Fragmentation of Transversely Polarized Quarks Probed in Transverse Momentum Distributions

John Collins

REVIEW

Fragmentation of Transversely Polarized Quarks Probed in Transverse Momentum Distributions

John Collins

High Energy Physics - Phenomenology · Submitted 6 Aug 1992 · 20 references

Pith's verdict: The paper that defined the Collins function: the definition and the symmetry argument hold up, the TMD factorization is asserted rather than proved, and the appendix's Sivers prohibition is the one place the author is overconfident.

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arXiv IDhep-ph/9208213 (version 2)

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CitationJohn Collins. "Fragmentation of Transversely Polarized Quarks Probed in Transverse Momentum Distributions." arXiv:hep-ph/9208213 (1992). https://pith.science/paper/DNPTXTAK

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Editor's note

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Collins is defining a new object here, and it's the one that stuck: eq. (4), a fragmentation function depending on the transverse spin of the fragmenting quark, producing a sin(phi) azimuthal asymmetry about the jet axis. The symmetry argument is the strong part. Helicity conservation in the hard scattering forces the spin flip into the fragmentation, where final-state interactions can supply the phase that the distribution side is forbidden from having. He computes the spin-transfer coefficient explicitly (eq. 21: 100% forward, still 80% at 90 degrees) and gets a clean, leading-twist prediction for SIDIS with an unpolarized beam. The sigma-model calculation in Sec. 6 is a toy, but it does the job it is meant to do: it shows the effect is permitted and traces it to chiral symmetry breaking plus a phase difference between the scalar and vector pieces of the dressed propagator. That is a real physical statement, not decoration. The paper is also honest about Sudakov dilution and about the fact that no quantitative prediction is possible yet. It has aged well for exactly that reason. Soft spots, in order of weight. The TMD factorization in eqs. (13)-(14) is asserted, not proved; he says so twice, and flagging it rather than faking a derivation was the right call. The appendix is the one place he is overconfident: the time-reversal argument against the Sivers function is performed on the gauge-non-invariant bilocal, even though Sec. 2.1 states that a gauge link is required. That is a genuine gap, and it is written as a prohibition rather than a conjecture. It does not touch the fragmentation result, but nobody should read the appendix as settled. Third, Im(A*B) is never computed; he says there is presumably no reason for it to be small, which is a guess, and the 10% asymmetry estimate is a guess layered on that guess. He flags both. The citation pattern is fine: Efremov-Mankiewicz-Tornqvist and Carlitz et al. are credited for the handedness and two-particle ideas, and the single-particle TMD fragmentation function is genuinely not in them. This deserves referee time, and it is worth citing if you work on TMDs or spin-dependent fragmentation.

Referee report

Significance

If the central claim holds, this is an important paper: it identifies a leading-twist observable sensitive to transverse quark spin in fragmentation, at a time when twist-2 transverse-spin observables were scarce. Several features deserve explicit credit. The definition in Eq. (4) is given from first principles and is unambiguous, and the accompanying discussion of why the time-reversal argument that kills the Sivers asymmetry does not apply to fragmentation is a clean and physically correct distinction. The hard-scattering spin-transfer coefficient is computed rather than assumed, and I have checked Eqs. (20)-(23): the helicity amplitudes, the coefficient C = 2(1-y)/(2-2y+y²) in Eq. (21), and the spin-averaged and spin-dependent matrix elements in Eqs. (22)-(23) are mutually consistent. The prediction is falsifiable and comes with stated kinematic expectations (the sin φ shape, the kinematic zero at k⊥ = 0, the valence-region enhancement, the charge/flavor pattern in Sec. 4). The model calculation, while schematic, is a genuine attempt to show that no symmetry forbids the effect and to connect it to spontaneous chiral symmetry breaking.

