Final-State Interactions and Single-Spin Asymmetries in Semi-Inclusive Deep Inelastic Scattering

Dae Sung Hwang; Ivan Schmidt; Stanley J. Brodsky

REVIEW

Final-State Interactions and Single-Spin Asymmetries in Semi-Inclusive Deep Inelastic Scattering

Stanley J. Brodsky, Dae Sung Hwang, Ivan Schmidt

High Energy Physics - Phenomenology · Submitted 31 Jan 2002 · 12 references

Pith's verdict: The structural claim — final-state gluon exchange gives a leading-twist, IR-finite single-spin asymmetry — is sound and worth citing; the soft spot is the model-set magnitude and the unperformed fragmentation convolution to pion data.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 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 →

· 4 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/0201296 (version 2)

Pith IDJGLLPTM3, Pith's permanent record of this paper and its review

CitationDae Sung Hwang, Ivan Schmidt, Stanley J. Brodsky. "Final-State Interactions and Single-Spin Asymmetries in Semi-Inclusive Deep Inelastic Scattering." arXiv:hep-ph/0201296 (2002). https://pith.science/paper/JGLLPTM3

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

Worth your time, and worth citing: this is the paper that makes the case that final-state gluon exchange produces a leading-twist single-spin asymmetry, and the structural argument holds up under reading. The core is short and clean. The one-loop amplitude of Fig. 2b scales in the Bjorken limit because the -g^{+−} piece of the gauge propagator supplies a q^- that cancels the q^- in the denominator; that is a property of the gauge link, not of the model. The two proton spin amplitudes then pick up Coulomb phases from g1 and g2 (Eqs. 19-20), each infrared divergent, with the difference finite — you can see the endpoint cancellation directly in the Feynman parameter integrals, where the extra factor of alpha in g2 does the work. The observation that the required phase is the same physics as the proton anomalous magnetic moment is the kind of remark that reorganizes how you think about the problem. And they compute rather than fit: alpha_s = 0.3, m = 0.3 GeV, lambda = 0.8 GeV are stated representative values, not tuned to HERMES. Where it is soft, and it is soft in a specific place: the magnitude. Eq. 21 and Fig. 4 rest on the ratio of Lz=1 to Lz=0 matrix elements, and the paper carries the perturbative model's numerator structure over to QCD by assertion — 'determined by orbital angular momentum constraints.' Angular momentum fixes the spinor structure, not the radial weight or the relative Fock-state normalization. There is no error band on Fig. 4. And the step from current-quark jet to measured pion asymmetry is stated, not done: they say the convolution with D_{q→π}(z,Q²) is required and defer it to later work. So the paper establishes the mechanism and the scaling; it does not close the loop to the HERMES numbers, and it is upfront about that. Two smaller things. The non-factorization and non-transversity claims in the abstract are argued rather than proven — reasonable, but assertions. And the paper sidesteps rather than confronts the Collins T-odd argument: it says the effect is not a distribution function at all, which may well be right, but the relation to the Sivers-function literature is left for the reader to reconstruct. Send it out. The structural claim deserves referee scrutiny and the model dependence deserves a careful report.

Referee report

Significance

If correct, the result is important: it identifies a leading-twist, T-odd mechanism for single-spin asymmetries that does not require transversity, and it connects the asymmetry to the same spin-flip matrix elements responsible for the proton anomalous magnetic moment. The structural observation — that the q− cancellation in the −g+− propagator makes the rescattering leading twist, and that the α→1 endpoint divergence cancels in g1−g2 while surviving in each term separately — is robust and has been influential. The paper is honest that the numerical estimate is model-based and that the fragmentation convolution is not performed. The main strengths are the clean light-cone derivation and the falsifiable prediction for the r⊥ dependence; the main weakness is that the quantitative comparison to HERMES/SMC is left for future work.

Major objections (4)

