Diffractive Leptoproduction of Vector Mesons in QCD

A. H. Mueller; J. F. Gunion; L. Frankfurt; M. Strikman; Stanley J. Brodsky

REVIEW

Diffractive Leptoproduction of Vector Mesons in QCD

Stanley J. Brodsky, L. Frankfurt, J. F. Gunion, A. H. Mueller, M. Strikman

High Energy Physics - Phenomenology · Submitted 14 Feb 1994 · 26 references

Pith's verdict: The paper that made exclusive vector meson leptoproduction a pQCD calculation; the structural claims (Q⁻⁶, longitudinal dominance, A-dependence ∝ [xG_A]²) have held up, and the soft spots are all in the normalization, which the authors flag themselves.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 9 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/9402283 (version 2)

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

CitationA. H. Mueller, J. F. Gunion, L. Frankfurt, M. Strikman, Stanley J. Brodsky. "Diffractive Leptoproduction of Vector Mesons in QCD." arXiv:hep-ph/9402283 (1994). https://pith.science/paper/QPQXANRI

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Bottom line: this is the paper that turned diffractive vector meson leptoproduction into a perturbative QCD calculation, and the structural results have survived thirty years of HERA and fixed-target data. Read it for the factorization argument and the A-dependence, not for the numbers in Section 2.5, which the authors themselves tell you not to trust too far. What is genuinely new here relative to Donnachie-Landshoff and Ryskin is the use of the relativistic light-cone distribution amplitude for light mesons rather than a non-relativistic or constituent-quark vertex. That buys three things: the inverse moment η_V as the single non-perturbative number controlling the leading-twist amplitude, the prediction that longitudinal photon and longitudinal meson dominate with a 1/Q⁶ falloff, and the identification of the nuclear cross section ratio with the square of the nuclear gluon density (Eq. 2.38). The derivation is clean, the double-log approximations are stated up front in the introduction and again in Section 2.2, and the factor-of-4 disagreement with Ryskin in the non-relativistic limit is stated openly rather than buried. That is how you write a paper like this. The soft spots are real but they are all in the normalization. The step from Eq. 2.15 to 2.16 fixes the ℓ-integral by matching to the known F_L–gluon relation rather than deriving it; the authors say so in as many words. The claim that relaxing the restriction (2.19) gives only small corrections rests on an impact-parameter expansion where ℓ⊥b⊥ is order one for the dominant configurations, so the quoted ~10% is a heuristic, not a bound — but again, normalization only, and the authors already concede that normalizations may not be reliable. The one place the paper is more assertive than its evidence is the Q⁻⁸ transverse prediction, which is argued by analogy with the photon case rather than derived; the reader is right to flag that as the unacknowledged soft spot. The NMC comparison is honest but loose: η_V = 3 versus 5 alone spans a factor of ~3 in cross section, and the scale ambiguity in α_s xG adds more. 'Consistent' is fair; 'agreement' would be overstating it. This is for anyone doing dipole models, exclusive production at HERA or EIC, or nuclear gluon shadowing — it is the reference you cite for the two-gluon exchange formula. Yes, send it to referees.

Referee report

Significance

If the factorization holds, this is a foundational result: it extends the domain of perturbative QCD to exclusive diffractive processes at small x and large Q², and it supplies a set of falsifiable, parameter-free structural predictions — the Q⁻⁶ scaling of σ_L, the dominance of longitudinal polarization for both the virtual photon and the vector meson, the Q⁻⁸ fall-off of σ_T, the universality of the t-dependence, and the A-dependence proportional to the square of the nuclear gluon distribution. The only inputs are the measured leptonic decay constant f_V, the inverse moment η_V of the distribution amplitude, and the gluon density from global fits; the flavor charge e_f cancels between the amplitude and f_V, which is a genuine and non-trivial simplification. The paper is also commendably explicit about its approximations: the introduction and §2.2 state that the calculation is leading-logarithmic, even leading-double-logarithmic, and that the normalizations may not be completely reliable. The prediction that the A-dependence of forward diffractive leptoproduction equals that of F_L and of the squared gluon structure function is a concrete, testable statement that has since becomea

Major objections (3)

