Color-Octet Fragmentation and the psi' Surplus at the Tevatron

Eric Braaten; Sean Fleming

REVIEW

Color-Octet Fragmentation and the psi' Surplus at the Tevatron

Eric Braaten, Sean Fleming

High Energy Physics - Phenomenology · Submitted 23 Nov 1994 · 16 references

Pith's verdict: The founding paper of the color-octet production program: a clean, honest mechanism proposal whose quantitative case is a one-parameter normalization fit, not a discrimination between competing channels.

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arXiv IDhep-ph/9411365 (version 1)

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CitationEric Braaten, Sean Fleming. "Color-Octet Fragmentation and the psi' Surplus at the Tevatron." arXiv:hep-ph/9411365 (1994). https://pith.science/paper/X4DF5HTO

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Editor's note

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Braaten and Fleming are proposing a new production mechanism for the psi' surplus, and this is the paper that put color-octet fragmentation on the map. The core is simple: g* -> c cbar in a color-octet 3S1 state, hadronizing into psi' plus light hadrons, with the fragmentation function in Eq. (3) lifted from their earlier chi_cJ calculation. The 1/alpha_s^2 enhancement over the color-singlet channel is the whole argument, and it is cleanly made. The abstract itself is properly conditional (abstract:s1), which matters for how you read the rest of it. What is genuinely new and deserves credit: the mechanism, the fitted = 0.0042 GeV^3, the v^4 sanity check against the 0.11 GeV^3 color-singlet value (factor 25, roughly v^4 for v^2 ~ 1/3), and the CLEO-based re-determination of in Eq. (6), which cuts the earlier H'_8 estimate by a factor of 2 and moves the J/psi prediction. That last number is independent of the psi' fit and is the most solid piece of the paper. Where it is soft: Eq. (7) is a normalization fitted to the same CDF points it explains, with no error bar, and 'the shape fits perfectly' is asserted rather than shown, no chi-squared, no residuals. That is normal for a Letter of this era, but it means the paper demonstrates viability, not dominance. The stress-test is right that the feed-down alternatives from Ref. [7] get a plausibility sentence rather than a calculation. I would add that the paper's own Eq. (6) makes chi_c2 -> gamma psi' a live competitor, and only the small radiative branching keeps it from being serious; the paper should have said that out loud. I would push back on calling the fit circular, though. A one-parameter normalization of a shape is standard practice, and the authors flag it in the figure caption. The real gap is discrimination between channels, not circularity. The jet-association and transverse-polarization predictions are falsifiable and are not used to fix the constant, which is the right way to propose a mechanism. For anyone working on quarkonium production this is required reading; it is the origin of the color-octet production program. Send it out.

Referee report

Significance

If the mechanism is confirmed, this is the first identification of a color-octet-dominated quarkonium production channel and a cornerstone of the NRQCD factorization program; it would resolve a long-standing order-of-magnitude discrepancy and would reorganize the interpretation of charmonium production across processes. The paper earns credit for several things: the short-distance input is a published calculation quoted correctly rather than rederived; the v^4 consistency check is a genuine, if order-of-magnitude, test; the relation between the χ_c2 matrix element and the measured B→χ_c2 branching fraction (Eqs. 5-6) is a parameter-free link to independent data; and the two proposed signatures (light-hadron jet association and transverse polarization) are falsifiable predictions that can be checked with existing detectors. The abstract is appropriately hedged (abstract:s1, 'we suggest'), which is the right register for a proposal of this kind.