[Section 2, Eq. (21)] As typeset, Eq. (21) appears dimensionally inconsistent: Py is an asymmetry and must be dimensionless, but the printed expression carries dimensions of inverse mass to the fourth. The bracket [r⊥² + Δ(1−Δ)(−M² + m²/Δ + λ²/(1−Δ))] appears in the denominator, whereas the structure of g1−g2 and h in Eqs. (10), (19), (20) suggests it should appear in the numerator (with the 1/r⊥² prefactor retained), which would restore dimensionless Py. Please verify the algebra and correct the equation; if Fig. 4 was generated from the printed form, the numerical estimates in the figure need to be rechecked.
[Section 2, paragraph after Eq. (21); Section 4] The statement that the asymmetry 'does not factorize into a product of distribution function and fragmentation function' is too strong as written and risks being read as a claim that no factorization holds at all. What the calculation shows is that the asymmetry is not given by the ordinary collinear quark distribution times a fragmentation function, but requires a T-odd quark-gluon correlator of the form <p|ψ̄q A ψq|p>. That object can be reorganized into a gauge-link-dressed, T-odd distribution, so the precise claim is about which correlator appears, not about the absence of factorization. Please sharpen the wording in the abstract (abstract:s4) and in Section 4, and cite the relevant Sivers-type literature so the reader can locate the statement.
[Section 2, paragraph after Eq. (21)] The sentence 'The matrix elements of the proton to its constituents will have the same numerator structure as the perturbative model since they are determined by orbital angular momentum constraints' fixes the spinor structure of the Lz = 1 and Lz = 0 amplitudes but not the radial wavefunction or the relative weight of the Fock components. Consequently the magnitude in Eq. (21) and Fig. 4 is set by the model parameters (m = 0.3 GeV, λ = 0.8 GeV, αs = 0.3) and by the scalar-diquark truncation, which omits the axial-vector diquark component of the proton. The paper should state explicitly that Eq. (21) is a model estimate rather than a QCD prediction, and should identify which features (the r⊥ fall-off, the sign, the αs(r⊥²) scaling, the proportionality to the anomalous magnetic moment) are expected to be universal and which are model-dependent.
[Section 3, last paragraph] The convolution with the quark fragmentation function Dq→π(z,Q²) that would connect the jet-level asymmetry to the measured pion asymmetry is stated but not performed, so the paper does not demonstrate that the mechanism reproduces the HERMES/SMC magnitudes. The authors acknowledge this ('Detailed comparisons with experiment will be presented elsewhere'), and I do not ask for the convolution here; the request is that the abstract and introduction make the acknowledgment explicit, so that a reader does not infer a completed data comparison from the juxtaposition of the HERMES/SMC motivation with Fig. 4.

Minor objections (8)

[References] The paper discusses a T-odd, FSI-induced single-spin asymmetry without citing Sivers' original work on the time-reversal-odd distribution (Phys. Rev. D41, 83 (1990); D43, 261 (1991)). Given that the mechanism is closely related, a citation and a sentence locating the present result relative to that work would help the reader.
[Section 2, Eq. (21) and throughout] The symbol Δ is used both for the quark light-cone fraction and, after Eq. (21), for Bjorken xbj. This conflicts with the standard use of Δ for a momentum transfer and makes the equations harder to follow; a notation such as xB or ξ would be clearer.
[Figure 4] The caption should identify which panel is (a), (b), (c), (d) and state explicitly that Py is the jet-level asymmetry while KPy includes the kinematic factor K = (Q/ν)√(1−y). As printed, the reader must infer the panel assignments from the axis labels.
[Abstract and Section 3] The abstract cites both AUL and AUT, but the calculation is for the transverse asymmetry AUT (Py). The relation between the two via the kinematic factor K is explained in Section 3 but not flagged in the abstract; a clause noting that the calculation addresses AUT would avoid confusion.
[Section 1, paragraph 3] The statement that 'the only source of a nonzero complex phase in leptoproduction in the light-front frame are final-state interactions' should be qualified: it holds given that the tree-level hard amplitude is real, and initial-state interactions are the relevant source in related processes such as Drell-Yan. A sentence noting this would strengthen the argument.
[Section 2, paragraph after Eq. (20)] The verification in light-cone gauge using the principal-value prescription is asserted but not shown. A short sentence or footnote indicating the structure of the light-cone-gauge calculation would make the gauge-invariance claim checkable.
[Section 1, paragraph 2] The analogy with the proton anomalous magnetic moment is physically suggestive but is not derived; the text should say explicitly that it is an analogy between the required spin-flip matrix elements, not an identity between the two observables.
[Section 2, Eq. (3)] The perturbative scalar wavefunction φ is introduced without justification of its normalization or of the choice of the perturbative form for a bound-state problem. A sentence on the normalization convention and on the sense in which Eq. (3) is representative would help.

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

The paper

The paper claims

The proton's large single-spin asymmetry in semi-inclusive deep inelastic scattering can come from gluon exchange after the quark is struck, at leading twist, without any transversity distribution.

The reading

The HERMES and SMC experiments see a surprisingly large azimuthal asymmetry when a transversely polarized proton is struck and a pion comes out, and the standard factorization picture of hard inclusive scattering has no obvious place to put it. This paper argues that the asymmetry needs no new distribution function: it arises because the outgoing quark, after the photon has knocked it free, exchanges a gluon with the proton's leftover spectators, and that rescattering imprints a spin-dependent complex phase. The phase is Coulomb-like, depends on the orbital angular momentum of the proton's constituents, and differs between the two proton spin amplitudes $J^z_p=+1/2$ and $-1/2$ that feed the same final state. Because the two amplitudes have different phases, their interference survives at leading twist, so the asymmetry is not suppressed by powers of $Q^2$ at fixed $x_{bj}$. The authors also stress a negative corollary: this mechanism does not factorize into a distribution function times a fragmentation function, and it is not the transversity distribution $h_1$ (called $h_1$ elsewhere; here written $h_1$ or $h_1$ in the text as $h_1$).