Major objections (3)

[§3.3, Eqs. (13)-(14); §3.4, Eq. (17)] The SIDIS prediction rests on the transverse-momentum-dependent factorization ansatz of Eqs. (13)-(14), which is asserted rather than derived ('A similar theorem should apply here'; 'We expect that a proof can be given just as in the Drell-Yan case'). The authors are commendably explicit that this is an expectation, and I do not ask for the theorem to be proved here. What I do ask is that the conditional status be carried forward to where the prediction is stated: Sec. 4 and the abstract present the sin φ asymmetry as a prediction of the new function, without reminding the reader that the mapping from ΔD̂ to the measured asymmetry depends on an unproved low-q⊥ factorization. A sentence in Sec. 4 stating this, and a statement of the kinematic window in which the ansatz is expected to hold, would make the paper's logical structure honest without weakening it. Relatedly, the Sudakov dilution is mentioned in §3.3 but never estimated; even a qualitative statement of how the asymmetry is expected to scale with Q at fixed q⊥ would help experimentalists judge feasibility.
[Appendix] The appendix concludes that a Sivers-type azimuthal asymmetry in the k⊥ distribution is 'prohibited because QCD is time-reversal invariant', and states that this 'contradicts Sivers' suggestion'. The argument is performed on the bilocal operator without the gauge link, yet §2.1 explicitly notes that 'an appropriate path ordered exponential of the gluon field is needed' for a gauge-invariant definition. This matters here: the PT argument in the appendix uses only the fermion bilinear, and the Wilson line connecting the two fermion fields is not invariant under the same transformation in the same way, particularly for future- versus past-pointing links. The conclusion should therefore be softened, or the argument redone with the gauge link made explicit. A concrete test is available: repeat the appendix's chain of equalities with the path-ordered exponential inserted and check whether the relative sign between the L and R helicity states that gives f̂(LR) = -f̂(LR) survives. This does not affect the paper's central claim about fragmentation, where the final-state interaction argument is independent of this point, but it is a named correctness claim about another author's result and should be stated with the appropriate caveat.
[§6, Eqs. (25) and (28)] The unpolarized model fragmentation function in Eq. (25) is independent of z, which is surprising: the delta function δ⁺((k-p)²-M²) in Eq. (24) and the propagator denominators should leave a nontrivial z dependence after the k⁻ integration, and a fragmentation function that is flat in z over the whole range is not physical. Please recheck the k⁻ integration and, if the z independence is an artifact of the approximations stated (on-shell quark, massless pion, lowest order), say so explicitly. This bears on Eq. (28): the discussion of the apparent z → 0 blow-up is framed as a cancellation, but with A = B = 1 on shell the factor Im A*B vanishes, so the ratio goes to zero rather than merely staying finite. The wording should reflect what the formula actually does, and the z dependence of the analyzing power should be stated once Eq. (25) is corrected.

Minor objections (7)

[§3.4, Eq. (17) and Fig. 3] The rotation of the transversity vector s′ from the initial hadron to the hard-scattering frame is described only in words and a figure. A short explicit formula, or a statement of the rotation angle in terms of the lepton-quark scattering angle, would remove ambiguity for anyone trying to implement the prediction.
[§2.2, Eqs. (4)-(5)] The symbol Δ_T is used in Eq. (2) for the ratio of quark to hadron polarization and again as part of the symbol ΔD̂ in Eq. (4). Since the two quantities have different meanings, a notational distinction would help the reader.
[§3.4, Eq. (15)] The coefficient q⊥M/(q⊥²+M²) is introduced as a rough dimensional estimate. It would be useful to say explicitly that M here is a generic hadronic scale and not a fitted parameter, so that the reader does not mistake Eq. (15) for a prediction of the shape.
[§4] The paper correctly warns that the unpolarized cross section itself has an azimuthal dependence and that one must measure the spin asymmetry rather than the raw azimuthal distribution. A sentence on how the two can be separated experimentally, for example by forming the difference between opposite target polarizations, would strengthen the experimental guidance in what is described as the section of most use to experimentalists.
[§5] The hadron-hadron discussion is very brief and ends with 'More theoretical analysis is needed here.' Either expand it enough to be usable, or label it clearly as a prospect rather than a result.
[References] Reference 5, the companion paper on measuring transversity densities, is listed as 'in preparation'. Since the present paper's hadron-hadron remarks lean on that work, the reader should be told what is and is not contained here.
[§1] There are several typographical and production problems in the text as submitted, including 'Methods for treating twist-3 effects are currently begin developed' (should be 'being developed') and broken inter-word spacing throughout the abstract and body. These should be cleaned up in the final version.