Major objections (3)

[Fig. 1 and Eq. (7)] The normalization of the color-octet curve is fixed by the same CDF data it is meant to explain, and the text states that the matrix element was 'adjusted to make the normalization agree with the data.' That is a legitimate way to establish viability, but it means the rate is not predicted, and the paper should say so explicitly rather than let the reader infer a prediction. The remaining empirical content is the shape agreement, which is asserted ('the shape of the color-octet fragmentation contribution fits the data perfectly') without a chi-squared, residuals, the number of data points, or the pT window. Because the leading-order input is a delta function at z=1 (Eq. 3), the shape after Altarelli-Parisi evolution is the actual test, and it should be quantified. Please report chi-squared per degree of freedom over the quoted pT range, and state plainly that the fit demonstrates that the mechanism can account for the surplus, not that it does.
[Introduction, paragraph dismissing feed-down (Ref. [7])] The introduction sets aside feed-down from higher P-wave, D-wave, and |c-cbar-g> states with the sentence that 'there is reason to question whether the production rate can be large enough and whether the branching fraction into ψ' can be large enough.' That is an assertion, not a calculation, and it is load-bearing for the word 'dominant' in the abstract (abstract:s1) and in the body. A crude order-of-magnitude estimate of at least one competing channel, using the same NRQCD matrix elements the paper already deploys, would make the dominance claim defensible. I note that the specific channel sometimes raised as a competitor, χ_c2 → γψ', is kinematically forbidden because m(χ_c2) ≈ 3556 MeV lies below m(ψ') ≈ 3686 MeV, so that particular concern does not land; the relevant competitors are the states above the ψ' threshold, and those are the ones that need at least an estimate.
[Fig. 1 and the paragraph preceding Eq. (7)] The pT range over which the fit is performed and the lower pT cut are not stated. Fragmentation dominance requires pT well above m_c, and the relative weight of the dotted (leading-order), dashed (color-singlet fragmentation), and solid (color-octet fragmentation) curves in Fig. 1 depends sensitively on the window chosen. Please state the pT range of the CDF data used, the cut applied, and whether the fit is over the full range or only the large-pT tail. This also bears on the interpretation of the fitted matrix element, since a fit dominated by moderate pT would not test the fragmentation regime the paper claims to identify.

Minor objections (6)

[Eq. (1) and surrounding text] The text refers to 'local 4-fermon operators'; this should read '4-fermion operators.'
[Fig. 1 caption] The caption should give the pT range, the data point uncertainties, and the fitted value of the normalization, so that the figure is interpretable without the body text.
[Photoproduction discussion, Ref. [15]] The photoproduction prediction rests on Ref. [15], listed as 'in progress.' Either state the result or flag explicitly that the prediction is contingent on forthcoming work, so the reader can weigh it appropriately.
[Eq. (3) and the paragraph following it] The fragmentation scale is set to mu = pT/z and evolved with Altarelli-Parisi. The sensitivity of the fitted matrix element to the choice of scale, and to varying mu by a factor of two, should be stated as an uncertainty on Eq. (7).
[Eq. (6) and the J/ψ discussion] The downward revision of <O_8^{χ_c2}(3S1)> and the resulting factor-of-5 J/ψ discrepancy rest on the CLEO branching fraction (0.25 ± 0.11)%, a 44% measurement. The quoted uncertainty on Eq. (6) should be propagated explicitly into the J/ψ statement so that the reader can see how much of the factor-of-5 gap is theoretical and how much is experimental.
[Abstract] The phrase 'prompt ψ's' is awkward; 'prompt ψ' mesons' would read better.

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The paper

The paper claims

The paper argues that the factor-30 surplus of prompt psi-prime mesons seen at the Tevatron is not an anomaly but the signature of a new production channel: gluon fragmentation into a pointlike color-octet $c$-$bar c$ pair that later binds,

The reading

For years the working picture was that charmonium is made at short distances as a color-singlet $c$-$bar c$ pair, with the psi-prime treated as a nonrelativistic bound state of small relative velocity $v$. That picture falls about a factor of 30 short of the prompt psi-prime rate measured by CDF at large transverse momentum, even after parton fragmentation is included. The paper's proposal is that the missing piece is a color-octet channel: a gluon splits into a $c$-$bar c$ pair in a pointlike $^3S_1$ octet state, and that state then evolves nonperturbatively into a psi-prime plus light hadrons. The bookkeeping that makes this credible is a competition between couplings rather than a proof: the octet short-distance coefficient is of order $1/m_c^3$ times one power of $alpha_s$ instead of three, buying two powers of $1/alpha_s$ that can offset the $v^4$ suppression of the octet matrix element. If the proposal holds, the surplus stops being an anomaly and becomes a measurement of one nonperturbative number, and the psi-primes observed at the Tevatron should almost always sit inside jets of light hadrons and be transversely polarized.