What carries the argument

The load-bearing object is the phase difference $Delta chi = chi_1 - chi_2$ between the two proton spin amplitudes, generated by the one-loop final-state rescattering graph. Concretely, the tree amplitude carries a real coefficient $h$, while the one-loop amplitude contributes $h + i e_1 e_2 g_i / 8 pi$; the numerator structure of the light-front wavefunctions, $psi^{uparrow}_{+1/2} = (M + m/x) phi$ for the spin-conserving piece and $psi^{uparrow}_{-1/2} = -(k_1 + i k_2)/x, phi$ for the spin-flip piece, is fixed by orbital angular momentum and holds for perturbative and non-perturbative couplings alike. The spin-flip numerator's factor of transverse momentum produces an extra $alpha$ in the Feynman-parametrized loop integral, which is exactly what makes $g_1 neq g_2$ and hence $Delta chi neq 0$. The asymmetry is then proportional to $sin Delta chi$. A second piece of machinery is the scaling argument: in Feynman gauge only the $-g^{+-}$ part of the gauge propagator survives in the Bjorken limit, supplying a factor $q^-$ that cancels the $q^-$ in the propagator denominator, so the loop graph scales rather than being suppressed.

Extended reading notes

Core claim

The paper's central claim is that final-state interactions from gluon exchange between the outgoing quark and the target spectator system produce single-spin asymmetries in deep inelastic lepton-proton scattering at leading twist in perturbative QCD, meaning the rescattering corrections are not power-law suppressed at large photon virtuality $Q^2$ at fixed $x_{bj}$. The authors set up the necessary condition first: a transverse-spin correlation requires two amplitudes $M[gamma^* p(J^z_p) to F]$ with $J^z_p = pm 1/2$ coupling to the same final state $|F>$, with different complex phases, so the asymmetry is proportional to $mathrm{Im}(M[J^z_p=+1/2]^* M[J^z_p=-1/2])$. These are the same amplitudes whose interference generates the proton's anomalous magnetic moment, and their orbital angular momenta must differ by $Delta L_z = 1$. In a quark-diquark model of the proton they compute the interference of the tree graph with the one-loop graph in which the outgoing quark exchanges a gauge particle with the spectator, and they find that the one-loop coefficients $g_1$ and $g_2$ for the spin-parallel and spin-flip amplitudes differ, with the difference traceable to the extra Feynman parameter $alpha$ picked up by the orbital angular momentum factor in the spin-flip numerator. Each phase $chi_i = tan^{-1}(e_1 e_2 g_i / 8 pi h)$ is infrared divergent on its own, but the difference $chi_1 - chi_2$, which is what enters the asymmetry, is infrared finite. The resulting asymmetry $P_y$ falls as $alpha_s(r_perp^2), x_{bj}, M, r_perp ln r_perp^2 / r_perp^2$ at large transverse momentum $r_perp$ of the current jet, a fall-off in $r_perp^2$ rather than $Q^2$.

Load-bearing premise

The calculation is done in a quark-diquark model with a perturbative scalar wavefunction, and the paper assumes that the ratio of the orbital-angular-momentum-one spin-flip amplitude to the spin-conserving amplitude carries over unchanged to real QCD, so that the phase difference and the size of the asymmetry survive beyond the model.

Editorial extensions

If this is right

The single-spin asymmetry from final-state interactions should persist at large $Q^2$ at fixed $x_{bj}$ rather than dying as $1/Q^2$, which distinguishes it from higher-twist explanations.
The asymmetry should scale roughly as $alpha_s(r_perp^2)$ times the proton's anomalous magnetic moment, so its normalization is tied to a known quantity rather than a free fit.
The effect is predicted to fall as $r_perp ln r_perp^2 / r_perp^2$ in the transverse momentum of the current quark jet relative to the photon direction, a shape that can be checked with jet observables such as thrust.
The asymmetry does not factorize into a distribution function times a fragmentation function, and is not the transversity distribution, so it cannot be absorbed into existing transversity-based descriptions of the Collins effect.
The same amplitude-interference mechanism is proposed to extend to single-spin asymmetries in other hard reactions such as $e^+ e^- to Lambda^{uparrow} X$ and $p p to Lambda^{uparrow} X$.

Reading between the lines

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

If the effect is real and leading twist, then the standard statement that semi-inclusive deep inelastic scattering factorizes into quark distributions times fragmentation functions needs a caveat for spin observables even where it holds for the unpolarized cross section, which would put this mechanism in direct tension with transversity-based extractions of the nucleon's tensor charge.
The mechanism predicts a definite sign and shape for the asymmetry as a function of $x_{bj}$ and jet transverse momentum, so combined HERMES, COMPASS, and Jefferson Lab measurements at several beam energies could in principle separate this rescattering contribution from a Collins-type contribution by their different $Q^2$ and $r_perp$ behavior.
Because the phase difference is driven by the ratio of $L_z=1$ to $L_z=0$ matrix elements, the size of the asymmetry is a direct handle on the orbital angular momentum content of the proton, and a measurement of its magnitude would constrain light-front wavefunction models independently of the anomalous magnetic moment.
The same interference logic should apply wherever a produced colored particle can rescatter off a spectator system, which suggests looking for analogous leading-twist asymmetries in diffractive or nuclear targets where the spectator system is larger.