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The paper

The paper claims

Collins argues that the azimuthal arrangement of hadrons around a jet axis carries the transverse spin of the quark that started the jet, and that this imprint is described by a new leading-power fragmentation function rather than a power-S

The reading

Collins asks whether the transverse spin of the quark that initiates a jet can be read off from how the hadrons in that jet are arranged around the jet axis. His answer is yes: a transversely polarized quark should fragment with a $/sin/varphi$ dependence on the azimuthal angle about the jet axis, and that dependence is carried by a new fragmentation function $/Delta/hat D$ that survives at leading power (twist-2) instead of being suppressed by the hard scale. The practical payoff is a spin asymmetry in semi-inclusive deep inelastic scattering that needs only an unpolarized electron beam on a transversely polarized nucleon, plus an analogous asymmetry in singly polarized hadron-hadron collisions with two high-$p_/perp$ hadrons nearly back-to-back in azimuth. Because the effect requires a quark helicity flip inside the fragmentation process, Collins argues it gives a direct handle on spontaneous chiral symmetry breaking in hadronization, which is otherwise hard to isolate experimentally.

What carries the argument

The load-bearing object is the transversity-weighted fragmentation function of eq. (4): a quark-to-hadron matrix element with a $/gamma^+/gamma_5/gamma_/perp/cdot s_/perp$ Dirac insertion, which unlike the unpolarized fragmentation function is not forbidden by time-reversal invariance because hadronization involves nonperturbative final-state interactions with nontrivial phases. This function is fed into an unintegrated factorization ansatz, eq. (14), in which the measured hadron's transverse momentum is the sum of the incoming parton's intrinsic transverse momentum and the transverse momentum generated in fragmentation. The second piece of machinery is the helicity-amplitude computation of the hard scattering, which shows that the hard process transfers transverse spin from the incoming to the outgoing quark with a real, flavor-independent coefficient $C$, so that the whole spin dependence of the low-$q_/perp$ cross section collapses into one factor multiplying the product of the transversity distribution and the new fragmentation function.

Extended reading notes

Core claim

The central claim is that the single-hadron transverse-momentum distribution inside a jet depends on the transverse spin of the fragmenting quark, and that this dependence defines a new twist-2 fragmentation function $/Delta/hat D_{H/a}(z,k_/perp,s_/perp)$, written in eq. (4) as a bilocal quark matrix element with a $/gamma^+/gamma_5/gamma_/perp/cdot s_/perp$ insertion. The allowed angular form is $/epsilon^{/kappa/lambda/mu/nu} s_{/kappa/perp} k_{/lambda/perp} p_{H/mu} n_/nu$, i.e. a $/sin/varphi$ modulation about the jet axis with a kinematic zero at $k_/perp=0$. Collins then embeds this function in a transverse-momentum-dependent factorization formula for semi-inclusive deeply inelastic scattering, computes the hard spin-transfer coefficient from elastic electron-quark helicity amplitudes as $C=(1-y)/(1-y+/tfrac{1}{2}y^2)$ — 100% at small scattering angle, still about 80% at $90^/circ$ — and concludes that the cross section for an unpolarized electron on a transversely polarized nucleon contains a $/sin/varphi$ asymmetry proportional to the product of the quark's transverse polarization in the nucleon, the spin transfer $C$, and the analyzing power of the fragmentation. He estimates a roughly 10% asymmetry, largest in the valence region ($x_{/rm Bj}/gtrsim 0.3$, $z/gtrsim 0.3$) and at $k_/perp$ of a few hundred MeV. A simple chiral-Lagrangian model reproduces the structure, giving $/Delta/hat D/hat D /propto 2M/,/mathrm{Im}(A^*B)/(k_/perp^2+M^2)/,/(1-z)/z/, (s_{y/perp}k_x - s_{x/perp}k_y)$, which vanishes when the quark mass term (chiral symmetry breaking) is switched off.

Load-bearing premise

The whole prediction rests on a transverse-momentum-dependent factorization formula for the low-$q_/perp$ cross section that the paper asserts rather than proves, saying only that a similar theorem should apply here and that a proof is expected to follow the Drell-Yan case.