[§2.5, numerical comparison with NMC data] The numerical comparison with the NMC and E-665 data is performed at x ≈ 0.06 and Q² = 10 GeV², but Eq. (2.33) was derived in the leading ln(1/x) approximation, and ln(1/0.06) ≈ 2.8 is not large. The quoted agreement, dσ_L/dt ≈ (13–47) nb/GeV² versus the empirical (14–27) nb/GeV², should therefore be presented as an order-of-magnitude consistency check rather than as a test of the leading-logarithmic formula, and the authors should state at what values of x and Q² they expect the approximation to be under control. As written, the sentence 'which is close to the empirical diffractive ρ leptoproduction cross section' overstates what the comparison at this kinematics can establish.
[§2.5, comparison with Ryskin [4]] The paper states that its J/ψ prediction is a factor of 4 below that of Ref. [4] when both use the same nonrelativistic δ(z−1/2) approximation, but it does not identify where the factor arises. Since the two calculations share the same wavefunction ansatz and the same two-gluon mechanism, the discrepancy should be traceable to a specific ingredient — the color factor N_c², the value η_ψ ≈ 2, or the normalization of Eq. (2.16). A short paragraph isolating the origin would materially strengthen confidence in the absolute normalization, which is otherwise the weakest quantitative element of the paper.
[§2.2, paragraph following Eq. (2.19)] The authors acknowledge that the derivation requires ℓ_⊥²/Q² ≪ 1 and then integrate ℓ_⊥² up to Q², and they argue that the resulting corrections are 'numerically small' via an impact-parameter expansion in ℓ_⊥·b_⊥. For the dominant configurations, ℓ_⊥ ~ Q and b_⊥ ~ 1/Q, so the expansion parameter is O(1) rather than small, and the estimate that the fourth-order term carries a factor 1/4! is not a controlled parametric suppression. Because the numerical comparison in §2.5 depends on this step, the authors should either quantify the correction (for example by evaluating the exact impact-parameter expression numerically) or state explicitly that the normalization carries an O(1) uncertainty from relaxing Eq. (2.19). The leading-power Q⁻⁶ scaling and the A-dependence are unaffected, so this is a normalization issue rather than a structural one.

Minor objections (9)

[§2.6] The phrase 'transversely polarized svector mesons' contains a typographical error and should read 'transversely polarized vector mesons'.
[Eq. (2.12)] The right-hand side of Eq. (2.12) begins with a stray multiplication sign before the factor 16π³; please check the typesetting of this equation.
[§2.5, Eq. (2.35) and following sentence] Eq. (2.35) contains only the ratio Γ_V m_V η_V² and no e_f² factors, yet the text writes 'R(φ,ρ) ∼ 1.0 × e_f²(φ)/e_f²(ρ)'. The e_f² factors are a naive expectation being factored out, not part of the prediction, and the wording should make this explicit so that readers do not look for e_f in Eq. (2.35).
[§2.5, unnumbered equation after Eq. (2.34)] The real-part formula involving (1 + i π/2 d/d ln x) xG is displayed without a number and without derivation; it should be numbered and the origin of the π/2 d/d ln x prescription briefly justified or referenced.
[§2.6] The assertion that the q q̄ component of a transversely polarized vector meson decreases at least as fast as z or (1−z) at the endpoints is stated without derivation. Since this endpoint behavior underlies the Q⁻⁸ prediction for σ_T, a reference or a one-line argument would help the reader assess it.
[§2.7, Eq. (2.38)] The equality between the diffractive cross section ratio and [F_LA/F_LN]² holds at leading order, where F_L ∝ α_s xG; the text should say so explicitly, since at higher orders the identification of F_L with xG is modified and the equality becomes approximate.
[§2.3, Eq. (2.29)] The factor 1/2 in the definition of η_V should be explained; it follows from the longitudinal ψ_V normalization together with the z(1−z) weight, and a parenthetical remark would save the reader a reconstruction.
[§2.2, Eq. (2.16)] The color factor T_R/N_c and the sentence about averaging over color and matching anti-color deserve a brief clarification, since the N_c² in the denominator of Eq. (2.33) follows directly from this step and readers will want to check it.
[§2.5] The theoretical range (13–47) nb/GeV² overlaps the empirical range (14–27) nb/GeV² only at its lower edge, and the η = 5 case (36–47) lies a factor of about two above the data. The text should be more precise about which distribution-amplitude choice is being tested and which is disfavored.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The forward cross section for diffractive leptoproduction of a vector meson can be computed in perturbative QCD, fixed by the meson's light-cone wave function and the target's gluon density.

The reading

The paper argues that the forward differential cross section for a virtual photon to diffractively produce a vector meson off a nucleon or nucleus is a legitimate perturbative QCD calculation, not merely a model. The amplitude factorizes into three pieces: the photon splitting into a quark-antiquark pair, that pair scattering almost instantaneously off the target through two-gluon exchange, and the pair recombining into the meson. Carrying this through gives $dσ/dt|_{t=0} = 8π^4 f_V^2 α_{EM} α_s^2(Q) η_V^2 [xG(x,Q)]^2 / (Q^6 N_c^2)$ for a longitudinal photon producing a longitudinal meson, with the transverse channel suppressed by two further powers of $Q$. Because the same two-gluon object appears for a nuclear target, the atomic-number dependence of the cross section becomes the square of the nuclear gluon density, turning a leptoproduction measurement into a probe of gluon shadowing and of color transparency.

