The role of Cahn and Sivers effects in Deep Inelastic Scattering

A. Kotzinian; A. Prokudin; F. Murgia; M. Anselmino; M. Boglione; U. D'Alesio

REVIEW

The role of Cahn and Sivers effects in Deep Inelastic Scattering

M. Anselmino, M. Boglione, U. D'Alesio, A. Kotzinian, F. Murgia, A. Prokudin

High Energy Physics - Phenomenology · Submitted 20 Jan 2005 · 34 references

Pith's verdict: The Cahn-effect half is a clean, useful fit; the Sivers half is a 13-parameter ansatz railed against its own positivity bound, and should be read as an existence proof rather than a determination.

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arXiv IDhep-ph/0501196 (version 2)

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CitationA. Kotzinian, A. Prokudin, F. Murgia, M. Anselmino, M. Boglione, U. D'Alesio. "The role of Cahn and Sivers effects in Deep Inelastic Scattering." arXiv:hep-ph/0501196 (2005). https://pith.science/paper/JJCMEH23

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Editor's note

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Worth your time, but read the two halves differently. The Cahn-effect analysis (Sec. III) is the solid part: two Gaussian widths, ⟨k⊥²⟩ = 0.25 and ⟨p⊥²⟩ = 0.20 GeV², fitted jointly to EMC φh and P_T² distributions and to E665 ⟨cos φh⟩, with the exact-kinematics and O(k⊥/Q) curves lying almost on top of each other in Figs. 4–6. That agreement is the real evidence that the truncation is under control, and the authors are upfront about the ~1 GeV/c ceiling where NLO takes over. The machinery itself is Cahn and Kotzinian; the new thing is carrying exact k⊥ through both distribution and fragmentation and applying it consistently. Fine, useful, and I'd cite it for those numbers alone. The Sivers extraction is where I'd slow down, and the stress-test note is right on the numbers. Look at Table 1: N_d^v = −1.0 ± 1.8, N_ū = 1.0 ± 1.9, N_d̄ = −1.0 ± 1.9. Three of six normalizations sit exactly on the |N_q| ≤ 1 bound that Eq. (62) imposes for positivity, with symmetric errors wider than the entire allowed interval. Those are not confidence intervals; the data are excluding values, not measuring them. The paper says as much in words — 'not well constrained', 'large uncertainties are still possible' — so this is acknowledged, not hidden, but the table still reads like a measurement and the abstract's 'predictions ... in agreement with recent preliminary data' [abstract:s3] oversells what the text correctly calls a consistency check. On the other hand, I'd push back on treating the A_UL result as equally fragile. The smallness there is driven mainly by the kinematic suppression sin θγ ≈ 2 m_p x_B/Q in Eq. (55), so the 'negligible and opposite sign' conclusion survives even if the Sivers parameters are junk. That negative result is the most durable thing in the paper. Minor: the comparison with the pp Sivers functions of Ref. [7] is asserted in prose with no figure; a plot would have cost little. For anyone working on transverse spin or TMD extraction, yes, engage with it — as a template and a set of sign/kinematic expectations, not as a determination of the Sivers function. Send it out; the referees should press on the Table 1 errors and the abstract wording, not on the Cahn analysis.

Referee report

Significance

The Cahn-effect analysis is a clean, well-controlled two-parameter extraction from several independent datasets, and the explicit demonstration that the O(k⊥/Q) truncation reproduces the exact-kinematics result in Figs. 4–6 is a useful validation of the approximation used throughout. The Sivers extraction is a timely and physically motivated attempt to connect SIDIS and pp single-spin asymmetries within a single TMD framework, and the out-of-sample COMPASS comparison in Fig. 10 is the right kind of falsifiable test. The paper is honest about the preliminary nature of the data and about the open question of Sivers universality. The main weakness is that the quantitative status of the extracted Sivers functions is weaker than the headline claims suggest.