Editorial extensions

If this is right

Semi-inclusive deep inelastic scattering of an unpolarized electron beam on a transversely polarized nucleon should show a $/sin/varphi$ asymmetry in the hadron distribution about the jet axis, of order 10% in the valence region.
The asymmetry must vanish as $k_/perp/to 0$, peak at $k_/perp$ of a few hundred MeV, and turn into a higher-twist effect at large $k_/perp$, giving a distinctive shape that can be checked independently of the overall normalization.
The asymmetry should differ between $/pi^+$, $/pi^-$, $/pi^0$ and $K^+$ in a pattern that reflects which valence quark the hadron shares with the target and how strange quark-antiquark pairs are created in fragmentation.
The same function should produce a spin asymmetry in singly polarized hadron-hadron collisions when two high-$p_/perp$ hadrons are measured nearly back-to-back in azimuth.
The size of the fragmentation analyzing power measures how strongly the fragmentation process couples to spontaneous chiral symmetry breaking, since the effect requires a quark helicity flip and vanishes in the chiral limit of the model calculation.

Reading between the lines

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

The appendix rules out a spin-dependent transverse-momentum distribution in the initial hadron by a combined parity and time-reversal argument, while allowing the analogous asymmetry in fragmentation because hadronization has final-state interactions with nontrivial phases. That contrast suggests the dividing line is not spin versus no spin but the presence or absence of rescattering phases, so a
Because the model result scales with the quark mass generated by chiral symmetry breaking, the measured analyzing power is in effect a hadronic-scale measurement of how much of the constituent quark mass survives inside a jet; comparing the asymmetry for pions and kaons would probe whether the same mass generation operates for strange quarks.
The Sudakov broadening the author flags as spin-independent will smear the transverse-momentum distribution and dilute the asymmetry as the hard scale rises. Measuring the asymmetry as a function of $Q$ at fixed $x$, $z$ and $k_/perp$ would test whether that dilution is purely kinematic or whether spin-dependent evolution is also present.
A nonzero asymmetry in the two-hadron hadron-hadron channel, where the initial-state spin enters only through a valence quark, would let one separate the transversity distribution of the nucleon from the fragmentation analyzing power without needing a lepton beam.

Original abstract

It is shown that the azimuthal dependence of the distribution of hadrons in a quark jet is a probe of the transverse spin of the quark initiating the jet. This results in a new spin-dependent fragmentation function that acts at the twist-2 level. One example of a process where it contributes is semi-inclusive deeply inelastic scattering with a transversely polarized nucleon target but with an {\em unpolarized} electron beam. This process is treated in detail. Another process is the cross section for singly polarized hadron-hadron scattering when two high $p_{\perp}$ hadrons are measured in the final state and are close to back-to-back in azimuth. The new fragmentation function is sensitive to the coupling of the fragmentation process to (spontaneous) chiral symmetry breaking.

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, 4,913 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · 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.

It is shown that the azimuthal dependence of the distribution of hadrons in a quark jet is a probe of the transverse spin of the quark initiating the jet. This results in a new spin-dependent fragmentation function that acts at the twist-2 level. One example of a process where it contributes is semi-inclusive deeply inelastic scattering with a transversely polarized nucleon target but with an {\em unpolarized} electron beam. This process is treated in detail. Another process is the cross section for singly polarized hadron-hadron scattering when two high $p_{\perp}$ hadrons are measured in the final state and are close to back-to-back in azimuth. The new fragmentation function is sensitive to the coupling of the fragmentation process to (spontaneous) chiral symmetry breaking.

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	It is shown that the azimuthal dependence of the distribution of hadrons in a quark jet is a probe of the transverse spin of the quark initiating the jet.	result 0.80	0.80	0.84	asserted 1.00
s1	This results in a new spin-dependent fragmentation function that acts at the twist-2 level.	contribution 0.50	0.80	0.22	asserted 1.00
s2	One example of a process where it contributes is semi-inclusive deeply inelastic scattering with a transversely polarized nucleon target but with an {\em unpolarized} electron beam.	contribution 0.70	0.32	0.06	asserted 0.91
s3	This process is treated in detail.	contribution 0.66	0.60	0.02	asserted 0.75
s4	Another process is the cross section for singly polarized hadron-hadron scattering when two high $p_{\perp}$ hadrons are measured in the final state and are close to back-to-back in azimuth.	contribution 0.87	0.37	0.05	asserted 0.96
s5	The new fragmentation function is sensitive to the coupling of the fragmentation process to (spontaneous) chiral symmetry breaking.	interpretation 0.92	0.59	0.10	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.90.

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.** Kinematics of semi-inclusive deeply inelastic scattering.