What carries the argument

The load-bearing device is the three-factor factorization of Eq. (2.8), combined with the step in Eq. (2.16) that replaces the integral over the two-gluon exchange amplitude, weighted by $ℓ_⊥^2$, with $i 4π^2 T_R α_s (s+Q^2) xG(x,Q^2) / N_c$. That identification is what converts a Feynman-diagram calculation into a formula written in terms of a measured gluon density. The meson enters only through the distribution amplitude $φ_V(Q,z) = ∫ d^2k_⊥ ψ_V(k_⊥,z)/16π^3$ and its inverse moment $η_V ≡ 12 ∫ dz φ_V(z)/[z(1-z)] / ∫ dz φ_V(z)$, normalized to $f_V$ through the decay-constant relation derived in the Appendix. The whole result holds in the leading $ℓn(1/x)$ and leading $ℓn(Q^2/Λ_{QCD}^2)$ approximation, which is what allows a single scale $Q^2$ and a single $x$ to appear in $G$; the authors note that a single-logarithmic treatment in terms of an unintegrated gluon distribution is possible but would not yield so simple a formula.

Extended reading notes

Core claim

The central claim is that diffractive leptoproduction of vector mesons at small $x$, large $Q^2$, and small momentum transfer is controlled by a factorization theorem in perturbative QCD: the amplitude is a convolution of the photon's perturbative splitting amplitude, the on-shell scattering amplitude of the quark-antiquark pair off the target, and the non-perturbative distribution amplitude $φ_V(z,Q)$ of the outgoing meson. The scattering is two-gluon exchange, and the integral over the exchanged gluon is identified with the ordinary gluon distribution $xG(x,Q)$ evaluated at $x = Q^2/s$ and scale $Q^2$. Three consequences follow on the authors' terms. Longitudinal photons producing longitudinally polarized mesons dominate at large $Q^2$, with $σ_L$ falling as $Q^{-6}$, while transverse production falls at least as $Q^{-8}$ because it is fed by end-point configurations where the quark carries nearly all the momentum. The overall normalization is fixed by the meson's leptonic decay constant $f_V$ and by $η_V$, the inverse moment of the distribution amplitude, taken as 3 for the asymptotic form and about 3.3 to 3.5 for the form suggested by QCD sum rules; at $Q^2 = 10$ GeV$^2$ this gives 13 to 47 nb GeV$^{-2}$ against an empirical 14 to 27 nb GeV$^{-2}$ extracted from fixed-target data. And for a nuclear target the forward cross section scales as the square of the nuclear gluon distribution, $A^{2α_g}$, so its measured $A$-dependence tests color transparency and constrains gluon shadowing without any final-state absorption correction.

Load-bearing premise

The derivation assumes the quark-antiquark pair scatters off the target in a time much shorter than both the photon splitting time and the meson formation time, which is what lets the pair be treated as on-shell during the collision and lets the gluon-exchange integral collapse to an ordinary gluon density at a single scale.

Editorial extensions

If this is right

The longitudinal-to-transverse ratio $σ_L/σ_T$ should rise with $Q^2$, since $σ_L ∝ Q^{-6}$ while transverse production is suppressed by at least $Q^{-8}$; the measured polarization of the produced meson therefore tests the picture directly.
The $t$-dependence is universal across meson species, set by a two-gluon form factor of the target rather than by the meson, so the diffractive slope should be similar for $ρ$, $φ$, $J/ψ$, and $Υ$ at large $Q^2$.
Ratios of vector-meson yields at $Q^2 ≫ m_V^2$ reduce to ratios of $Γ_V m_V η_V^2$, so $φ/ρ$ and $J/ψ/ρ$ comparisons become measurements of distribution amplitudes and of SU(3) flavor breaking.
Coherent forward production on nuclei should scale as the square of the nuclear gluon density, providing a clean color-transparency test and a constraint on gluon shadowing that is independent of final-state absorption.
Because the cross section goes as the square of a steeply rising gluon density, it should rise strongly with energy at small $x$; the authors estimate up to a factor of about 100 between fixed-target and collider energies at $Q^2 \sim 10$ GeV$^2$, which would also distort the apparent $Q^2$ dependence.