Original abstract

Recent measurements from the HERMES and SMC collaborations show a remarkably large azimuthal single-spin asymmetries A_{UL} and A_{UT} of the proton in semi-inclusive pion leptoproduction. We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton-proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q^2 at fixed x_{bj}. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p = + 1/2 and -1/2 to the same final state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L_z of the proton's constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution delta q(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.

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, 4,702 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.35 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.72 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Recent measurements from the HERMES and SMC collaborations show a remarkably large azimuthal single-spin asymmetries A_{UL} and A_{UT} of the proton in semi-inclusive pion leptoproduction. We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton-proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q^2 at fixed x_{bj}. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p = + 1/2 and -1/2 to the same final state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L_z of the proton's constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution delta q(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.

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	Recent measurements from the HERMES and SMC collaborations show a remarkably large azimuthal single-spin asymmetries A_{UL} and A_{UT} of the proton in semi-inclusive pion leptoproduction.	background 1.00	0.04	0.04	asserted 1.00
s1	We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton-proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q^2 at fixed x_{bj}.	result 0.75	0.93	0.87	asserted 1.00
s2	The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p = + 1/2 and -1/2 to the same final state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment.	interpretation 0.67	0.47	0.13	asserted 1.00
s3	We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L_z of the proton's constituents and is thus distinct for different proton spin amplitudes.	result 0.48	0.83	0.12	asserted 1.00
s4	The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution delta q(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.	result 0.65	0.83	0.17	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.94.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The final-state interaction in the semi-inclusive

**Figure 2.** The tree (a) and one-loop (b) graphs for

**Figure 3.** The light-cone frame used is p = (p +, p−, ~p⊥) = (P +, M2/P +,~0⊥) and q = (q +, q−,~q⊥) with q + = 0. The virtual photon and produced hadron define the production plane which we will take as the ˆz − xˆ plane. ↑ / ↓ gives the spin projection J z q = ± 1 2 of the spin- 1 2 constituent. Here e1 and e2 are the electric charges of q and (qq)0, respectively, and g is the coupling constant of the proton-q-(qq)0 vertex. The first term in (5) to (8) is the Born contribution of the tree graph. The crucial result will be the fact that the contributions g1 and g2 from the one-loop diagram…

**Figure 4.** Model predictions for the single spin asymmetry of

Figures reproduced from arXiv:hep-ph/0201296 by the authors.

References

Works cited (12)

[1]

HERMES Collaboration, A. Airapetian et al. , Phys. Rev. Lett. 84 , 4047 (2000); Phys. Rev. D64 , 097101 (2001)

View on Pith 2000
[2]

A. Bravar, for the SMC Collaboration, Nucl. Phys. B (Proc. Suppl.) 79 , 520 (1999)

View on Pith 1999
[3]

E704 Collaboration, A. Bravar et al. , Phys. Rev. Lett. 77 , 2626 (1996)

View on Pith 1996
[4]

K. Heller, in Proceedings of Spin 96, C. W. de Jager, T. J. Ketel and P. Mulders, Eds., World Scientific (1997)

View on Pith 1997
[5]

S. J. Brodsky, P. Hoyer, N. Marchal, S. Peigne and F. Sannino, hep-ph/0104291

View on Pith Pith review arXiv
[6]

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

View on Pith 1980
[7]

S. J. Brodsky and G. P. Lepage, in: Perturbative Quantum Chromodynamics, edited by A. H. Mueller (World Scientific, Singapore 1989)

View on Pith 1989
[8]

S. J. Brodsky and S. D. Drell, Phys. Rev. D22 , 2236 (1980)

View on Pith 1980
[9]

S. J. Brodsky, D. S. Hwang, B. Q. Ma and I. Schmidt, Nucl.\ Phys.\ B 593 , 311 (2001)

View on Pith 2001
[10]

S. J. Brodsky, A. H. Hoang, J. H. K\"uhn and T. Teubner, Phys.\ Lett.\ B 359 , 355 (1995)

View on Pith 1995
[11]

J. C. Collins, Nucl.\ Phys.\ B 396 , 161 (1993)

View on Pith 1993
[12]

D. Boer and P. J. Mulders, Phys. Rev. D57 , 5780 (1998)

View on Pith 1998

Forward citations

Cited by 46 Pith papers

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

Sivers Tomography from Charge and Angle Only
hep-ph 2026-05 conditional novelty 8.0 of 10