Major objections (4)

[Table 1, §IV.A Eq. (62)] Three of the six Sivers normalization parameters sit exactly on the positivity bound |N_q| ≤ 1 imposed in Eq. (62): N_d^v = −1.0 ± 1.8, N_ū = 1.0 ± 1.9, N_d̄ = −1.0 ± 1.9. A parameter confined to [−1, 1] cannot carry a symmetric uncertainty larger than the allowed range, so the quoted errors are not interpretable as confidence intervals; MINUIT errors at a boundary are known to be unreliable. The same concern applies to M′² = 0.36 ± 0.43 (GeV/c)², whose error exceeds its central value and admits unphysical negative values. The χ²/d.o.f. = 0.89 is therefore being achieved with several parameters railed at the prior edge, and the table presents as measurements numbers that are, for d-valence and both sea flavors, essentially the boundary of the allowed box. This is load-bearing because the COMPASS prediction of Fig. 10 and the A_UL estimate of Fig. 11 are computed from these same values. The authors should either report the fit with the bound removed (or relaxed) to show where the data actually place these parameters, or state explicitly in the table caption and in §IV.B that the d-valence and sea normalizations are bounded rather than determined, and propagate that into the interpretation of the derived predictions.
[§IV.B, Fig. 10, abstract sentence s3] The claim that the extracted Sivers functions 'give predictions for the COMPASS measurement ... in agreement with recent preliminary data' is stated more strongly than Fig. 10 supports. The preliminary COMPASS points shown are largely consistent with zero within their error bars, so 'agreement' here is a weak test that a broad range of Sivers parameter sets would also pass. Combined with the degeneracy of Table 1 noted above, a reader cannot distinguish a genuine out-of-sample success from the fact that a wide, weakly constrained parameter set happens to overlap the data. The authors should quantify the comparison (e.g. a χ² against the preliminary points, or a statement of which parameter combinations the COMPASS points actually constrain) rather than describing it as agreement.
[§III → §IV, Eqs. (65)–(67)] The Gaussian widths ⟨k⊥²⟩ and ⟨p⊥²⟩ are fixed from the Cahn-effect fit of §III and then held fixed in the Sivers fit of §IV, but the 20% variation shown as the shaded band in Figs. 5 and 6 is not propagated into the Table 1 errors. Since the approximate asymmetry of Eqs. (65)–(67) depends explicitly on these widths through ⟨k⊥²⟩̂ and ⟨P_T²⟩̂, the quoted Sivers parameter errors underestimate the total uncertainty. The authors should either propagate the width uncertainty into Table 1 or state clearly that the quoted errors are conditional on the fixed widths, and indicate how much the Sivers parameters and the Fig. 10/11 curves shift under a 20% variation of ⟨k⊥²⟩ and ⟨p⊥²⟩.
[§IV.B, Fig. 11, Eq. (57)] The statement that 'the Sivers mechanism contributes with opposite signs to the transverse and longitudinal SSA, as can be seen from Eqs. (57) and (58)' is presented as a dynamical property of the Sivers mechanism, but the relative minus sign follows directly from the kinematic projection S_T = −sin θγ (1,0,0) in Eq. (55), which makes S_T·(P̂×k̂⊥) = −sin θγ sin φ. This is a frame-dependent geometric factor, not a statement about the Sivers function itself, and the phrasing risks being read as a physical prediction. Relatedly, 'negligible' in the abstract and conclusions should be quantified against the uncertainty band of Fig. 11, since in several bins the shaded band is comparable to the central curve.

Minor objections (6)

[Appendix A, Fig. 4] Appendix A shows that the exact expression contains a cos 2φh term, and the dashed curve in Fig. 4 hints at a positive cos 2φh contribution at small φh, but the fit form of Eq. (38) retains only cos φh. It would help to state explicitly whether the extracted widths would shift if a cos 2φh term were included in the fit.
[§IV.B] The number of data points entering the Sivers fit and the definition of χ² are not given, so the reader cannot judge the χ²/d.o.f. = 0.89 in Table 1. Please state both.
[abstract sentence s2, §IV.B] The statement that the SIDIS and E704 Sivers functions are 'not inconsistent' is qualitative; no statistical measure of consistency is provided. Since the paper itself says the comparison 'cannot be considered as conclusive', it would be clearer to say 'compatible within present uncertainties' and to state which observables would discriminate.
[§IV.B, comparison with Ref. [7]] The remark that the Table 1 functions 'would overestimate the data at small xF' and that this 'could be easily corrected by gluon contributions' is speculative and is not backed by a calculation in the manuscript. Either show the comparison or flag it explicitly as a conjecture.
[Figs. 8–11] The figure captions should state the number of data points per panel and clarify that the third column of Figs. 8 and 9 contains predictions, not data, so that the distinction is unambiguous to a reader skimming the figures.
[Eqs. (50), (55), abstract] There are typographical issues: the abstract renders 'p↑p' as 'pup p', and the inline notation 'Asin φπU L' in §IV and the conclusions is hard to parse; please use the superscript/subscript form consistently, e.g. A_UL^{sin φπ}.