Reading between the lines

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

If the $Q^{-6}$ longitudinal law and the two-gluon form factor are right, the same object should control exclusive diffractive dijet and two-photon channels, so cross-channel ratios could test the universality of the two-gluon form factor without relying on absolute normalization.
The sensitivity to $η_V$ makes leptoproduction an indirect measurement of meson distribution amplitudes; a lattice or sum-rule determination of $η_V$ that disagreed with the value needed to fit the data would be a sharper signal than the normalization comparison itself.
Since the nuclear prediction is a ratio of gluon densities squared, comparing it on the same target, at the same $x$ and $Q^2$, with the nuclear longitudinal structure function $F_L^A$ would test whether one gluon density enters both — a stronger statement than either measurement alone.
The authors' own caveat that a leading-double-logarithmic normalization may not be fully reliable suggests the $Q^2$ scaling and the $A$-dependence are the durable predictions, while the absolute rate is the piece most likely to shift under a single-logarithmic treatment using an unintegrated gluon distribution.

Original abstract

We demonstrate that the distinctive features of the forward differential cross section of diffractive leptoproduction of a vector meson can be legitimately calculated in perturbative QCD in terms of the light-cone $q \bar q$ wave function of the vector meson and the gluon distribution of the target. In particular, we calculate the $Q^2$ and nuclear dependence of the diffractive leptoproduction of vector mesons and estimate the cross section. The production of longitudinally polarized vector mesons by longitudinally polarized virtual photons is predicted to be the dominant component, yielding a cross section behaving as $Q^{-6}$. The nuclear dependence of the diffractive cross sections, which follows from a factorization theorem in perturbative QCD, provides important tests of color transparency as well as constraints on the shadowing of the gluon structure functions and the longitudinal structure functions of nuclei.

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, 3,816 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.59 · compares with prior results 0.07 · 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.

We demonstrate that the distinctive features of the forward differential cross section of diffractive leptoproduction of a vector meson can be legitimately calculated in perturbative QCD in terms of the light-cone $q \bar q$ wave function of the vector meson and the gluon distribution of the target. In particular, we calculate the $Q^2$ and nuclear dependence of the diffractive leptoproduction of vector mesons and estimate the cross section. The production of longitudinally polarized vector mesons by longitudinally polarized virtual photons is predicted to be the dominant component, yielding a cross section behaving as $Q^{-6}$. The nuclear dependence of the diffractive cross sections, which follows from a factorization theorem in perturbative QCD, provides important tests of color transparency as well as constraints on the shadowing of the gluon structure functions and the longitudinal structure functions of nuclei.

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	We demonstrate that the distinctive features of the forward differential cross section of diffractive leptoproduction of a vector meson can be legitimately calculated in perturbative QCD in terms of the light-cone $q \bar q$ wave function of the vector meson and the gluon distribution of the target.	contribution 0.87	0.92	0.79	asserted 1.00
s1	In particular, we calculate the $Q^2$ and nuclear dependence of the diffractive leptoproduction of vector mesons and estimate the cross section.	contribution 0.94	0.95	0.12	asserted 0.99
s2	The production of longitudinally polarized vector mesons by longitudinally polarized virtual photons is predicted to be the dominant component, yielding a cross section behaving as $Q^{-6}$.	result 1.00	0.77	0.21	asserted 0.83
s3	The nuclear dependence of the diffractive cross sections, which follows from a factorization theorem in perturbative QCD, provides important tests of color transparency as well as constraints on the shadowing of the gluon structure functions and the longitudinal structure functions of nuclei.	interpretation 0.99	0.33	0.16	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.88.

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

References

Works cited (26)

[4]

M. G. Ryskin, Z. Phys. C57, 89–92 (1993)

View on Pith 1993
[1]

V. N. Gribov, B. L. Ioﬀe, and I. Ya. Pomeranchuk, Yad. Fiz., 2, 768 (1965); B. L. Ioﬀe, Phys. Lett. 30 123 (1968)

View on Pith 1965
[2]

A. Donnachie and P. Landshoﬀ, Phys. Lett. 185B, 403 (1987); Nucl. Phys. B311, 509 (1989)

View on Pith 1987
[3]

J. R. Cudell, Nucl. Phys. B336, 1 (1990)

View on Pith 1990
[5]

S. J. Brodsky and G. P. Lepage, Phys. Rev. D22, 2157 (1980)

View on Pith 1980
[6]

B. Z. Kopeliovich, J. Nemchick, N. N. Nikolaev, and B. G. Zakharov , KF A- IKP-TH-1993-27, (1993)

View on Pith 1993
[7]

B. Bl¨ attel, G. Baym, L. L. Frankfurt, and M. Strikman, Phys. R ev. Lett. 71, 896 (1993)

View on Pith 1993
[8]

L. Frankfurt, G. A. Miller, and M. Strikman, Phys. Lett. 304B, 1 (1993)

View on Pith 1993
[9]

S. Catani, M. Ciafaloni, and F. Hautmann, Phys. Lett. B307, 147–153 (1993)

View on Pith 1993
[10]