The OPCC observable is IRC finite and factorizes into the Sivers distribution plus a perturbatively calculable charge-weighted jet function, eliminating dependence on non-perturbative fragmentation functions via charg...
Leading-twist Single-transverse-spin asymmetries: Drell-Yan and Deep-Inelastic Scattering
hep-ph 2002-03 conditional novelty 8.0 of 10

The Sivers asymmetry is not forbidden by time reversal; the Wilson line in the quark-density operator forces it to reverse sign between semi-inclusive deep-inelastic scattering and Drell-Yan.
Strongly Coupled Soft Functions
hep-ph 2026-08 conditional novelty 7.0 of 10

The cusp anomalous dimension at strong coupling is obtained for all rapidity separations from two competing string saddles, and the transversely-separated two-cusp Wilson loop scales as (b_perp^2 Lambda^2)^{-Re Gamma_cusp}.
Parton distributions in the shockwave formalism
hep-ph 2025-10 conditional novelty 7.0 of 10

A single shockwave Feynman-rule framework reproduces and extends prior small-x parton distributions, yielding new quark GTMD/GPD/PDF and diffractive-TMD results.
Energy Correlators Resolving Proton Spin
hep-ph 2025-09 unverdicted novelty 7.0 of 10

The work establishes a correspondence between spin-dependent energy correlators and polarized TMDs/NECs using SCET, yielding N3LL/N2LL predictions for correlation patterns in current and target fragmentation regions.

Show 41 more citing papers

Emergence, Formation and Dynamics of Hot QCD Matter
hep-ph 2024-12 conditional novelty 7.0 of 10

A doctoral thesis deriving the QCD correlation functions that control quarkonium dissociation and recombination in the quark-gluon plasma, and showing that hydrodynamization in a simplified QCD kinetic theory matches ...
First measurement of transverse-spin-dependent azimuthal asymmetries in the Drell-Yan process
hep-ex 2017-04 conditional novelty 7.0 of 10

The first Drell-Yan measurement of transverse-spin azimuthal asymmetries finds a positive Sivers asymmetry, consistent with the predicted sign change relative to SIDIS, though at roughly one standard deviation.
Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions
hep-ph 2014-04 accept novelty 7.0 of 10

A systematic next-to-eikonal expansion of the gluon propagator in a nuclear background yields new gradient-decorated Wilson-line operators; the first correction cancels in the unpolarized pA gluon cross section but dr...
No Generalized TMD-Factorization in the Hadro-Production of High Transverse Momentum Hadrons
hep-ph 2010-01 conditional novelty 7.0 of 10

Generalized transverse-momentum-dependent factorization, which inserts process-dependent Wilson lines into separate TMD parton distributions, fails in a non-Abelian gauge theory at the two-gluon level, as shown by a s...
Nucleon Tomography with 0-jettiness
hep-ph 2025-06 conditional novelty 6.0 of 10

Applying a 0-jettiness veto to transverse single-spin asymmetries in W/Z production at RHIC enhances the asymmetry signal, sharpening the test of the Sivers sign change.
Six-dimensional light-front Wigner distributions of the proton
hep-ph 2025-05 conditional novelty 6.0 of 10

All 16 leading-twist six-dimensional light-front quark Wigner distributions for the proton are computed in a spectator-diquark model, extending earlier five-dimensional and unpolarized-only results.
Global analysis of the Sivers functions at NLO+NNLL in QCD
hep-ph 2020-09 conditional novelty 6.0 of 10

The first NLO+NNLL global fit of the Sivers function describes low-energy SIDIS/DY data well but underpredicts RHIC W/Z asymmetries unless the Qiu-Sterman DGLAP evolution is approximated as the unpolarized one.
Is the Momentum Sum Rule Valid for Nuclear Structure Functions ?
hep-ph 2019-08 reject novelty 6.0 of 10

The paper contends that the momentum sum rule is not valid for nuclear parton distribution functions because the operator product expansion fails for nuclear targets.
Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
hep-ph 2018-01 accept novelty 6.0 of 10

The energy-energy correlation's soft function is proven identical to the transverse-momentum soft function, which supplies three-loop anomalous dimensions and next-to-next-to-next-to-leading-log resummation for the EEC.
Gluon and Wilson loop TMDs for hadrons of spin $\leq$ 1
hep-ph 2016-07 conditional novelty 6.0 of 10

The paper provides the full leading-twist parametrization of gluon TMD correlators for spin-0, spin-1/2, and spin-1 hadrons, and classifies which gluon TMDs dominate at small x by matching them to Wilson loop TMDs.
Extraction of Quark Transversity Distribution and Collins Fragmentation Functions with QCD Evolution
hep-ph 2015-05 accept novelty 6.0 of 10

First extraction of quark transversity and Collins fragmentation functions including TMD evolution, from a joint fit to BELLE, BABAR, HERMES, COMPASS and JLab Collins asymmetry data.
The QCD Evolution of the Sivers Function
hep-ph 2011-10 conditional novelty 6.0 of 10

