by roughly a factor of two.
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hep-ph 2019-06 unverdicted novelty 5.0 of 10

Loop-induced CS and selected CO SPS contributions to prompt J/ψ pairs are too small or kinematically limited to account for LHC data or affect DPS control regions.
Measurement of $J/\psi$ polarization in $pp$ collisions at $\sqrt{s}=7$ TeV
hep-ex 2013-07 accept novelty 5.0 of 10

Prompt J/psi mesons produced at the LHC show a small longitudinal polarization (average lambda_theta = -0.145 +/- 0.027), with the two azimuthal parameters consistent with zero.
Inelastic Production of J/psi Mesons in Photoproduction and Deep Inelastic Scattering at HERA
hep-ex 2010-02 accept novelty 5.0 of 10

Inelastic J/psi photoproduction and electroproduction cross sections and polarisation parameters from H1 are described by k_T-factorisation colour-singlet calculations but undershot by roughly a factor of three by col...
QCD radiative correction to color-octet $J/\psi$ inclusive production at B Factories
hep-ph 2009-11 conditional novelty 5.0 of 10

NLO QCD corrections roughly double the color-octet J/psi production rate at B factories, and Belle data then imply a color-octet matrix element below 2.0 x 10^-2 GeV^3.
Hard probes in heavy ion collisions at the LHC: heavy flavour physics
hep-ph 2003-11 conditional novelty 4.0 of 10

The report sets NLO QCD and quarkonium benchmark cross sections for LHC pp and pA collisions, showing that ratios across energies and beam species extrapolate to a few percent while absolute rates carry factor-of-two ...
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hep-ph 2012-12 conditional novelty 3.0 of 10

A global NLO NRQCD fit to unpolarized J/psi yields determines three color-octet matrix elements that reproduce held-out data and HERA/LHC polarization, but fail against Tevatron polarization.
On the mechanisms of heavy-quarkonium hadroproduction
hep-ph 2008-11 conditional novelty 3.0 of 10

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How the literature uses it

33 arXiv papers cite this in 48 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

The prediction agrees with measurements from the CDF collaboration at intermediate values of p_T, but disagrees at the large values of p_T measured.

Prompt J/psi Polarization at the Tevatron · 0.97

Papers citing it · 25 sentences without a confident label

Contests it 3 papers

Unfortunately, the predictions of the polarizations of prompt $ψ(2S)$ [ref] and prompt $J/ψ$ [ref] were disfavored by the CDF measurement at Run I of the Fermilab Tevatron [ref] .

Recent Developments in Heavy-Quarkonium Phenomenology · Introduction · contest 0.87
However, NRQCD predicts polarisation [ref] that is not observed in LHC data [ref] .

Non-Relativistic Quantum Chromodynamics in Parton Showers · Introduction · contest 0.77
However, based on it, prediction of prompt $$ hadroproduction at leading order (LO) in $_s$ is significantly transversely polarized [ref] which contradicts with the measurement by the CDF Collaboration [ref] , where one found that the produced $$ is almost unpolarized and even slightly longitudinally polarized as $p_T$ increases.

Relativistic effect of $J/\psi$ hadroproduction in large $p_T$ region · Introduction · contest 0.79

Uses its method or tool 1 paper

Employing the method given in Refs. [ref] , one can compute the polarized cross sections $σ_T$ and $σ_L$ in the hadron CM frame from Eq. ([ref]).

Polarization of prompt J/psi in proton-proton collisions at RHIC · Introduction · 1.00

Uses its data or values 8 papers

The numerical values for the relevant NRQCD matrix elements are given in Table I of Ref. [ref] .[ The color-octet matrix elements $⟨O_8^H (^1S_0) ⟩$ and $⟨O_8^H (^3P_J) ⟩$ are determined not separately but as a linear combination $M_r^H=⟨O^H_8(^1S_0)⟩+ r ⟨O^H_8 (^3P_0) ⟩/m_c^2$ which depends on the variable $r$ given in Ref. [ref] .] For the PDF's, we choose MRST98LO [ref] as the default value and CTEQ5L [ref] for comparison.

Polarization of prompt J/psi in proton-proton collisions at RHIC · Introduction · 0.91
In this work, we use $⟨O_8^J/ψ (^3S_1) ⟩= 3.9×10^-3$ $GeV^3$ [ref] , $⟨O_8^Υ (^3S_1) ⟩= 1.5×10^-1$ $GeV^3$ [ref] .

p p -> J/psi+Upsilon+X as a clean probe to the quarkonium production mechanism · Introduction · 1.00
We use numerical values for the NRQCD matrix elements (ME) given in Ref. [ref] .

Polarization of prompt J/psi in pp -> J/psi+X at sqrt{s}=200 GeV · $p_T$ distributions · 1.00

Compares with it 1 paper

However, the CO LDMEs used in the present paper are actually moderate compared to those in some other Refs. [ref] .

Double heavy quarkonia production with color-octet channels at Z factory and at the CEPC/FCC-ee · Uncertainties · 0.99

Cites it as background 7 papers

The quarkonia directly produced at high transverse momentum, , are predicted to be transversely polarized [ref] with respect to the direction of their own momentum.

Measurement of the prompt J/psi and psi(2S) polarizations in pp collisions at sqrt(s) = 7 TeV · Introduction · 0.89
For the production of $J/ψ$'s with large transverse momentum $p_T$, the most important contribution in NRQCD at leading order (LO) in $α_s$ comes from the $$ channel, which suggests that the produced $J/ψ$'s should be transversely polarized [ref] .

$J/\psi$ polarization in the CGC+NRQCD approach · Introduction · 0.83
In spite of the great importance of Non-relativistic QCD(NRQCD) factorization in study of processes involving heavy quarkonia(see, for example, Refs. [ref] ), such factorization theorem for inclusive production of heavy quarkonia remains a non-trivial issue( [ref] ).

Cancellation of Infrared Divergence in Inclusive Production of Lepton Pair Near the Threshold of Heavy Quarkonia · Introduction · 0.98

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] [10]

B. A. Kniehl and J. Lee, Report No. DESY 00-107 and hep-ph/0007292

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