Gluon Fragmentation into Heavy Quarkonium

Eric Braaten; Tzu Chiang Yuan

REVIEW

Gluon Fragmentation into Heavy Quarkonium

Eric Braaten, Tzu Chiang Yuan

High Energy Physics - Phenomenology · Submitted 2 Mar 1993 · 9 references

Pith's verdict: The founding fragmentation paper: the η_c derivation is clean and checkable, the ψ result is quoted without intermediate steps, and the erratum note in the revised version is not itemized.

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arXiv IDhep-ph/9303205 (version 1)

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CitationEric Braaten, Tzu Chiang Yuan. "Gluon Fragmentation into Heavy Quarkonium." arXiv:hep-ph/9303205 (1993). https://pith.science/paper/2FOYCPC3

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Editor's note

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This is the paper that made fragmentation the default story for quarkonium at high p_T, and it earns that place. The physics argument is simple and right: the fragmentation contribution is down by a power of α_s but up by (E/m_Q)^2, so it wins at high energy. What's genuinely new here is the leading-order fragmentation function for g → η_c in closed form (Eq. 8), derived end to end from the g* → η_c g amplitude in Eqs. (5)–(7), plus the g → ψ function in Eqs. (9)–(15), plus the observation that Altarelli–Parisi evolution sums the log(μ/m_Q) and visibly hardens the z-distribution. The η_c chain is the part I'd actually check, and it checks: amplitude, spin/color sum, phase space, closed form. The aside on Z → ψ c c̄ being two orders of magnitude above Z → ψ gg because of the (M_Z/M_ψ)^2 enhancement is a nice piece of physical reasoning, and the note that Hagiwara–Martin–Stirling were missing a 1/(16π^2) is the kind of correction that saves other people time. The crossover estimates (p_T ≈ 3M_ηc, 2M_ψ) are crude but the paper presents them as estimates, which is honest. Two soft spots. First, the ψ function is dropped in as a final result — 'rather involved, we present only the final result' — so Eqs. (9)–(15) are unverifiable as printed; the amplitude is adapted from the published e+e- → ψ gg work of Ref. [4], which is fine as a source, but the adaptation itself is not shown. Second, the revised version thanks Mangano for pointing out an error in an earlier version without saying what the error was or which results it touched. That is a real gap for anyone building on these numbers. On the stress-test's main worry: the color-singlet R(0) normalization does set every quoted probability, and relativistic corrections are acknowledged but not estimated, so the numbers carry unquantified normalization uncertainty. But the framework claim — that fragmentation is perturbatively computable and dominates asymptotically — does not depend on the value of R(0) at all; it's a scaling argument. So I'd call that a bound on the numbers, not on the thesis. Worth a serious referee, and worth reading if you work on quarkonium production or on parton fragmentation more generally.

Referee report

Significance

If correct, this is an important and durable result: it identifies a production mechanism that grows as (E/m_Q)^2 relative to the short-distance processes that had dominated previous calculations, and it makes that mechanism quantitatively calculable rather than merely kinematic. Several features deserve explicit credit. The eta_c result is a genuine closed form, and it passes an internal consistency check that the manuscript does not spell out but that a reader can perform: the z-integral of the bracket in Eq. (8) is exactly 1/3, so the stated probability 4.6e-5 follows analytically from the quoted inputs alpha_s(2m_c)=0.26 and |R(0)|^2=(0.8 GeV)^3 with M_eta_c=2.98 GeV. The psi integrand is given in full (Eqs. (10)-(15)), so the result is reproducible in principle even though the derivation is omitted. The prediction that fragmentation dominates above p_T of order a few times the quarkonium mass is falsifiable and was subsequently testable at the Tevatron. The correction noted to the fragmentation probability of Ref. [7] (a missing 1/(16 pi^2)) is a useful service to the literature. The framework, not the specific numbers, is the lasting contribution, and the framework is soundly

Major objections (3)