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The paper

The paper claims

The azimuthal asymmetries of semi-inclusive deep inelastic scattering can be described with a single Gaussian model of intrinsic quark and hadron transverse momenta, and the leftover spin asymmetry then yields quark Sivers functions that, f

The reading

The paper asks whether the small transverse momenta that quarks carry inside the proton, and that hadrons carry inside the fragmenting quark jet, can be pinned down from ordinary unpolarized data and then reused, without refitting, to explain a spin asymmetry. The authors compute the Cahn effect — the $(-4(2-y)$-type $)$ $(-)$ dependence of the unpolarized $lp to l h X$ cross section on the angle $varphi_h$ between the lepton plane and the hadron plane — with exact leading-order kinematics and Gaussian transverse-momentum Ansätze, and fit it against EMC and E665 data to obtain $langle k_perp^2 rangle = 0.25$ and $langle p_perp^2 rangle = 0.20$ in $(mathrm{GeV}/c)^2$. Those numbers are then frozen and used to fit simple parametric Sivers functions, the spin-and-transverse-momentum correlation in the proton, to the HERMES measurement of $A_{UT}^{sin(varphi_pi - varphi_S)}$. The payoff claimed is consistency: the same functions, with no adjustment, land near the preliminary COMPASS points taken at a different beam energy and target, and they contribute almost nothing — with the wrong sign — to the HERMES longitudinal asymmetry $A_{UL}^{sin varphi_pi}$, which suggests that asymmetry is not Sivers-driven at all.

What carries the argument

The load-bearing object is the Sivers function $Delta^N f_{q/p^uparrow}(x,k_perp)$, the part of the quark distribution that flips sign with the azimuth of the quark transverse momentum relative to the proton spin, entering the cross section through $S_T cdot (hat P times hat k_perp) = sin(varphi - varphi_S)$. It is parameterized as $2 N_q(x), h(k_perp), f_{q/p}(x,k_perp)$ with $N_q(x) = N_q x^{a_q}(1-x)^{b_q}(a_q+b_q)^{a_q+b_q}/(a_q^{a_q} b_q^{b_q})$ and $h(k_perp) = sqrt{2e}, k_perp/M' exp(-k_perp^2/M'^2)$, a form chosen so that $|N_q(x)| le 1$ automatically satisfies the positivity bound and so that the $k_perp$ integral can be done analytically. The Gaussian widths $langle k_perp^2 rangle$ and $langle p_perp^2 rangle$ are what convert a measured $P_T$ distribution into a constraint on the unintegrated functions, and the combination $langle P_T^2 rangle = langle p_perp^2 rangle + z_h^2 langle k_perp^2 rangle$ is the bridge between the unpolarized fit and the polarized prediction.

Extended reading notes

Core claim

The central claim is that a two-parameter description of intrinsic transverse motion, extracted purely from the azimuthal and $P_T$ dependence of the unpolarized semi-inclusive cross section, is sufficient to support a quantitative extraction of the quark Sivers functions from a single weighted spin asymmetry. Concretely, the authors fit $langle k_perp^2 rangle = 0.25 (mathrm{GeV}/c)^2$ and $langle p_perp^2 rangle = 0.20 (mathrm{GeV}/c)^2$ to the EMC $varphi_h$ distributions, the EMC $P_T^2$ spectra and the E665 $langle cos varphi_h rangle$ versus $P_T^{cut}$ data, showing that the exact-kinematics and $O(k_perp/Q)$ treatments agree closely up to $P_T approx 1$ GeV/$c$. Holding those widths fixed, they fit 13 parameters describing valence and sea Sivers functions for $u$ and $d$ quarks to HERMES $A_{UT}^{sin(varphi_pi - varphi_S)}$ data with $chi^2/mathrm{d.o.f.} = 0.89$, finding $N_{u_v} = 0.42 pm 0.18$ and $N_{d_v} = -1.0 pm 1.8$. The resulting functions reproduce preliminary COMPASS $A_{UT}^{sin(varphi_h - varphi_S)}$ on a deuteron target at 160 GeV/$c$ within the large errors, are not inconsistent with the Sivers functions previously fitted to $p^uparrow p to pi X$ data, and give a negligible, oppositely signed contribution to HERMES $A_{UL}^{sin varphi_pi}$.

Load-bearing premise

That the $sin(varphi_h - varphi_S)$ moment of the HERMES asymmetry receives contributions from the Sivers term alone, so that the measured number maps directly onto the 13-parameter Sivers ansatz rather than onto a mixture with Collins or higher-twist effects.