**Figure 2.** Parton model for semi-inclusive deeply inelastic scattering.

**Figure 3.** Relation between spin vectors for initial and final state quar

**Figure 4.** Lowest order graph for fragmentation of quark to pion. Th

Figures reproduced from arXiv:hep-ph/9208213 by the authors.

References

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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.
The transverse momentum distribution of hadrons within jets
hep-ph 2017-05 accept novelty 6.0 of 10

The transverse momentum of hadrons relative to the jet axis factorizes in terms of standard transverse-momentum-dependent fragmentation functions evaluated at the jet scale, giving direct access to the poorly constrai...
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.
A Unified Treatment of the QCD Evolution of All (Un-)Polarized TMD Functions: Collins Function as a Study Case
hep-ph 2014-02 conditional novelty 6.0 of 10

All sixteen leading-twist TMD distribution and fragmentation functions share a single, spin-independent QCD evolution kernel, derived here to NNLL accuracy and applied to the Collins function.
Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k_T
hep-ph 2011-10 conditional novelty 6.0 of 10

The authors define fully unintegrated beam and fragmenting jet functions, compute their one-loop matching coefficients onto standard PDFs and FFs, and correct two previously published mixing coefficients.
Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering
hep-ph 2011-07 accept novelty 6.0 of 10

Weighting semi-inclusive deep inelastic scattering by Bessel functions of the hadron transverse momentum yields observables in which TMD convolutions become products and soft-gluon factors cancel.
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...
Transverse force distributions in the proton from lattice QCD
hep-lat 2025-02 conditional novelty 5.0 of 10

Lattice QCD computes the transverse spatial distribution of the colour-Lorentz force on the struck quark in a proton, finding local forces up to about 3 GeV/fm, larger than the QCD string tension.
The gluon Sivers function and its process dependence from RHIC data
hep-ph 2019-08 conditional novelty 5.0 of 10

A combined analysis of RHIC pion and D-meson spin asymmetries yields first rough constraints on the two independent gluon Sivers functions in the CGI-GPM.
Statistical analysis of the azimuthal asymmetry in the $J/\psi$ leptoproduction in unpolarized $ep$ collisions
hep-ph 2019-08 conditional novelty 5.0 of 10

In a selected kinematic region, the measured cos(psi) and cos(2psi) azimuthal asymmetries of J/psi leptoproduction can separate the color-singlet model, the 1S0[8]-dominant NRQCD picture, and the equal-color-octet NRQ...
Hadron Fragmentation Inside Jets in Hadronic Collisions
hep-ph 2015-06 accept novelty 5.0 of 10

An analytical NLO calculation recasts hadron-in-jet production in pp collisions as a convolution of partonic cross sections with universal jet functions, validated to within 3% of a prior Monte Carlo result.
Fragmentation contribution to the transverse single-spin asymmetry in proton-proton collisions
hep-ph 2012-12 conditional novelty 5.0 of 10

The authors derive the collinear twist-3 fragmentation contribution to the transverse single-spin asymmetry in p↑p → hX, including quark-quark and quark-gluon-quark correlators, and present the result as a compact for...
Model Independent Evolution of Transverse Momentum Dependent Distribution Functions (TMDs) at NNLL
hep-ph 2012-08 conditional novelty 5.0 of 10

The authors derive an NNLL resummation of the TMD evolution kernel that is parameter-free in the perturbative region and matches the CSS approach when the running coupling is treated consistently.
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.
Resummation for Polarized Semi-Inclusive Deep-Inelastic Scattering at Small Transverse Momentum
hep-ph 2006-02 accept novelty 5.0 of 10

The authors derive NLL-resummed cross sections for five polarized SIDIS channels and find numerically that resummation and non-perturbative effects largely cancel in the longitudinal double-spin asymmetry.
Collins effect in pion-in-jet production in polarized $pp$ and $ep$ collisions
hep-ph 2026-07 accept novelty 4.5 of 10

Collins asymmetries for pion-in-jet production match STAR pp data and yield large, clean predictions at EIC kinematics that probe transversity including its sea component.
Impact of Future Dihadron Production Measurements on the Transversity Distributions and Tensor Charges of the Nucleon
hep-ph 2026-05 unverdicted novelty 4.0 of 10