What carries the argument

The machinery is the heavy-quarkonium factorization formula $D_{g to X}(z,mu) = sum_n d_n(z,mu), langle 0 | O^X_n | 0 rangle$, in which the short-distance coefficients $d_n$ are independent of the quarkonium state and the state dependence sits entirely in nonperturbative matrix elements. Its work here is to make the octet contribution calculable from a single number and to allow that number to be extracted from one experiment and reused elsewhere. The second piece of machinery is the velocity-scaling bookkeeping: matrix elements scale as powers of $v$, short-distance coefficients as powers of $alpha_s$, and because $v^2$ is only about $1/3$ for charmonium while $alpha_s/pi$ is much smaller, the ordering must count both. That counting is what turns an ostensibly suppressed octet term into a candidate leading contribution.

Extended reading notes

Core claim

The central claim is that gluon fragmentation into a $c$-$bar c$ pair in a color-octet $^3S_1$ state, followed by nonperturbative evolution into a psi-prime plus light hadrons, dominates prompt psi-prime production at large $p_T$. Using the factorization of fragmentation functions into short-distance coefficients and long-distance matrix elements, the authors write $D_{g to psi'}(z,mu) = pi alpha_s(2m_c)/(24 m_c^3), delta(1-z), langle 0 | O^{psi'}_8(^3S_1) | 0 rangle$, a form they prefer over the $H'_8$ notation used in the earlier $chi_{cJ}$ calculation because it separates the $alpha_s/m_c^3$ short-distance factor from the long-distance matrix element. Adjusting the normalization of this single contribution to the CDF data yields $langle 0 | O^{psi'}_8(^3S_1) | 0 rangle = 0.0042$ GeV$^3$, and the authors note that the shape of the resulting curve fits the data. Their consistency check is that this value is smaller than the color-singlet matrix element, about $0.11$ GeV$^3$ from the leptonic decay rate, by a factor of roughly 25, which is what $v^4$ suppression would suggest. The paper also re-derives the analogous $chi_{c2}$ octet matrix element from a CLEO measurement of $B to chi_{c2} + X$, obtaining $(0.016 pm 0.007)$ GeV$^3$, about half an earlier estimate, which pushes the standard $J/psi$ prediction to roughly a factor of 5 below the data and leaves room for an octet contribution there too.

Load-bearing premise

The load-bearing premise is that a single nonperturbative color-octet matrix element, whose value is obtained by normalizing the calculation to the same CDF data it is meant to explain, carries the entire factor-30 excess rather than the surplus arising from feed-down of higher charmonium states or from some other source.

Editorial extensions

If this is right

Prompt psi-primes at large $p_T$ at the Tevatron should almost always be accompanied by a jet of light hadrons, with transverse momentum of order $m_c v$ or less relative to the jet axis, unlike the isolated psi-primes that leading-order fusion processes produce.
The color-octet fragmentation mechanism produces psi-primes that are fully transversely polarized at leading order in $alpha_s$, so the angular distribution of leptonic decays is a direct signature.
The extracted matrix element can be carried to other high-energy processes; in photoproduction only the $^1S_0$ and $^3P_J$ octet matrix elements enter at leading order, and they can be pinned down from the elastic peak near $z to 1$.
The revised $chi_{c2}$ octet matrix element lowers the standard $J/psi$ prediction to about a factor of 5 below the CDF data, leaving room for an octet contribution to $J/psi$ of comparable size to the psi-prime one.
Annihilation does not get the same enhancement as production: the octet contribution to psi-prime decay into light hadrons gains only one power of $1/alpha_s$, so a large production rate need not imply a large octet decay rate.