Editorial extensions

If this is right

The widths $langle k_perp^2 rangle = 0.25$ and $langle p_perp^2 rangle = 0.20$ $(mathrm{GeV}/c)^2$ become a reusable input for any leading-order calculation of semi-inclusive deep inelastic scattering in the low-$P_T$ region.
The Sivers functions fitted here make definite, checkable predictions for COMPASS positively and negatively charged hadron asymmetries as functions of $x_B$, $z_h$ and $P_T$, and for kaon asymmetries $A_{UT}^{sin(varphi_K - varphi_S)}$ at HERMES.
Because the Sivers contribution to $A_{UL}^{sin varphi_pi}$ comes out small and of opposite sign to the transverse case, the measured longitudinal asymmetry must be attributed mainly to the Collins mechanism or to higher-twist terms.
The comparison with Sivers functions extracted from $p^uparrow p to pi X$ leaves open, but does not exclude, the possibility that a single set of Sivers functions describes both semi-inclusive deep inelastic scattering and proton-proton pion production.
The agreement between the exact-kinematics and $O(k_perp/Q)$ evaluations up to $P_T approx 1$ GeV/$c$ justifies using the much simpler approximate formulas in future fits.

Reading between the lines

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

The extraction is only as clean as the assumption that the $sin(varphi_h - varphi_S)$ moment isolates the Sivers term; the paper invokes the weighting argument but never tests for leakage from the Collins mechanism or from higher twist, so the fitted parameters could be absorbing physics that the ansatz does not contain.
The Gaussian, flavour-independent, $x$- and $z$-independent widths are a strong simplification; a measurement of $langle k_perp^2 rangle$ separately in $u$ and $d$ quark samples, or its variation with $x_B$, would directly probe whether this scaffolding is adequate.
Because the Sivers functions in semi-inclusive deep inelastic scattering and in Drell-Yan are expected to carry opposite signs, a Drell-Yan asymmetry measurement in the same $x$ range would be a sharp, independent test of the sign convention adopted here.
The 13-parameter fit rests on a small data set with large errors, so the central values of the sea-quark parameters are essentially unconstrained; a future global fit combining HERMES, COMPASS and Jefferson Lab kinematics would be the natural way to shrink them.

Original abstract

The role of intrinsic $\bfk_\perp$ in inclusive and semi-inclusive Deep Inelastic Scattering processes ($\ell p \to \ell h X$) is studied with exact kinematics within QCD parton model at leading order; the dependence of the unpolarized cross section on the azimuthal angle between the leptonic and the hadron production planes (Cahn effect) is compared with data and used to estimate the average values of $k_\perp$ both in quark distribution and fragmentation functions. The resulting picture is applied to the description of the weighted single spin asymmetry $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ recently measured by the HERMES collaboration at DESY; this allows to extract some simple models for the quark Sivers functions. These are compared with the Sivers functions which succeed in describing the data on transverse single spin asymmetries in $\pup p \to \pi X$ processes; the two sets of functions are not inconsistent. The extracted Sivers functions give predictions for the COMPASS measurement of $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ in agreement with recent preliminary data, while their contribution to HERMES $A_{UL}^{\sin\phi_\pi}$ is computed and found to be small. Predictions for $A_{UT}^{\sin(\phi_K - \phi_S)}$ for kaon production at HERMES are also given.

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, 4,694 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.24 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.22 · compares with prior results 0.94 · 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.