J. D. Bjorken in Proceedings of the International Symposium on Electron and Photon Interactions at High Energies , p. 281–297, Cornell (1971); J. D. Bjorken and J. B. Kogut, Phys. Rev. D8, 1341 (1973)

View on Pith 1971
[11]

L. Frankfurt and M. Strikman, Phys. Rept. 160, 235 (1988)

View on Pith 1988
[12]

V. L. Chernyak and A. R. Zhitnitski, Phys. Rep. 112, 173 (1984)

View on Pith 1984
[13]

EMC, J. J. Aubert et al., Phys. Lett. 161B, 203 (1985); J. Ashman et al., Z. Phys. C39, 169 (1988)

View on Pith 1985
[14]

NMC, P. Amaudruz et al., Z. Phys. C54, 239 (1992). 32

View on Pith 1992
[15]

NMC Collaboration, A. Sandacz, Exclusive ρ0 Muoproduction at Large Q2, paper contributed to the poster session at the Few Body XIV Conference , Amsterdam, 1993

View on Pith 1993
[16]

Guang Yin Fang, et al., FERMILAB-CONF-93-305, October 1993

View on Pith 1993
[17]

A. D. Martin, W. J. Stirling, and R. G. Roberts, Phys. Lett. B306, 145 (1993)

View on Pith 1993
[18]

S. J. Brodsky and A. H. Mueller, Phys. Lett. 206B, 685 (1988)

View on Pith 1988
[19]

D. R. Yennie, Rev. Mod. Phys. 47, 311 (1975). T. H. Bauer et al. , Rev. Mod. Phys. 50, 261 (1978)

View on Pith 1975
[20]

H. Cheng and T. T. Wu, Phys. Rev. 183, 1324 (1969)

View on Pith 1969
[21]

J. Bjorken, J. Kogut, and D. Soper, Phys. Rev. D3, 1382 (1971)

View on Pith 1971
[22]

L. Frankfurt, M. Strikman, and S. Liuti, Phys. Rev. Lett. 65, 1725 (1990); Proceeding of PANIC 93 (in press)

View on Pith 1990
[23]

Harry L. Melanson, et al. , FERMILAB-CONF-93-165-E, Presented at the 28th Rencontres de Moriond: QCD and High Energy Hadronic Int eractions, Les Arcs, France, 20–27 March 1993

View on Pith 1993
[24]

I. F. Ginzburg and D. Yu. Ivanov, Nucl. Phys. B388, 376 (1992), and references therein. 33 FIGURE CAPTIONS

View on Pith 1992
[25]

A typical two-gluon exchange contribution to the amplitude for γ∗(q)p → V (q + ∆)(p − ∆)

View on Pith
[26]

Light-cone perturbation theory graphs for the scattering of a quark-antiquark pair by a colorless target. 34 This figure "fig1-1.png" is available in "png" format from: http://arxiv.org/ps/hep-ph/9402283v2 This figure "fig1-2.png" is available in "png" format from: http://arxiv.org/ps/hep-ph/9402283v2

View on Pith Pith review arXiv

Forward citations

Cited by 20 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Gluon Unpolarized, Polarized, and Transversity GPDs from Lattice QCD: Lorentz-Covariant Parametrization (Part I)
hep-lat 2024-12 conditional novelty 7.0 of 10

A Lorentz-covariant tensor basis and projection set is constructed that isolates all eight leading-twist gluon GPDs from lattice QCD matrix elements for spin-0 and spin-1/2 hadrons.
Relativistic corrections to exclusive photoproduction of Quarkonia near-threshold
hep-ph 2025-06 conditional novelty 6.0 of 10

The leading relativistic correction to near-threshold photoproduction of J/psi and Upsilon is derived; for J/psi it is so large that the standard moment-expansion analysis of the proton's gluon gravitational form fact...
QCD Analysis of Near-Threshold Photon-Proton Production of Heavy Quarkonium
hep-ph 2021-03 conditional novelty 6.0 of 10

At threshold the heavy-quarkonium photoproduction amplitude reduces to the gluon energy-momentum-tensor matrix element, so J/psi data can be used to extract the proton's gluonic gravitational form factors.
Relativistic corrections to the vector meson light front wave function
hep-ph 2020-06 conditional novelty 6.0 of 10

A J/psi light-front wave function constrained by NRQCD decay matrix elements, including the first velocity correction, reproduces the measured Q-squared dependence of exclusive J/psi production better than the fully n...
Gluon Tomography from Deeply Virtual Compton Scattering at Small-x
hep-ph 2017-03 conditional novelty 6.0 of 10

In the small-x dipole framework, the DVCS cos 2phi azimuthal correlation is generated by the elliptic gluon Wigner distribution and reduces, in the collinear limit, to the helicity-flip gluon GPD contribution.