Reading between the lines

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

Because the normalization is fixed by fitting the very data it explains, the real content of the fit is the shape of the $p_T$ distribution and its agreement across the measured range; an independent determination of the same matrix element from a different process would be the test that actually separates this explanation from a one-parameter curve that happens to fit.
The polarization prediction is the sharper discriminator, since it does not depend on the overall normalization and would distinguish octet fragmentation from feed-down of higher charmonium states even if both reproduce the rate.
If the octet matrix elements are universal across processes as the factorization assumes, then a joint fit to Tevatron production, elastic photoproduction, and $B$-meson decay should overdetermine them; a mismatch between the value needed here and the value needed elsewhere would point to a breakdown rather than to a new mechanism.
The same two-powers-of-$1/alpha_s$ versus $v^4$ argument applies to any quarkonium state whose color-singlet short-distance coefficient is suppressed, so the logic naturally extends to the $J/psi$ and to bottomonium, where the velocity counting is more favorable.

Original abstract

The production rate of prompt $\psi'$'s at large transverse momentum at the Tevatron is larger than theoretical expectations by about a factor of 30. As a solution to this puzzle, we suggest that the dominant $\psi'$ production mechanism is the fragmentation of a gluon into a $c \bar c$ pair in a pointlike color-octet S-wave state, which subsequently evolves nonperturbatively into a $\psi'$ plus light hadrons. The contribution to the fragmentation function from this process is enhanced by a short-distance factor of $1/\alpha_s^2$ relative to the conventional color-singlet contribution. This may compensate for the suppression by $v^4$, where $v$ is the relative momentum of the charm quark in the $\psi'$. If this is indeed the dominant production mechanism at large $p_T$, then the prompt $\psi'$'s that are observed at the Tevatron should almost always be associated with a jet of light hadrons.

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, 4,429 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.45 · human participants 0.01 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.85 · compares with prior results 0.86 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The production rate of prompt $\psi'$'s at large transverse momentum at the Tevatron is larger than theoretical expectations by about a factor of 30. As a solution to this puzzle, we suggest that the dominant $\psi'$ production mechanism is the fragmentation of a gluon into a $c \bar c$ pair in a pointlike color-octet S-wave state, which subsequently evolves nonperturbatively into a $\psi'$ plus light hadrons. The contribution to the fragmentation function from this process is enhanced by a short-distance factor of $1/\alpha_s^2$ relative to the conventional color-singlet contribution. This may compensate for the suppression by $v^4$, where $v$ is the relative momentum of the charm quark in the $\psi'$. If this is indeed the dominant production mechanism at large $p_T$, then the prompt $\psi'$'s that are observed at the Tevatron should almost always be associated with a jet of light hadrons.

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 production rate of prompt $\psi'$'s at large transverse momentum at the Tevatron is larger than theoretical expectations by about a factor of 30.	background 0.91	0.10	0.07	asserted 1.00
s1	As a solution to this puzzle, we suggest that the dominant $\psi'$ production mechanism is the fragmentation of a gluon into a $c \bar c$ pair in a pointlike color-octet S-wave state, which subsequently evolves nonperturbatively into a $\psi'$ plus light hadrons.	contribution 0.79	0.43	0.73	hedged possibility 0.82
s2	The contribution to the fragmentation function from this process is enhanced by a short-distance factor of $1/\alpha_s^2$ relative to the conventional color-singlet contribution.	interpretation 0.36	0.58	0.09	asserted 1.00
s3	This may compensate for the suppression by $v^4$, where $v$ is the relative momentum of the charm quark in the $\psi'$.	interpretation 0.93	0.25	0.06	hedged possibility 1.00
s4	If this is indeed the dominant production mechanism at large $p_T$, then the prompt $\psi'$'s that are observed at the Tevatron should almost always be associated with a jet of light hadrons.	interpretation 0.96	0.18	0.36	hedged possibility 0.64

What kind of paper the classifier reports this is: theoretical result 0.67 · evidence from argument 0.92.