The role of intrinsic $\bfk_\perp$ in inclusive and semi-inclusive Deep Inelastic Scattering processes ($\ell p \to \ell h X$) is studied with exact kinematics within QCD parton model at leading order; the dependence of the unpolarized cross section on the azimuthal angle between the leptonic and the hadron production planes (Cahn effect) is compared with data and used to estimate the average values of $k_\perp$ both in quark distribution and fragmentation functions. The resulting picture is applied to the description of the weighted single spin asymmetry $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ recently measured by the HERMES collaboration at DESY; this allows to extract some simple models for the quark Sivers functions. These are compared with the Sivers functions which succeed in describing the data on transverse single spin asymmetries in $\pup p \to \pi X$ processes; the two sets of functions are not inconsistent. The extracted Sivers functions give predictions for the COMPASS measurement of $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ in agreement with recent preliminary data, while their contribution to HERMES $A_{UL}^{\sin\phi_\pi}$ is computed and found to be small. Predictions for $A_{UT}^{\sin(\phi_K - \phi_S)}$ for kaon production at HERMES are also given.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The role of intrinsic $\bfk_\perp$ in inclusive and semi-inclusive Deep Inelastic Scattering processes ($\ell p \to \ell h X$) is studied with exact kinematics within QCD parton model at leading order; the dependence of the unpolarized cross section on the azimuthal angle between the leptonic and the hadron production planes (Cahn effect) is compared with data and used to estimate the average values of $k_\perp$ both in quark distribution and fragmentation functions.	contribution 0.90	0.87	0.13	asserted 0.99
s1	The resulting picture is applied to the description of the weighted single spin asymmetry $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ recently measured by the HERMES collaboration at DESY; this allows to extract some simple models for the quark Sivers functions.	contribution 0.54	0.84	0.12	asserted 0.92
s2	These are compared with the Sivers functions which succeed in describing the data on transverse single spin asymmetries in $\pup p \to \pi X$ processes; the two sets of functions are not inconsistent.	result 0.88	0.76	0.21	asserted 0.61
s3	The extracted Sivers functions give predictions for the COMPASS measurement of $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ in agreement with recent preliminary data, while their contribution to HERMES $A_{UL}^{\sin\phi_\pi}$ is computed and found to be small.	result 1.00	0.90	0.27	asserted 1.00
s4	Predictions for $A_{UT}^{\sin(\phi_K - \phi_S)}$ for kaon production at HERMES are also given.	result 0.70	0.90	0.06	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from analysis of existing data 0.98.

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

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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.** Such a dependence, resulting from ˆs 2 + ˆu 2 , Eqs. (8) and (9), was suggested by Cahn [3], in semi-inclusive DIS, assuming that the fragmentation process q → hX is essentially collinear and the direction of the final detected hadron is close to that of the quark. Smearing effects due to the fragmentation process were also taken into account [3, 4, 23]. In the next subsection we shall consider SIDIS processes, fully taking into account the intrinsic motion and the angular dependence in the fragmentation process; we shall see that indeed a dependence on an azimuthal angle remains,…

**Figure 2.** FIG. 2: Kinematics of the fragmentation process.

**Figure 3.** FIG. 3: Three dimensional kinematics of the SIDIS process.

**Figure 4.** shows our fits to two sets of data [6], corresponding to two different ranges of xF . The solid bold line shows the result we obtain by taking into account only O(k⊥/Q) contributions, Eq. (38), whereas the dashed line corresponds to the exact result at all orders in k⊥/Q, Eq. (31). The (− cosφh) behaviour, explicit in Eq. (38), is indeed shown by the data. A possible positive contribution from a cos(2φh) term seems to be visible at small values of φh (dashed line). Other interesting EMC data [31] concern the P 2 T dependence of the cross section for µp and µd scattering at incident…

**Figure 5.** FIG. 5: The normalized cross section

**Figure 9.** FIG. 9: Predictions for kaon asymmetries

**Figure 10.** FIG. 10: COMPASS preliminary data [16] on

Showing 10 of the paper's 11 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0501196 by the authors.

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A.V. Efremov, K. Goeke and P. Schweitzer, Phys. Lett. B568 (2003) 63 18 0 0.1 0.2 A UT sin (fp- fS ) p0 p0 p0 0 0.1 0.2 A UT sin (fp- fS ) p+ p+ p+ 0 0.1 0.2 0.25 0.5 zh A UT sin (fp- fS ) p- 0 0.2 xbj p- 0 0.5 1 PT (GeV) p- FIG. 8: HERMES data on Asin(φπ −φS )U T [10] for scattering oﬀ a transversely polarized proton targ et and pion production. The curv...

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Forward citations

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Polarized jet anisotropy at the Electron-Ion Collider
hep-ph 2026-08 conditional novelty 8.0 of 10

Jet-induced soft-gluon anisotropy imposes a parity selection rule on polarized asymmetries: even and odd harmonics of the Sivers and worm-gear functions have opposite left-right symmetry.
Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum
hep-ph 2008-03 accept novelty 7.0 of 10

The low- and high-transverse-momentum descriptions of semi-inclusive deep inelastic scattering agree for some structure functions and disagree for others; the cos(phi_h) disagreement exposes a failure of naive twist-t...
Next-to-next-to-leading power corrections to unpolarized Semi-Inclusive Deep Inelastic Scattering
hep-ph 2026-01 conditional novelty 6.0 of 10

Analytic 1/Q² corrections to the four unpolarized SIDIS structure functions are derived from the rapidity-factorization 'gauge-completion' approach, giving f1⊗D1 and h1^⊥⊗H1^⊥ convolutions with numerical estimates for...
Origin of single transverse-spin asymmetries in high-energy collisions
hep-ph 2020-02 conditional novelty 6.0 of 10

A simultaneous fit to spin-asymmetry data from SIDIS, Drell-Yan, electron-positron annihilation, and proton-proton collisions supports a common multi-parton origin for single transverse-spin asymmetries and yields ten...
Investigations into the flavor dependence of partonic transverse momentum
hep-ph 2013-09 conditional novelty 6.0 of 10

Fitting HERMES multiplicities with flavor-dependent Gaussian widths shows favored pion fragmentation functions have about 20% smaller mean transverse momentum than unfavored and kaon fragmentation functions.