Show 15 more citing papers

Paving the Way Towards Precision Physics in Saturation Studies Through Exclusive Diffractive Light Neutral Vector Meson Production
hep-ph 2016-12 conditional novelty 6.0 of 10

The first next-to-leading-order impact factor for the photon-to-vector-meson (rho, phi, omega) transition in the QCD shockwave approach is derived for arbitrary kinematics, with all divergences shown to cancel against...
Towards a fitting procedure for deeply virtual Compton scattering at next-to-leading order and beyond
hep-ph 2007-03 conditional novelty 6.0 of 10

A Mellin-Barnes plus conformal-partial-wave formalism reproduces DVCS Compton form factors to NNLO in a conformal scheme and yields a joint DVCS/DIS fit with chi-squared per point near 0.8, at the cost of dropping ske...
Diffractive Vector-Meson Production from the Light-Front Quark Model
hep-ph 2026-09 conditional novelty 5.0 of 10

In the color-dipole picture with light-front quark-model wave functions, the Melosh-Wigner spin structure (S-1) describes light-meson diffractive observables better, while the spin-improved structure (S-2) better desc...
Probing nuclear structure with the Balitsky-Kovchegov equation in full impact-parameter dependence
hep-ph 2025-09 unverdicted novelty 5.0 of 10

Extends the full impact-parameter Balitsky-Kovchegov equation to nuclei and supplies saturation-sensitive predictions for DIS and vector-meson production, including a tetrahedral oxygen model.
Momentum fraction and hard scale dependence of double parton scattering
hep-ph 2025-06 unverdicted novelty 5.0 of 10

Global fit of an x- and μ-dependent Gaussian model for transverse double parton distributions to LHC and Tevatron data extracts parameters for calculating effective cross sections in other observables.
Coherent J/psi photoproduction in ultra-peripheral PbPb collisions at sqrt(s[NN]) = 2.76 TeV with the CMS experiment
nucl-ex 2016-05 accept novelty 5.0 of 10

CMS measures coherent J/psi photoproduction in ultra-peripheral PbPb collisions at 2.76 TeV, finding a cross section about three standard deviations below the impulse approximation and consistent with nuclear gluon shadowing.
Elastic and Proton-Dissociative Photoproduction of J/psi Mesons at HERA
hep-ex 2013-04 accept novelty 5.0 of 10

H1 measures elastic and proton-dissociative J/psi photoproduction cross sections versus momentum transfer and photon-proton energy, finding the elastic cross section rises with energy (delta = 0.67) significantly fast...
Exclusive photoproduction of a heavy vector meson in QCD
hep-ph 2004-01 conditional novelty 5.0 of 10

The authors derive one-loop hard-scattering amplitudes for gamma p -> V p in collinear QCD factorization plus NRQCD, and find NLO corrections are large, stabilizing Upsilon but leaving J/psi outside theoretical control.
Proof of Factorization for Deeply Virtual Compton Scattering in QCD
hep-ph 1998-01 accept novelty 5.0 of 10

Factorization for deeply virtual Compton scattering holds to all orders in perturbative QCD, up to power-suppressed corrections, independent of the produced photon's virtuality.
Incoherent diffractive J/Psi-production in high energy nuclear DIS
hep-ph 2010-11 conditional novelty 4.0 of 10

Incoherent diffractive J/psi production in lepton-nucleus DIS is predicted to be strongly suppressed relative to A times the proton cross section, scaling as A^(1/3) in the black-disc limit, with the amount of suppres...
Probing Quantum Phenomena through Photoproduction in Relativistic Heavy-Ion Collisions
nucl-ex 2025-04 conditional novelty 3.0 of 10

A review of coherent vector meson photoproduction in ultra-peripheral heavy-ion collisions, centered on two-source interference and the claim that the observed spin patterns probe quantum entanglement analogies.
Overview of high-density QCD studies with the CMS experiment at the LHC
nucl-ex 2024-05 accept novelty 3.0 of 10

CMS synthesizes its 2010-2018 heavy-ion results into a single case that the quark-gluon plasma is a strongly coupled liquid, that jets and quarkonia are suppressed in it in ordered ways, and that collective behavior e...
Heavy quarks and jets as probes of the QGP
hep-ph 2022-03 accept novelty 2.0 of 10

A comprehensive review connecting jet, heavy-flavor, and quarkonium measurements at RHIC and the LHC to the theoretical descriptions of parton energy loss, diffusion, and quarkonium suppression in the quark-gluon plasma.
Generalized Parton Distributions
hep-ph 2003-07 accept novelty 2.0 of 10

A comprehensive 2003 review consolidating the theory of generalized parton distributions: their definitions, symmetries, scale evolution, models, and the exclusive processes that measure them.
Quarkonium Production at High-Energy Colliders
hep-ph 2001-06 accept novelty 2.0 of 10

NRQCD factorization with colour-octet matrix elements fitted to Tevatron data reproduces quarkonium cross sections, but its transverse-polarisation prediction is not confirmed by the first CDF measurement.