[Crossover estimate, paragraph beginning 'In hadron colliders, short distance processes dominate...'] The crossover estimate is not scale-consistent. The short-distance cross sections d sigma/dt for gg -> g eta_c and gg -> g psi are evaluated at the hard scale of order p_T, but the fragmentation probability multiplying them is the initial one at mu = 2m_c, i.e. alpha_s^2 |R(0)|^2/(9 pi M^3). The manuscript's own Figs. 3 and 4 show that evolution from 2m_c to 20m_c changes the fragmentation function substantially, and the appropriate factorization scale for a gluon of energy of order p_T is of order p_T, not 2m_c. Since the quoted crossover points p_T ~ 3 M_eta_c and p_T ~ 2 M_psi, and the summary claim that fragmentation dominates below 10 GeV, rest directly on this comparison, the authors should repeat the estimate using D(z,mu) evolved to mu of order p_T and state how much the crossover point moves. If the shift is small the claim is strengthened; if it is large the 'less than 10 GeV' statement should be qualified.
[Acknowledgments (revision note)] The revised version states 'We thank M.L. Mangano for pointing out an error in an earlier version of this paper' but does not say what the error was or which results it affected. Because Eqs. (8) and (9) and the probabilities 4.6e-5, 2.8e-6 and 5.3e-7 are quoted and used downstream, a reader cannot tell whether the eta_c closed form, the psi double integral, the numerical probabilities, or only the comparison with Ref. [7] changed. A single sentence identifying the corrected expression or number would remove the ambiguity and protect the users of these results.
[Eq. (9) and Eqs. (10)-(15)] The psi fragmentation function is presented as a final result with no derivation and, unlike the eta_c case, no independent check. The full integrand is given, which mitigates the concern, but the reader has no way to confirm that the double integral in Eq. (9) has been implemented correctly, and the number 2.8e-6 together with the p_T ~ 2 M_psi crossover and the Z^0 -> psi c cbar discussion all rest on it. At least one limiting-behavior check should be supplied, for example the z -> 1 endpoint behavior or the small-r limit of the integrand, or a statement that the numerical integration reproduces a known result in some kinematic limit. Given that this is a Letter, a short verification paragraph rather than a full derivation would suffice.

Minor objections (7)

[Eq. (5) and crossover paragraph] The symbol s is used for the invariant mass squared q^2 of the fragmenting gluon in Eqs. (5)-(7) and again for the Mandelstam variable s = 4 p_T^2 in the crossover discussion. The two uses are far apart in the text but the clash is avoidable; a different symbol for the virtual-gluon invariant mass would help.
[Eq. (8) and following text] The numerical inputs are given for alpha_s(2m_c) and |R(0)|^2 but not for m_c itself, although the value of m_c enters the phase-space endpoint and the relation 2m_c = M_eta_c used in the denominator. Please state the numerical quark masses used for the charmonium and bottomonium cases.
[Abstract and title] The abstract and title refer to 'S-wave quarkonium states', but only the 1S states eta_c, J/psi and Upsilon are computed; the 2S states are not treated. Either restrict the wording to 1S or state explicitly that the 2S states are left for future work.
[Figs. 3 and 4] The figures show only the shape of D(z,mu) at mu = 2m_c and 20m_c. Since the text emphasizes that evolution can significantly increase the production rate at small z, it would be useful to quote the integrated fragmentation probabilities at mu = 20m_c alongside the initial values, so the size of the evolution effect is stated numerically rather than left to the reader's eye.
[Eq. (3) and Eq. (4)] The text states that only the g -> g splitting function is needed at leading order. It would be worth one sentence justifying the neglect of the quark feed-in to the gluon evolution, namely that D_q is generated only at higher order in alpha_s so its contribution to D_g is suppressed relative to the boundary term.
[Paragraph on Ref. [7]] The statement that the fragmentation probability of Hagiwara, Martin and Stirling is missing a factor 1/(16 pi^2) is a useful correction. It would be helpful to state the corrected numerical value of their probability explicitly so that the comparison is unambiguous.
[Paragraph on the Upsilon] The claim that Eq. (9) applies to the 3S1 bottomonium state with M_psi -> M_Upsilon, 2m_c -> 2m_b and the appropriate R(0) deserves a brief justification, since the r = 4m_Q^2/s integration range and hence the numerical result change between the charm and bottom cases.

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The paper

The paper claims

Gluon fragmentation into S-wave heavy quarkonium is computed to leading order in QCD, yielding explicit fragmentation functions for the eta_c and J/psi that are then evolved with Altarelli-Parisi equations.