Show 21 more citing papers

Calculation of TMD Evolution for Transverse Single Spin Asymmetry Measurements
hep-ph 2011-12 conditional novelty 6.0 of 10

Applying Collins-Soper-Sterman transverse-momentum evolution to an existing Sivers function fit reproduces preliminary COMPASS proton asymmetries from HERMES-scale input, with no refitting to COMPASS.
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.
Twist-3 effects in fully inclusive jet production from $e^+e^-$ annihilation
hep-ph 2026-07 conditional novelty 5.0 of 10

Twist-3 corrections to e+e- -> hadron + inclusive jet are derived including weak interactions, yielding two azimuthal asymmetries that can expose the Collins fragmentation function at future colliders.
Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum
hep-ph 2019-12 conditional novelty 5.0 of 10

Drell-Yan data alone fix the unpolarized TMD parton distribution and the rapidity anomalous dimension well enough that SIDIS multiplicities are then described with only four additional fragmentation parameters, suppor...
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.
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.
A strategy towards the extraction of the Sivers function with TMD evolution
hep-ph 2012-04 conditional novelty 5.0 of 10

Applying TMD evolution to the Sivers extraction lowers the total chi-squared from 316 to 256, with the improvement concentrated in the high-Q² COMPASS proton data.
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.
The Boer-Mulders effect in unpolarized SIDIS: an analysis of the COMPASS and HERMES data on the $\cos 2 \phi$ asymmetry
hep-ph 2009-12 conditional novelty 5.0 of 10

A two-parameter fit to COMPASS and HERMES cos 2 phi asymmetry data supports the interpretation that the Boer-Mulders transverse-spin distribution drives the observed asymmetry.
Sivers Effect for Pion and Kaon Production in Semi-Inclusive Deep Inelastic Scattering
hep-ph 2008-05 conditional novelty 5.0 of 10

A global fit to HERMES and COMPASS pion and kaon Sivers asymmetries yields u, d, and sea-quark Sivers distributions, with the strange-antiquark Sivers function pinned at the positivity bound.
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.
Predictions for double spin asymmetry A_{LT} in Semi Inclusive DIS
hep-ph 2006-03 conditional novelty 5.0 of 10

The paper computes the SIDIS double-spin asymmetry A_LT from helicity distributions via the Lorentz invariance and Wandzura-Wilczek relations, predicting small effects that grow to a few percent only with ad hoc choic...
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...
Applications of the WW-type approximation to SIDIS
hep-ph 2019-07 unverdicted novelty 4.0 of 10

Applies the WW-type approximation to relate TMDs and FFs and approximate the complete SIDIS cross-section up to power-suppressed terms.
Intrinsic transverse parton momenta in deeply inelastic reactions
hep-ph 2010-03 conditional novelty 4.0 of 10

The Gauss model describes intrinsic transverse parton momenta in SIDIS and Drell-Yan well, and the widths extracted from the two processes are compatible, supporting TMD factorization.
Sivers effect in Drell-Yan processes
hep-ph 2009-01 conditional novelty 4.0 of 10

Sivers asymmetries in Drell-Yan are estimated to reach up to about 15 percent at PAX and around 10 percent at RHIC, large enough to test the predicted sign change relative to SIDIS.
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.
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 later papers used it

61 later papers cite it

Evidence: substantial. 42 of the citing papers share no author with it, and 21 of those carry a confident label from Pith's citation classifier.

Pith read 19 of the 128 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

5 later papers by other authors are listed below: 1 used its method or tool and 4 used its data or values. 7 more papers by the same authors are listed: 7 used its data or values.

Uses its method or tool 1 of 4 papers with this label

Used the SIDIS cross section described in this paper in its Monte Carlo generator.