How later papers used it

57 later papers cite it

Evidence: substantial. 49 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 17 of the 71 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 1 used its method or tool and 1 compared its own results with it.

Uses its method or tool 1 of 5 papers with this label

Associated the gluon distribution function with the vector meson photoproduction amplitude using this paper's two-gluon exchange model in perturbative QCD.

Coherent photoproductions of $J/\Psi$ and $\Upsilon$ mesons in pp and PbPb ultraperipheral collisions from dynamical gluon distribution (2016) · 0.93 · paraphrased: the licence does not allow quoting

Compares with it 1 of 3 papers with this label

Obtained a result that agrees with the classic result from another work and is four times the result found in this paper.

The dipole picture and the non-relativistic expansion (2019) · 0.86 · paraphrased: the licence does not allow quoting

How the literature uses it

50 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 · 39 sentences without a confident label

Uses its method or tool 3 papers

In this study we use the simple amplitude calculated from leading order two-gluon exchange in perturbative QCD [ref] and corrected for other relevant effects (such as relativistic corrections, inclusion of the real part of the scattering amplitude, next-to-leading order NLO effects, etc, see for instance [ref] ) through a phenomenological multiplicative correction factor $ζ_V$.

Gluon distributions in nuclei probed at the CERN Large Hadron Collider · Introduction · 0.95
In the dipole approximation the cross section of $γ+ T→J/ψ+T$ process can be calculated in the Leading Order of PQCD [ref] [equation] Here $Γ_ee$ is width of the leptonic decay of $J/ψ$ and $G_T (x,μ^2 )$ is density of gluons with fraction $x=M_J/ψ^2/s_γT$ of momentum of the target ($s_γT$ is the invariant energy for $γ- T$ scattering), and $μ^2$ is the scale which we choose to be $μ^2 =M_J/ψ^2/4$.

Coherent rho and J/psi photoproduction in ultraperipheral processes with electromagnetic dissociation of heavy ions at RHIC and LHC · $J/ψ$ production · 0.88
Then the cross section can be written in the form [equation] where in the leading order the coherent $J/ψ$ photoproduction off the proton target can be described by the perturbative QCD formula [ref] [equation] Here the slope $B_J/ψ$ is parametrized by the expression [equation] with $s_0=100$ GeV$^2$ reasonably describing the data.

The LHC potential for study of the small x gluon physics in ultraperipheral collisions of 3.5 TeV protons · Introduction · 0.86

Compares with it 3 papers

This can be obtained by writing the LO photon wave-function in eq. eq:lo [equation] In the dilute limit, this becomes [equation] Using the relation between $Q_s$ and the gluon density from [ref] [equation] and the relation between quarkonium's wave-function at the origin and its decay into electrons [equation] we get [equation] which agrees with the classic result from [ref] (and is four times the result found in [ref] ).

The dipole picture and the non-relativistic expansion · Leading order · 0.86
Adopting the G$_1$ model for the proton eff, the calculation with the photon wave function of Ref. [ref] returns a value $σ_eff^γp(Q^2=100 ^2) ∼7.52$ mb while the predictions from Ref. [ref] would give $σ_eff,asy ∼7.5$ mb, showing remarkable agreement.

Enlighting the transverse structure of the proton via double parton scattering in photon-induced interactions · Numerical results for $σ_eff^γp$ · 0.98
The calculation of Ref. [ref] recovers the same nonrelativistic result in the dipole picture (see also Ref. [ref] ).

Relativistic corrections to the vector meson light front wave function · Introduction · 0.82

Cites it as background 14 papers

This process is dominated by the two gluon exchange [ref] and can be formulated in the generalized parton distribution (GPD) [ref] framework [ref] .

Near Threshold Heavy Quarkonium Photoproduction at Large Momentum Transfer · Introduction · 0.87
Due to this unique sensitivity to the gluonic structure in the nucleon, there have been extensive studies on the exclusive productions of the $J/ψ$ in various frameworks [ref] .

Small-$x$ gluon GPD constrained from deeply virtual $J/\psi$ production and gluon PDF through universal-moment parameterization · Introduction · 0.96
This property reflects the fact that the dynamics of a hadron produced in a hard scattering reaction is dominated by its valence Fock state where its quark constituents have small transverse separation $a_⊥∝1/ Q$, and thus propagate as a small-size color-singlet [ref] .