What was examined, and what was not

sources read

arXiv listing abstract v1

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

References

Works cited (16)

[7]

P. Cho, S. Trivedi and M. Wise, CALT-68-1943 (hep-ph 9408352 ); F.E. Close, RAL-94- 093 (hep-ph 9409203); D.P. Roy and K. Sridhar, CERN-TH.7434/94 (hep-ph 9409232); P. Cho and M. Wise, CALT-68-1954 (hep-ph 9410214)

View on Pith 1943
[8]

G.T. Bodwin, E. Braaten, and G.P. Lepage, Argonne preprint ANL -HEP-PR-94-24 (hep-ph 9407339)

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[12]

E. Braaten and T.C. Yuan, Phys. Rev. D50, 3176 (1994)

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[1]

V. Papadimitriou, CDF Coll., presented at the “Rencontres de la Va llee d’Aoste”, La Thuile, March 1994

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[2]

T. Daniels, CDF Coll., Fermilab-Conf-94/136-E

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R. Baier and R. R¨ uckl, Z. Phys. C19 251 (1983); F. Halzen, F. Herzog, E.W.N. Glover, and A.D. Martin, Phys. Rev. D30, 700 (1984); E.W.N. Glover, A.D. Martin, W.J. Stirling, Z. Phys. C38, 473 (1988); B. van Eijk and R. Kinnunen, Z. Phys. C41, 489 (1988)

View on Pith 1983
[4]

E. Braaten and T.C. Yuan, Phys. Rev. Lett. 71, 1673 (1993)

View on Pith 1993
[5]

E. Braaten, M.A. Doncheski, S. Fleming, and M. Mangano, Phys. L ett. B333, 548 (1994)

View on Pith 1994
[6]

M. Cacciari and M. Greco, Phys. Rev. Lett. 73, 1586 (1994); D.P. Roy and K. Sridhar, CERN-TH.7329/94 (hep-ph 9406386)

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[9]

W.E. Caswell and G.P. Lepage, Phys. Lett. 167B, 437 (1986)

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[10]

See, for example, G.A. Schuler, CERN preprint CERN-TH.7170/9 4 (hep-ph 9403387), and references therein. 8

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[11]

G.T. Bodwin, E. Braaten, T.C. Yuan, and G.P. Lepage, Phys. Rev . D46, R3703 (1992)

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[13]

CLEO Collaboration report CLEO CONF 94-11, submitted to the I nt. Conf. on High Energy Physics, Glasgow, July 1994 (Ref. GLS0248)

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[14]

P. Cho and M. Wise, CALT-68-1962 (hep-ph 9411303)

View on Pith 1962
[15]

E. Braaten and S. Fleming (in progress). Figure Captions

View on Pith
[16]

CDF data for prompt ψ′ production compared with theoretical calculations of the total leading order contributions (dotted curves), the total co lor-singlet fragmentation contributions (dashed curves), and the color-octet fragmenta tion contribution (solid curves). The normalization of the color-octet fragmentation con tribution has been adjusted to ﬁt the...

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Papers citing it · 34 sentences without a confident label

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Although the idea that a $c c̅$ meson could be produced predominantly through the $^3S_1^[8]$ channel is not new [ref] , it is now well known that the old idea of $^3S_1^[8]$ dominance for $J/ψ$ and $ψ(2S)$ production fails to describe large-$p_T$ hadroproduction data, especially for polarized cross sections, and it is likely that the mechanism for production of conventional charmonium is much more involved [ref] .