The scale evolution of the Sivers function is derived within TMD factorization and tabulated as Gaussian parameters for two existing fixed-scale fits, enabling predictions at new collision energies.
An Observation Concerning the Process Dependence of the Sivers Functions
hep-ph 2011-03 conditional novelty 6.0 of 10

The k-perp moment of the quark Sivers function and the twist-3 quark-gluon correlation function T_{q,F}(x,x) come out with opposite signs for both up and down quarks, a mismatch that survives after correcting a sign c...
Nonperturbative QCD Coupling and its $\beta$ function from Light-Front Holography
hep-ph 2010-02 conditional novelty 6.0 of 10

Light-front holography with a positive-sign dilaton yields a Gaussian nonperturbative QCD coupling whose beta function vanishes at both zero and infinite momentum transfer, matching the shape of the Bjorken-sum-rule charge.
Generalized parton correlation functions for a spin-1/2 hadron
hep-ph 2009-06 accept novelty 6.0 of 10

A complete classification of generalized parton correlation functions and generalized transverse momentum distributions for a spin-1/2 hadron shows that proposed nontrivial relations between generalized and transverse...
Dilepton production from polarized hadron hadron collisions
hep-ph 2008-09 accept novelty 6.0 of 10

The paper derives the full 48-structure-function angular distribution for polarized Drell-Yan and evaluates 24 of those structure functions at leading twist in terms of transverse-momentum-dependent parton distributions.
k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions
hep-ph 2007-05 conditional novelty 6.0 of 10

In a simplified abelian model, a one-loop single-spin asymmetry in back-to-back hadroproduction contains a term that no Wilson-line redefinition of the parton density can absorb, so k_T factorization with universal tr...
Semi-inclusive deep inelastic scattering at small transverse momentum
hep-ph 2006-11 accept novelty 6.0 of 10

The paper derives the complete lowest-order set of 18 semi-inclusive DIS structure functions through twist 3 in terms of transverse-momentum-dependent quark distributions and fragmentation functions, for all beam and ...
Collins effect in semi-inclusive deeply inelastic scattering and in electron positron annihilation
hep-ph 2006-03 conditional novelty 6.0 of 10

HERMES SIDIS and BELLE e+e- data are consistent with a Collins fragmentation function whose favoured and unfavoured pieces have opposite signs and comparable magnitude.
QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum
hep-ph 2004-04 accept novelty 6.0 of 10

A one-loop-verified, all-orders-argued QCD factorization theorem for low-transverse-momentum semi-inclusive deep-inelastic scattering, built on soft-subtracted transverse-momentum-dependent parton distributions and fr...
Extraction of transverse-momentum-dependent helicity distributions of the nucleon
hep-ph 2026-10 conditional novelty 5.0 of 10

An NNLO- and mass-corrected global fit of the helicity TMD g1L from SIDIS A_LL data constrains up and down quarks, leaves sea and gluon unconstrained, and passes excluded-data checks for the cos phi_h modulation.
Twist-4 GTMDs of sea quarks at zero skewness in the light-cone quark model
hep-ph 2026-09 conditional novelty 5.0 of 10

First model calculation of twist-4 GTMDs for anti-up and anti-down sea quarks inside the proton at zero skewness, using the light-cone quark model with baryon-meson fluctuation.
T-odd transverse momentum dependent gluon distributions for tensor polarized deuteron in a spectator model
hep-ph 2026-07 conditional novelty 5.0 of 10

Six leading-twist T-odd gluon TMDs of a tensor-polarized deuteron are derived analytically and evaluated numerically in a spectator model with single-gluon final-state interaction.
Electron-Ion Collision Environment: Distribution of Quark Spin and Orbital Angular Momentum
hep-ph 2026-07 conditional novelty 5.0 of 10

Using NJL density-dependent quark masses in a light-front dressed-quark model, the paper predicts O(10–40%) medium modifications of GTMDs linked to quark OAM, spin, and spin–orbit correlation, and defines eA/eP GTMD r...
T-odd Wigner Distributions in boost-invariant longitudinal position space and Spin-momentum correlation in proton
hep-ph 2024-08 unverdicted novelty 5.0 of 10

T-odd leading-twist GTMDs in σ-space exhibit -t-dependent oscillations with transverse-longitudinal interference, while Sivers and Boer-Mulders Wigner distributions encode proton spin-transverse momentum correlations.
QCD Evolution of the Sivers Asymmetry
hep-ph 2014-01 conditional novelty 5.0 of 10

A global fit with QCD evolution extracts quark Sivers functions from SIDIS data and predicts few-percent Drell-Yan and W asymmetries whose sign is expected to flip relative to SIDIS.
Distribution of linearly polarized gluons inside a large nucleus
hep-ph 2011-05 conditional novelty 5.0 of 10

In the color glass condensate framework, the dipole gluon distribution is exactly maximally linearly polarized at all transverse momenta, while the Weizsäcker-Williams distribution reaches maximal polarization only at...
TMD Parton Distribution and Fragmentation Functions with QCD Evolution
hep-ph 2011-01 conditional novelty 5.0 of 10