Pseudo-data from CLAS12, SoLID, and ePIC experiments are incorporated into the JAMDiFF analysis to forecast reduced uncertainties on transversity PDFs at intermediate-to-large x from JLab and across all x from EIC, pl...
Collins asymmetries for pion-in-jet production in polarized $\ell p$ collisions at the EIC
hep-ph 2026-05 unverdicted novelty 4.0 of 10

Collins asymmetries for pion-in-jet production in polarized lepton-proton collisions provide clearer access to transversity distributions at the EIC and test the universality of the Collins function.
Strong Interaction Physics at the Luminosity Frontier with 22 GeV Electrons at Jefferson Lab
nucl-ex 2023-06 conditional novelty 4.0 of 10

Doubling CEBAF's electron energy to 22 GeV would give a high-luminosity fixed-target program filling the kinematic gap between JLab at 12 GeV and the Electron-Ion Collider, according to simulation projections across e...
Single-spin asymmetries: the Trento conventions
hep-ph 2004-10 accept novelty 4.0 of 10

The paper fixes a common set of definitions, signs, and azimuthal-angle conventions for transverse-momentum-dependent parton distributions and fragmentation functions in semi-inclusive deep inelastic scattering.
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...
Azimuthal Asymmetries in Unpolarised Semi-Inclusive DIS at COMPASS
hep-ex 2022-01 unverdicted novelty 3.0 of 10

COMPASS extracts cos φ_h, cos 2φ_h and sin φ_h azimuthal asymmetries from 2016-2017 muon-hydrogen SIDIS data and reports qualitative agreement with prior isoscalar-target results after a new diffractive vector-meson b...
Update on transversity and Collins functions from SIDIS and e+ e- data
hep-ph 2008-12 conditional novelty 3.0 of 10

Refitting HERMES, COMPASS and Belle azimuthal asymmetries jointly tightens the extracted u and d transversity distributions and the favoured and unfavoured Collins fragmentation functions.
Parton Fragmentation Functions
hep-ph 2026-10 accept novelty 2.0 of 10

A comprehensive pedagogical review of parton fragmentation functions covering their operator definitions, DGLAP evolution, experimental probes, global fitting methodology, and extensions to spin, transverse momentum, ...
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...
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 ...
Parton Distribution Functions and their Generalizations
hep-ph 2025-07 unverdicted novelty 1.0 of 10

A textbook-style introduction to the definitions, QCD properties, experimental access, and current phenomenological status of PDFs and their generalizations.
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 the literature uses it

141 arXiv papers cite this in 187 sentences

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

Papers whose main result relates to this one's

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

States the same result 1 paper

We show how the transverse polarization of a quark initiating a jet can be probed by the azimuthal distribution of two hadrons (of large $z$) in the jet.

Measuring transversity densities in singly polarized hadron-hadron and lepton-hadron collisions · 0.90

Papers citing it · 84 sentences without a confident label

Contests it 1 paper

The original proof on the vanishing of the Sivers function [ref] , obtained applying space- and time-reversal to the quark fields in the operator definition of the parton densities, was then incomplete, because it ignored the presence of Wilson lines.

Azimuthal and Single Spin Asymmetries in Hard Scattering Processes · QCD developments · contest 0.91

Uses its method or tool 1 paper

In order to have access to all fracture functions one has to "measure" the scattered quark transverse polarization, for example exploiting he Collins effect [ref] – the azimuthal correlation of the fragmenting quark transverse polarization, $s'_T$, with the produced hadron transverse momentum, $p_⊥$:

Correlations between SIDIS azimuthal asymmetries in target and current fragmentation regions · Double hadron leptoproduction (DSIDIS) · 0.85

Cites it as background 89 papers

The distribution of fragmenting $π$ from a linearly polarized gluon is given by the Collins' function $H^(z,k_)$ [ref] .

Azimuthal Anisotropy at high transverse momentum in $p$-$p$ and $p$-$A$ collisions · Introduction · 0.83
In 1993, Collins suggested that it could be measured in SIDIS processes, where it appears coupled with another chiral-odd function [ref] , the so-called Collins fragmentation function $H_1q^h$.

High-statistics measurement of Collins and Sivers asymmetries for transversely polarised deuterons · Introduction · 0.87
The fragmentation of a transversely polarized quark in an unpolarized hadron is described by the function [ref] [equation] where $m_h$ is the hadron mass.

Recursive fragmentation of a polarized quark · The fragmentation functions and the Collins effect · 0.90

Discussion

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