Onset of color transparency in holographic light-front QCD · Introduction · 0.88

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]

M. G. Ryskin, Z. Phys. C57, 89–92 (1993)

View on Pith 1993

[2] [1]

V. N. Gribov, B. L. Ioﬀe, and I. Ya. Pomeranchuk, Yad. Fiz., 2, 768 (1965); B. L. Ioﬀe, Phys. Lett. 30 123 (1968)

View on Pith 1965

[3] [2]

A. Donnachie and P. Landshoﬀ, Phys. Lett. 185B, 403 (1987); Nucl. Phys. B311, 509 (1989)

View on Pith 1987

[4] [3]

J. R. Cudell, Nucl. Phys. B336, 1 (1990)

View on Pith 1990

[5] [5]

S. J. Brodsky and G. P. Lepage, Phys. Rev. D22, 2157 (1980)

View on Pith 1980

[6] [6]

B. Z. Kopeliovich, J. Nemchick, N. N. Nikolaev, and B. G. Zakharov , KF A- IKP-TH-1993-27, (1993)

View on Pith 1993

[7] [7]

B. Bl¨ attel, G. Baym, L. L. Frankfurt, and M. Strikman, Phys. R ev. Lett. 71, 896 (1993)

View on Pith 1993

[8] [8]

L. Frankfurt, G. A. Miller, and M. Strikman, Phys. Lett. 304B, 1 (1993)

View on Pith 1993

[9] [9]

S. Catani, M. Ciafaloni, and F. Hautmann, Phys. Lett. B307, 147–153 (1993)

View on Pith 1993

[10] [10]

J. D. Bjorken in Proceedings of the International Symposium on Electron and Photon Interactions at High Energies , p. 281–297, Cornell (1971); J. D. Bjorken and J. B. Kogut, Phys. Rev. D8, 1341 (1973)

View on Pith 1971

[11] [11]

L. Frankfurt and M. Strikman, Phys. Rept. 160, 235 (1988)

View on Pith 1988

[12] [12]

V. L. Chernyak and A. R. Zhitnitski, Phys. Rep. 112, 173 (1984)

View on Pith 1984

[13] [13]

EMC, J. J. Aubert et al., Phys. Lett. 161B, 203 (1985); J. Ashman et al., Z. Phys. C39, 169 (1988)

View on Pith 1985

[14] [14]

NMC, P. Amaudruz et al., Z. Phys. C54, 239 (1992). 32

View on Pith 1992

[15] [15]

NMC Collaboration, A. Sandacz, Exclusive ρ0 Muoproduction at Large Q2, paper contributed to the poster session at the Few Body XIV Conference , Amsterdam, 1993

View on Pith 1993

[16] [16]

Guang Yin Fang, et al., FERMILAB-CONF-93-305, October 1993

View on Pith 1993

[17] [17]

A. D. Martin, W. J. Stirling, and R. G. Roberts, Phys. Lett. B306, 145 (1993)

View on Pith 1993

[18] [18]

S. J. Brodsky and A. H. Mueller, Phys. Lett. 206B, 685 (1988)

View on Pith 1988

[19] [19]

D. R. Yennie, Rev. Mod. Phys. 47, 311 (1975). T. H. Bauer et al. , Rev. Mod. Phys. 50, 261 (1978)

View on Pith 1975

[20] [20]

H. Cheng and T. T. Wu, Phys. Rev. 183, 1324 (1969)

View on Pith 1969

[21] [21]

J. Bjorken, J. Kogut, and D. Soper, Phys. Rev. D3, 1382 (1971)

View on Pith 1971

[22] [22]

L. Frankfurt, M. Strikman, and S. Liuti, Phys. Rev. Lett. 65, 1725 (1990); Proceeding of PANIC 93 (in press)

View on Pith 1990

[23] [23]

Harry L. Melanson, et al. , FERMILAB-CONF-93-165-E, Presented at the 28th Rencontres de Moriond: QCD and High Energy Hadronic Int eractions, Les Arcs, France, 20–27 March 1993

View on Pith 1993

[24] [24]

I. F. Ginzburg and D. Yu. Ivanov, Nucl. Phys. B388, 376 (1992), and references therein. 33 FIGURE CAPTIONS

View on Pith 1992

[25] [25]

A typical two-gluon exchange contribution to the amplitude for γ∗(q)p → V (q + ∆)(p − ∆)

View on Pith

[26] [26]

Light-cone perturbation theory graphs for the scattering of a quark-antiquark pair by a colorless target. 34 This figure "fig1-1.png" is available in "png" format from: http://arxiv.org/ps/hep-ph/9402283v2 This figure "fig1-2.png" is available in "png" format from: http://arxiv.org/ps/hep-ph/9402283v2

View on Pith Pith review arXiv