Starting from existing fits and the Collins-Soper-Sterman formalism, the authors produce evolved transverse-momentum-dependent quark distributions and fragmentation functions and show that QCD evolution suppresses the...
The transverse momentum dependent distribution functions in the bag model
hep-ph 2010-01 accept novelty 5.0 of 10

In the MIT bag model the pretzelosity distribution equals minus the quark orbital angular momentum, and the transverse-momentum dependence of the distributions is well approximated by a Gaussian in the valence region.
Nucleon structure from mixed action calculations using 2+1 flavors of asqtad sea and domain wall valence fermions
hep-lat 2010-01 conditional novelty 5.0 of 10

Lattice QCD with 2+1 flavors puts the proton axial charge about 9% below experiment, the charge radii near two thirds of measured values, and the connected quark angular momentum at Ju+d = 0.238(8), with up and down o...
Extending Soft-Collinear-Effective-Theory to describe hard jets in dense QCD media
hep-ph 2008-08 conditional novelty 5.0 of 10

A new effective Lagrangian couples collinear quarks to Glauber gluons from a dense medium and reproduces known full-QCD results for jet broadening and the TMDPDF gauge link.
Transverse-momentum distributions in a diquark spectator model
hep-ph 2008-07 accept novelty 5.0 of 10

All leading-twist transverse-momentum-dependent parton distributions are derived analytically in a scalar-plus-axial-vector diquark spectator model, with nine parameters fitted to low-scale unpolarized and helicity da...
Relations between generalized and transverse momentum dependent parton distributions
hep-ph 2007-03 conditional novelty 5.0 of 10

In scalar-diquark and quark-target models, moments of T-odd TMDs (Sivers, Boer-Mulders) come out proportional to moments of specific GPDs, but no model-independent relation is established.
The effect of TMD evolution on the Sivers asymmetry in back-to-back $J/\psi+\gamma$ and $J/\psi+\text{jet}$ production at the Electron-Ion-Collider
hep-ph 2026-06 unverdicted novelty 4.0 of 10

After including TMD evolution, the Sivers asymmetry in these J/ψ processes at EIC kinematics remains sizable and largely independent of LDME choices, providing a robust probe of the gluon Sivers function.
Physics of the Electron-Ion Collider in China
hep-ph 2026-08 unverdicted novelty 3.0 of 10

A review of the EicC physics case argues that the proposed Chinese electron-ion collider, at 15-20 GeV collision energy, can complement the US EIC with high-precision measurements of sea-quark spin structure, proton m...
The 3D structure of the Nucleon in momentum space: TMD phenomenology
hep-ph 2025-01 conditional novelty 2.0 of 10

A review showing unpolarized quark TMD fits now reach collinear-PDF-like precision, while polarized and gluon TMDs remain less constrained.
TMD Handbook
hep-ph 2023-04 accept novelty 2.0 of 10

A multi-author reference volume that fixes conventions, gives field-theoretic definitions of TMD parton distributions and fragmentation functions, and surveys factorization, evolution, lattice methods, models, and phe...
The QCD Running Coupling
hep-ph 2016-04 accept novelty 2.0 of 10

A comprehensive review of the QCD running coupling across perturbative and nonperturbative regimes, closing with a proposal that effective charges defined directly from observables give the most unified definition of alpha_s.
Azimuthal and Single Spin Asymmetries in Hard Scattering Processes
hep-ph 2007-12 conditional novelty 2.0 of 10

Large left-right asymmetries in pion production off polarized protons are best described by a transverse-momentum-dependent Sivers function, but the factorization underpinning single-inclusive hadroproduction remains ...
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.
Transverse-Spin and Transverse-Momentum Effects in High-Energy Processes
hep-ph 2010-11 accept novelty 1.0 of 10

The review consolidates the theory and the HERMES, COMPASS, Belle and RHIC measurements of transverse-spin asymmetries, and the global fits that extract transversity and the Collins function from them.

How later papers used it

155 later papers cite it

Evidence: substantial. 124 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 22 of the 242 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

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 of 7 papers with this label

Accounted for the gauge links by introducing a phase to each light-cone amplitude as in this paper and estimated the phases from one gluon exchange interactions.

Quark orbital motions from Wigner distributions (2014) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

138 arXiv papers cite this in 219 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 · 147 sentences without a confident label

Contests it 1 paper

Substituting this result back into [ref] gives (cf. Eq. (31) in [ref] [As noted in Ref. [ref] , there should be an additional overall minus sign in front of Eq. (21) of Ref. [ref] , also in front of Eq. (31) of Ref. [ref] and Eqs. (31,33,36) of Ref. [ref] . ])

Single-Spin Asymmetries in Semi-inclusive Deep Inelastic Scattering and Drell-Yan Processes · Semi-Inclusive Deep Inelastic Scattering · contest 0.80

Uses its method or tool 4 papers

To include the lensing mechanism [ref] into the saturation framework, we will utilize the same quark–diquark model of the polarized proton as employed in [ref] .