The reading

When a proton collider produces a J/psi or an eta_c at very high transverse momentum, the usual picture is that the charm quark and antiquark are created directly in the hard collision. This paper argues that at high enough energy a different route dominates. A fast gluon is produced first, and that gluon then splits into the quarkonium state plus one or more ordinary partons. Because the splitting happens over a long time and a long distance (of order the inverse heavy-quark mass), the rate is enhanced by a factor of roughly (energy/mass)^2 relative to the direct process, which more than compensates for the extra power of the strong coupling it costs. The authors compute the probability distribution, called a fragmentation function, for a gluon to split into an eta_c and into a J/psi, working to leading order in the strong coupling. The eta_c case reduces to a compact closed-form expression. The J/psi case is a double integral whose integrand they write out explicitly. They then use the standard Altarelli-Parisi evolution equations to run these functions from the mass scale up to collider scales, summing the large logarithms of the scale ratio. Finally they estimate the transverse momentum at which fragmentation overtakes direct production, and argue it is low enough to matter for existing measurements. The key external input is the wavefunction of the bound state at the origin, taken from the measured leptonic width of the J/psi.

Extended reading notes

Core claim

The fragmentation functions D(z, mu) describing a gluon splitting into a heavy quarkonium state can be computed in perturbative QCD, and at high energy this fragmentation mechanism dominates quarkonium production because it is enhanced by (E/m_Q)^2. Concretely, Eq. (8) gives D_{g to eta_c}(z, 2m_c) in closed form, and Eqs. (9)-(15) give D_{g to psi}(z, 2m_c) as an explicit double integral, with Altarelli-Parisi evolution summing the logarithms of mu/m_Q at larger scales.

Load-bearing premise

The whole calculation rests on the nonrelativistic color-singlet model: the quarkonium is treated as a collinear c-cbar pair in a definite color-singlet spin state, with production amplitude proportional to the wavefunction at the origin R(0), and all binding and relativistic effects absorbed into that single number. This enters at Eq. (5), where the amplitude is written with the standard quarkonium Feynman rules of Ref. [3], and again where |R(0)|^2 = (0.8 GeV)^3 is fixed from the psi electronic width. If color-octet or relativistic contributions are comparable for S-wave states, the numerical fragmentation probabilities and the crossover estimates shift.

Original abstract

The dominant production mechanism for heavy quark-antiquark bound states in very high energy processes is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions $D(z,\mu)$ describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into S-wave quarkonium states to leading order in the QCD coupling constant. The leading logarithms of $\mu/m_Q$, where $\mu$ is the factorization scale and $m_Q$ is the heavy quark mass, are summed up using Altarelli-Parisi evolution equations.

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

The dominant production mechanism for heavy quark-antiquark bound states in very high energy processes is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions $D(z,\mu)$ describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into S-wave quarkonium states to leading order in the QCD coupling constant. The leading logarithms of $\mu/m_Q$, where $\mu$ is the factorization scale and $m_Q$ is the heavy quark mass, are summed up using Altarelli-Parisi evolution equations.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The dominant production mechanism for heavy quark-antiquark bound states in very high energy processes is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons.	background 1.00	0.06	0.07	asserted 1.00
s1	We show that the fragmentation functions $D(z,\mu)$ describing these processes can be calculated using perturbative QCD.	contribution 0.66	0.86	0.38	asserted 1.00
s2	We calculate the fragmentation functions for a gluon to split into S-wave quarkonium states to leading order in the QCD coupling constant.	contribution 0.92	0.96	0.28	asserted 1.00
s3	The leading logarithms of $\mu/m_Q$, where $\mu$ is the factorization scale and $m_Q$ is the heavy quark mass, are summed up using Altarelli-Parisi evolution equations.	method 0.93	0.76	0.17	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

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References

Works cited (9)

[4]

J.H. K¨ uhn and H. Schneider, Phys. Rev. D24, 2996 (1981); Z. Phys. C11, 263 (1981)

View on Pith 1981
[5]

V. Barger, K. Cheung, and W.-Y. Keung, Phys. Rev. D41, 1541 (1990)

View on Pith 1990
[7]

K. Hagiwara, A.D. Martin, and W.J. Stirling, Phys. Lett. B267, 527 (1991) and erratum (to be published)

View on Pith 1991
[1]

See, for example, R. Baier and R. R¨ uckl, Z. Phys. C19, 251 (1983)

View on Pith 1983
[2]

R.D. Field, Applications of Perturbative QCD , (Addison Wesley, 1989)

View on Pith 1989
[3]

J.H. K¨ uhn, J. Kaplan, and E.G.O. Saﬁani, Nucl. Phys. B157, 125 (1979); B. Guberina, J.H. K¨ uhn, R.D. Peccei, and R. R¨ uckl,Nucl. Phys. B174, 317 (1980)