Fully Differential Monte-Carlo Generator Dedicated to TMDs and Bessel-Weighted Asymmetries (2013) · 0.96 · paraphrased: the licence does not allow quoting

Uses its data or values 11 of 25 papers with this label · 7 by the same authors

Took ⟨k_t^2⟩ = 0.25 GeV^2 from this paper when numerically evaluating the integral I(x,Q^2).

Self-similarity and the Froissart bound (2014) · 0.98 · paraphrased: the licence does not allow quoting
Chose the Gaussian width p_un^2 = 0.25 GeV^2 for f_1^q(x,p_T^2) following the value given in this paper.

Updating Boer-Mulders functions from unpolarized pd and pp Drell-Yan data (2009) · 0.97 · paraphrased: the licence does not allow quoting
Fixed the width of the unpolarized fragmentation function K^2_D_1 = 0.20 GeV^2 from this paper's study of data on the Cahn effect.

Are there approximate relations among transverse momentum dependent distribution functions? (2007) · 0.88 · paraphrased: the licence does not allow quoting
Used the values ≈0.25 GeV^2 and ≈0.20 GeV^2 from this paper, extracted from the old EMC and FNAL SIDIS data.

Consistency tests for the extraction of the Boer-Mulders and Sivers functions (2017) · 0.95 · paraphrased: the licence does not allow quoting

By the same authors

Fixed the values of ⟨k_⊥^2⟩ and ⟨p_⊥^2⟩ to those found in this paper by analysing the Cahn effect in unpolarized SIDIS.

Sivers Effect for Pion and Kaon Production in Semi-Inclusive Deep Inelastic Scattering (2008) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper's value ⟨k_⊥q^2⟩ = 0.25 GeV^2 for quarks in a factorized Gaussian ansatz for the TMDs.

Sivers asymmetry in inelastic $J/\psi$ leptoproduction at the EIC (2021) (same authors) · 0.97 · paraphrased: the licence does not allow quoting
Used the width value 0.25 GeV^2 fitted by this paper in a Gaussian dependence on k_T for the unpolarized parton distribution.

Impact of double TMD effects on transversity measurements at RHIC (2011) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Used the Gaussian widths k_⊥^2 = 0.25 GeV^2 and p_T^2 = 0.20 GeV^2 from this paper.

Global fitting of single spin asymmetry: an attempt (2012) (same authors) · 0.98 · paraphrased: the licence does not allow quoting
Took parametrizations for unpolarized TMD PDF and TMD FF from this paper, with _f_1 = 0.25 GeV^2 and _D_1 = 0.2 GeV^2.

Next-to-next-to-leading power corrections to unpolarized Semi-Inclusive Deep Inelastic Scattering (2026) (same authors) · 0.99 · paraphrased: the licence does not allow quoting
Regarding the collinear FFs of the unpolarized light hadrons, $π$ and $K$, we adopt the DSS07 set [ref] , while for $M_D$ we assume a Gaussian model, compatible with previous extractions, with $⟨p_⊥^2 ⟩= 0.2 GeV^2$ [ref] .

Transverse $\Lambda$ polarization in $e^+e^-$ processes within a TMD factorization approach and the polarizing fragmentation function (2022) (same authors) · Double-hadron production data fit · 0.97
The unpolarized Gaussian widths are taken as $⟨p^2_⊥ ⟩= 0.2$ GeV$^2$ [ref] , for all hadrons.

$\Lambda$ polarizing fragmentation function from Belle $e^+e^-$ data (2021) (same authors) · Results · 0.99

How the literature uses it

53 arXiv papers cite this in 111 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

The extracted Sivers functions give predictions for the COMPASS measurement of $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ in agreement with recent data, while their contribution to HERMES $A_{UL}^{\sin\phi_\pi}$ is computed and found to be small.

Understanding the role of Cahn and Sivers effects in Deep Inelastic Scattering · 0.94

Papers citing it · 60 sentences without a confident label

Uses its method or tool 3 papers

We will use a theoretical scenario [ref] recently developed for the calculation of the Sivers function [ref] , which has reproduced its main features, such as the sign, the Burkardt sum rule [ref] , and the general trend of the parameterizations extracted from the available data [ref] .

Analyzing the Boer-Mulders function within different quark models · Introduction · 0.95
Following Refs. [ref] , we parametrize both the spin-averaged PDF $f_a/A(x, k_⊥^2)$ and FF $D_h/a(z, p_T^2)$ with a Gaussian form for the transverse components: f_a/A(x, k_⊥^2) = f_a/A(x) 1/πk_⊥^2e^-𝐤_⊥^2/k_⊥^2, D_h/a(z, p_T^2) = D_h/a(z) 1/πp_T^2 e^-𝐩_T^2/p_T^2 , such that they reduce to the usual collinear PDF $f_a/A(x)$ and FF $D_h/a(z)$ once integrated over the transverse momentum.