Lensing Mechanism Meets Small-$x$ Physics: Single Transverse Spin Asymmetry in $p^{\uparrow}+p$ and $p^{\uparrow}+A$ Collisions · Introduction · 0.95
We employ a model in which the proton is made out of a valence quark and a scalar color-charged diquark: this model was used previously in [ref] .

Single-Spin Asymmetries in Semi-inclusive Deep Inelastic Scattering and Drell-Yan Processes · The Sign of the Sivers Effect · 0.83
The odderon operator can be calculated using models such as the McLerran-Venugopalan (MV) model [ref] and the diquark model [ref] .

Charm Sivers function at EicC · theory · 0.85

Cites it as support 9 papers

In fact, final-state interactions from gluon exchange between the outgoing quarks and the target spectator system lead to single-spin asymmetries in semi-inclusive deep inelastic lepton-proton scattering which are not power-law suppressed at large photon virtuality $Q^2$ at fixed $x_bj$ [ref] .

Novel High Transverse Momentum Phenomena in Hadronic and Nuclear Collisions · Single-Spin Asymmetries from Rescattering · 0.99
In fact, final-state interactions from gluon exchange between the outgoing quarks and the target spectator system lead to single-spin asymmetries (SSAs) in semi-inclusive deep inelastic lepton-proton scattering which are not power-law suppressed at large photon virtuality $Q^2$ at fixed $x_bj$ [ref] .

Dynamic versus Static Structure Functions and Novel Diffractive Effects in QCD · Single-Spin Asymmetries and Other Leading-Twist Rescattering Effects · 1.00
In fact, final-state interactions from gluon exchange between the outgoing quarks and the target spectator system lead to single-spin asymmetries in semi-inclusive deep inelastic lepton-proton scattering which are not power-law suppressed at large photon virtuality $Q^2$ at fixed $x_bj$ [ref] .

Novel QCD Phenomena · Single-Spin Asymmetries from Final-State Interactions · 1.00

Cites it as background 51 papers

One mechanism relies on the so-called transverse momentum dependent (TMD) factorization [ref] , and describes the SSAs in terms of the spin-dependent part of TMD parton distribution functions (PDFs), known as the Sivers functions [ref] , or TMD fragmentation functions (FFs), known as the Collins functions [ref] .

An Observation Concerning the Process Dependence of the Sivers Functions · Introduction · 0.87
We now review how [ref] a transverse single-spin asymmetry (SSA) arises in semi-inclusive deep-inelastic scattering (SIDIS), at the level of one-gluon-exchange, and how it determines [ref] the Wilson line that defines parton densities.

k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions · Review of SIDIS and DY · 0.91
Two QCD mechanisms for generating SSAs have been proposed and applied extensively to phenomenology: the transverse momentum dependent (TMD) factorization approach [ref] and the collinear twist-3 factorization approach [ref] .

Transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering at next-to-leading order · Introduction · 0.97

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] [1]

HERMES Collaboration, A. Airapetian et al. , Phys. Rev. Lett. 84 , 4047 (2000); Phys. Rev. D64 , 097101 (2001)

View on Pith 2000

[2] [2]

A. Bravar, for the SMC Collaboration, Nucl. Phys. B (Proc. Suppl.) 79 , 520 (1999)

View on Pith 1999

[3] [3]

E704 Collaboration, A. Bravar et al. , Phys. Rev. Lett. 77 , 2626 (1996)

View on Pith 1996

[4] [4]

K. Heller, in Proceedings of Spin 96, C. W. de Jager, T. J. Ketel and P. Mulders, Eds., World Scientific (1997)

View on Pith 1997

[5] [5]

S. J. Brodsky, P. Hoyer, N. Marchal, S. Peigne and F. Sannino, hep-ph/0104291

View on Pith Pith review arXiv

[6] [6]

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

View on Pith 1980

[7] [7]

S. J. Brodsky and G. P. Lepage, in: Perturbative Quantum Chromodynamics, edited by A. H. Mueller (World Scientific, Singapore 1989)

View on Pith 1989

[8] [8]

S. J. Brodsky and S. D. Drell, Phys. Rev. D22 , 2236 (1980)

View on Pith 1980

[9] [9]

S. J. Brodsky, D. S. Hwang, B. Q. Ma and I. Schmidt, Nucl.\ Phys.\ B 593 , 311 (2001)

View on Pith 2001

[10] [10]

S. J. Brodsky, A. H. Hoang, J. H. K\"uhn and T. Teubner, Phys.\ Lett.\ B 359 , 355 (1995)

View on Pith 1995

[11] [11]

J. C. Collins, Nucl.\ Phys.\ B 396 , 161 (1993)

View on Pith 1993

[12] [12]

D. Boer and P. J. Mulders, Phys. Rev. D57 , 5780 (1998)

View on Pith 1998