View on Pith 1979
[6]

E. Braaten, K. Cheung, and T.C. Yuan, Northwestern preprint NUHEP-TH-93-2 (February, 1993)

View on Pith 1993
[8]

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

View on Pith 1992
[9]

E. Braaten and T.C. Yuan (in preparation). Figure Captions

View on Pith

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How the literature uses it

38 arXiv papers cite this in 62 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 citing it · 44 sentences without a confident label

Contests it 1 paper

Thus, our method overcomes the well-known issue of NRQCD gluon FFs, which often fail to satisfy this condition [ref] .

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Builds on it 1 paper

The short-distance coefficients for gluon fragmentation in this channel have been computed in relative order $v^0$ [ref] and relative order $v^2$ [ref] .

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Uses its method or tool 2 papers

The production of the $Q$ pair and its subsequent recombination into an HVM state can be calculated in the nonrelativistic QCD (NRQCD) framework [ref] which is an expansion in $α_s$ and $v$, the relative velocity of the quark-antiquark pair.

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We have carried out the integrations in two ways: (1) using the change of variables that was proposed in Refs. [ref] and is described in Appendix B of Ref. [ref] and (2) using the change of variables that is given in Eq. [ref].

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Results presented in this manuscript rely on the ZCW19$^+$ vector-quarkonium collinear NLO FF set, built in [ref] on the basis of initial-scale NRQCD inputs for constituent heavy-quark [ref] and gluon [ref] channels.

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We find that our $d^O(z,2m_Q,μ_0)$ is compatible with the numerical result in Refs. [ref] , and $d^P(z,2m_Q,μ_0)$ is compatible with the numerical result in Ref. [ref] .

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For gluon fragmentation into a heavy quark pair, Eq. ([ref]) and Eq. ([ref]) confirm the results in Refs. [ref] and [ref] , respectively.

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Based on the nonrelativistic quantum chromodynamics (NRQCD) factorization approach [ref] , Braaten and Fleming explained the large cross section by introducing the color-octet gluon fragmentation mechanism, which is the NRQCD extension of the color-singlet version proposed in Ref. [ref] .

Polarization of prompt J/psi in proton-proton collisions at RHIC · Introduction · 0.81
The corresponding SDCs in Eq. [ref] up to $𝒪(α_s^2)$ have been well established [ref] (see Refs. [ref] for a summary).

Next-to-next-to-leading-order QCD corrections to ${}^3S_1^{(8)}$ gluon fragmentation function for quarkonium · Introduction · 0.87
Initial LO evaluations of the fragmentation input for gluon and constituent heavy-quark channels into $S$-wave vector quarkonia (in color-singlet states) date back to the early 1990s [ref] , while NLO refinements have only emerged in more recent years [ref] .

Fully Heavy Pentaquarks with JETHAD: A High-Energy Viewpoint · Essentials of heavy-flavor fragmentation · 0.91

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] [4]

J.H. K¨ uhn and H. Schneider, Phys. Rev. D24, 2996 (1981); Z. Phys. C11, 263 (1981)

View on Pith 1981

[2] [5]

V. Barger, K. Cheung, and W.-Y. Keung, Phys. Rev. D41, 1541 (1990)

View on Pith 1990

[3] [7]

K. Hagiwara, A.D. Martin, and W.J. Stirling, Phys. Lett. B267, 527 (1991) and erratum (to be published)

View on Pith 1991

[4] [1]

See, for example, R. Baier and R. R¨ uckl, Z. Phys. C19, 251 (1983)

View on Pith 1983

[5] [2]

R.D. Field, Applications of Perturbative QCD , (Addison Wesley, 1989)

View on Pith 1989

[6] [3]

J.H. K¨ uhn, J. Kaplan, and E.G.O. Saﬁani, Nucl. Phys. B157, 125 (1979); B. Guberina, J.H. K¨ uhn, R.D. Peccei, and R. R¨ uckl,Nucl. Phys. B174, 317 (1980)

View on Pith 1979

[7] [6]

E. Braaten, K. Cheung, and T.C. Yuan, Northwestern preprint NUHEP-TH-93-2 (February, 1993)

View on Pith 1993

[8] [8]

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

View on Pith 1992

[9] [9]

E. Braaten and T.C. Yuan (in preparation). Figure Captions

View on Pith