Global fitting of single spin asymmetry: an attempt · Parametrization for the Sivers and ETQS function · 0.98
For this purpose, our main tool is an analysis based on a simple partonic picture in which the cross section is factorized, as in Refs. [ref] .

Transverse parton momenta in single inclusive hadron production in ${e^ + }{e^ - }$ annihilation processes · Final remarks · 0.98

Uses its data or values 21 papers

The results were found p_T^2= 0.25 GeV^2 in [ref] ,0.33 GeV^2 in [ref] , K_T^2= 0.20 GeV^2 in [ref] ,0.16 GeV^2 in [ref] , which are consistent within the unestimated uncertainties involved in the analyses.

Intrinsic transverse parton momenta in deeply inelastic reactions · Introduction · 0.82
A factorization between $k_T$ and $x$ dependence and a Gaussian dependence on $k_T$ will be assumed, i.e. we use for the unpolarized parton distribution [equation] with the value of the width $= 0.25 GeV^2$, fitted by [ref] .

Impact of double TMD effects on transversity measurements at RHIC · Distribution functions · 1.00
The widths of the unpolarized distribution function $f_1(x,k_⊥)$ are taken as $Δ^'^2_u=Δ^'^2_d= 0.53 GeV^2$ [ref] .

Semi-inclusive deeply inelastic neutrino and antineutrino nucleus scattering · The intrinsic asymmetries · 1.00

Compares with it 5 papers

They are compared with a parameterization of the HERMES data, corresponding to an experimental scale of $Q^2=2.5$ GeV$^2$ [ref] [It has been chosen to compare the results with the parameterization of [ref] and not with that of [ref] or [ref] just because, in the first case, it is easier to reconstruct the parameterization of the data, and their 1-sigma range has been kindly provided by the authors of Ref. [24].

A quark model analysis of the Sivers function · The calculation of the Sivers function in the Isgur-Karl model · 0.96
In any case, the good news is that the numbers for the Gauss widths from the works [ref] are confirmed numerically.

Intrinsic transverse parton momenta in deeply inelastic reactions · Determining parameters from HERMES, and cross check with CLAS · 0.82
As a matter of fact, the values of the average momentum $$ extracted from our fit is quite different (one order of magnitude smaller) from that previously extracted in several different fits [ref] .

A phenomenological analysis of azimuthal asymmetries in unpolarized semi-inclusive deep inelastic scattering · Analysis of and · 1.00

Cites it as support 1 paper

This approach, though neglecting tilde-functions from the QCD equations of motion (and the Boer-Mulders effect, see Ref. [ref] for more details), provides a quite satisfactory description of the available data [ref] .

Lorentz invariance relations between parton distributions and the Wandzura-Wilczek approximation · Lorentz invariance relations in a generalized Wandzura-Wilczek approximation · 0.97

Cites it as background 15 papers

Historically, these distributions have been extracted using semi-inclusive deep inelastic scattering (SIDIS) [ref] , where polarized TMDs imprint nontrivial angular correlations that link the parton's transverse motion to the nucleon's spin [ref] .

Polarized jet anisotropy at the Electron-Ion Collider · Introduction · 0.96
As mentioned in the introduction, different studies of unpolarised azimuthal distributions [ref] , hadron multiplicities [ref] and the Sivers SSA in SIDIS processes have been performed.

Role of transverse momentum dependence of unpolarised parton distribution and fragmentation functions in the analysis of azimuthal spin asymmetries · The Sivers case · 1.00
The first attempts to obtain information on the unpolarised TMDs were performed in Refs. [ref] .

Transverse spin effects in hard semi-inclusive collisions · The unpolarised TMD-PDFs · 0.84

Discussion

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A.V. Efremov, K. Goeke and P. Schweitzer, Phys. Lett. B568 (2003) 63 18 0 0.1 0.2 A UT sin (fp- fS ) p0 p0 p0 0 0.1 0.2 A UT sin (fp- fS ) p+ p+ p+ 0 0.1 0.2 0.25 0.5 zh A UT sin (fp- fS ) p- 0 0.2 xbj p- 0 0.5 1 PT (GeV) p- FIG. 8: HERMES data on Asin(φπ −φS )U T [10] for scattering oﬀ a transversely polarized proton targ et and pion production. The curv...

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