Hadroproduction data support tetraquark hypothesis for $\chi_{c1} (3872)$ · Conclusions · contest 0.73

Cites it as background 13 papers

According to the proposal [ref] , the prompt spin-triplet $S$-wave charmonia are dominantly produced from the color-octet spin-triplet $S$-wave charm-anticharm pairs $[cc̅_8(^3S_1)]$ that are fragmented from the gluons at large $p_T$.

Polarization of prompt J/psi in proton-proton collisions at RHIC · Introduction · 0.81
The theoretical landscape was revolutionized by the nonrelativistic QCD (NRQCD) factorization framework [ref] , a development propelled by two key theoretical breakthroughs in the mid-1990s: the color-octet mechanism proposed by Braaten and Fleming to resolve the $ψ'$ surplus puzzle observed at the Tevatron [ref] , and the prediction by Cho and Wise of nearly 100% transverse polarization for $J/ψ$ at large $p_T$ [ref] .

Next-to-next-to-leading-order QCD corrections to ${}^3S_1^{(8)}$ gluon fragmentation function for quarkonium · Introduction · 0.99
To solve the large discrepancy between data and theoretical predictions, the color-octet(CO) mechanism [ref] was proposed based on nonrelativistic QCD (NRQCD) factorization [ref] .

J/psi (psi') production at the Tevatron and LHC at O(\alpha_s^4v^4) in nonrelativistic QCD · Introduction · 0.92

Discussion

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P. Cho, S. Trivedi and M. Wise, CALT-68-1943 (hep-ph 9408352 ); F.E. Close, RAL-94- 093 (hep-ph 9409203); D.P. Roy and K. Sridhar, CERN-TH.7434/94 (hep-ph 9409232); P. Cho and M. Wise, CALT-68-1954 (hep-ph 9410214)

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G.T. Bodwin, E. Braaten, and G.P. Lepage, Argonne preprint ANL -HEP-PR-94-24 (hep-ph 9407339)

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E. Braaten and T.C. Yuan, Phys. Rev. D50, 3176 (1994)

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V. Papadimitriou, CDF Coll., presented at the “Rencontres de la Va llee d’Aoste”, La Thuile, March 1994

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T. Daniels, CDF Coll., Fermilab-Conf-94/136-E

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R. Baier and R. R¨ uckl, Z. Phys. C19 251 (1983); F. Halzen, F. Herzog, E.W.N. Glover, and A.D. Martin, Phys. Rev. D30, 700 (1984); E.W.N. Glover, A.D. Martin, W.J. Stirling, Z. Phys. C38, 473 (1988); B. van Eijk and R. Kinnunen, Z. Phys. C41, 489 (1988)

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E. Braaten and T.C. Yuan, Phys. Rev. Lett. 71, 1673 (1993)

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E. Braaten, M.A. Doncheski, S. Fleming, and M. Mangano, Phys. L ett. B333, 548 (1994)

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M. Cacciari and M. Greco, Phys. Rev. Lett. 73, 1586 (1994); D.P. Roy and K. Sridhar, CERN-TH.7329/94 (hep-ph 9406386)

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See, for example, G.A. Schuler, CERN preprint CERN-TH.7170/9 4 (hep-ph 9403387), and references therein. 8

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G.T. Bodwin, E. Braaten, T.C. Yuan, and G.P. Lepage, Phys. Rev . D46, R3703 (1992)

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CLEO Collaboration report CLEO CONF 94-11, submitted to the I nt. Conf. on High Energy Physics, Glasgow, July 1994 (Ref. GLS0248)

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P. Cho and M. Wise, CALT-68-1962 (hep-ph 9411303)

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E. Braaten and S. Fleming (in progress). Figure Captions

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CDF data for prompt ψ′ production compared with theoretical calculations of the total leading order contributions (dotted curves), the total co lor-singlet fragmentation contributions (dashed curves), and the color-octet fragmenta tion contribution (solid curves). The normalization of the color-octet fragmentation con tribution has been adjusted to ﬁt the...

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