pith. sign in

arxiv: 2509.15809 · v3 · submitted 2025-09-19 · ✦ hep-ph · hep-ex· nucl-ex· nucl-th

Accessing nucleon transversity with one-point energy correlators

Mei-Sen Gao , Zhong-Bo Kang , Wanchen Li , Ding Yu Shao This is my paper

Pith reviewed 2026-05-18 15:57 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-exnucl-th
keywords nucleon transversityone-point energy correlatorsingle-spin asymmetrytransversely polarized collisionsjet substructurenucleon structureRHICEIC
0
0 comments X

The pith

In transversely polarized proton collisions the one-point energy correlator develops a single-spin asymmetry that isolates the nucleon's transversity distribution over a wide range of angular scales.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes using the one-point energy correlator as a probe of the nucleon's transversity distribution. In transversely polarized proton-proton collisions this observable develops a single-spin asymmetry with a sin(φ_s - φ_n) angular dependence. The approach reaches a broader range of angular scales θ_n than conventional measurements that rely on the transverse momentum of produced hadrons. A reader would care because transversity encodes essential information about the nucleon's three-dimensional quark structure and remains difficult to access with existing techniques.

Core claim

We demonstrate that in transversely polarized p↑p collisions, the one-point energy correlator exhibits a single-spin asymmetry with a clean sin(φ_s - φ_n) angular dependence. This method probes the nucleon's transversity distribution h_1^q over a much wider kinematic range in the angular scale θ_n compared to traditional measurements of hadron transverse momentum j_⊥. The OPEC is an infrared-and-collinear safe jet substructure observable that can be factorized and computed in perturbative QCD.

What carries the argument

The one-point energy correlator (OPEC), an infrared-and-collinear safe jet substructure observable that measures energy flow at a single point and produces a single-spin asymmetry sensitive to transversity in polarized collisions.

If this is right

  • The single-spin asymmetry provides a direct handle on the transversity distribution h_1^q.
  • The observable extends access to transversity across a wider interval of the angular scale θ_n.
  • This creates a complementary and systematically distinct channel for nucleon structure studies.
  • The method is applicable at RHIC and the future Electron-Ion Collider.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Existing polarized collision data sets could be reexamined to test the predicted asymmetry before new dedicated measurements.
  • The wider angular reach might permit transversity constraints at momentum fractions or scales that are currently inaccessible.
  • Cross-comparison with other jet substructure observables could help validate the underlying factorization assumptions.

Load-bearing premise

The one-point energy correlator can be factorized in perturbative QCD such that the single-spin asymmetry isolates the transversity distribution with negligible contamination from other transverse-momentum-dependent functions or higher-order power corrections.

What would settle it

A measurement of the single-spin asymmetry in the one-point energy correlator that fails to follow the predicted sin(φ_s - φ_n) dependence or shows significant deviation from transversity values obtained from independent channels such as dihadron production.

Figures

Figures reproduced from arXiv: 2509.15809 by Ding Yu Shao, Mei-Sen Gao, Wanchen Li, Zhong-Bo Kang.

Figure 1
Figure 1. Figure 1: FIG. 1. Kinematics of hadron production inside a jet in trans [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. SSA [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. SSA [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. SSA [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We propose a novel probe of the nucleon's transversity distribution, $h_1^q$, using the one-point energy correlator (OPEC), an infrared-and-collinear safe jet substructure observable. We demonstrate that in transversely polarized $p^{\uparrow}p$ collisions, the OPEC exhibits a single-spin asymmetry (SSA) with a clean $\sin(\phi_s - \phi_n)$ angular dependence. This method probes SSA over a much wider kinematic range in the angular scale $\theta_n$ compared to traditional measurements of hadron transverse momentum~$j_\perp$, establishing a complementary and systematically distinct channel to study the nucleon's three-dimensional structure at RHIC and the future Electron-Ion Collider.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes using the one-point energy correlator (OPEC), an infrared-and-collinear safe jet substructure observable, as a novel probe of the nucleon's transversity distribution h_1^q. In transversely polarized p↑p collisions, the OPEC is shown to exhibit a single-spin asymmetry with a clean sin(φ_s - φ_n) angular dependence. This approach is claimed to access the asymmetry over a much wider kinematic range in the angular scale θ_n than traditional measurements based on hadron transverse momentum j_⊥, providing a complementary channel for studying nucleon three-dimensional structure at RHIC and the future EIC.

Significance. If the factorization holds and the SSA isolates transversity with negligible contamination, the proposal would extend the kinematic reach for h_1^q measurements using jet observables, offering a systematically distinct method from standard TMD factorization in SIDIS or Drell-Yan. The IR/collinear safety of OPEC is a potential strength for perturbative control.

major comments (2)
  1. [Proposal and factorization discussion] The central claim that the OPEC single-spin asymmetry factorizes to isolate h_1^q via a perturbative hard kernel with a clean sin(φ_s - φ_n) modulation rests on the assumption that power corrections and other TMDs (e.g., Boer-Mulders, twist-3) remain negligible across the extended θ_n range. This is least secure in the small-θ_n regime highlighted as an advantage, where the energy-flow definition may mix collinear and soft modes without the same parametric suppression of higher-twist operators as in standard TMD factorization.
  2. [Abstract and main proposal] No explicit derivation, perturbative calculation of the hard kernel, or numerical results are presented to substantiate the angular dependence or the convolution with transversity; the manuscript must include these to demonstrate that the SSA directly probes h_1^q without appreciable contamination.
minor comments (2)
  1. [Notation and definitions] Clarify the precise definition of the one-point energy correlator and the angular variables φ_s, φ_n, θ_n with explicit formulas or diagrams.
  2. [Introduction] Add comparisons or references to existing transversity extractions and energy correlator studies to contextualize the proposed advantage over j_⊥ measurements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and valuable feedback on our proposal to use one-point energy correlators for accessing nucleon transversity. We address each major comment below and outline the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Proposal and factorization discussion] The central claim that the OPEC single-spin asymmetry factorizes to isolate h_1^q via a perturbative hard kernel with a clean sin(φ_s - φ_n) modulation rests on the assumption that power corrections and other TMDs (e.g., Boer-Mulders, twist-3) remain negligible across the extended θ_n range. This is least secure in the small-θ_n regime highlighted as an advantage, where the energy-flow definition may mix collinear and soft modes without the same parametric suppression of higher-twist operators as in standard TMD factorization.

    Authors: We acknowledge that the suppression of power corrections in the small-θ_n regime requires careful justification, as the mixing of modes could potentially introduce higher-twist effects. Our manuscript emphasizes the IR and collinear safety of the OPEC as a means to maintain perturbative control, but we agree that a more detailed analysis of the factorization theorem and estimates of contamination from other TMDs would strengthen the argument. We will revise the manuscript to include an expanded discussion on the range of validity and potential power corrections. revision: yes

  2. Referee: [Abstract and main proposal] No explicit derivation, perturbative calculation of the hard kernel, or numerical results are presented to substantiate the angular dependence or the convolution with transversity; the manuscript must include these to demonstrate that the SSA directly probes h_1^q without appreciable contamination.

    Authors: The manuscript derives the single-spin asymmetry at leading order, showing that the sin(φ_s - φ_n) modulation arises from the transversity distribution convoluted with the hard scattering kernel for the OPEC observable. The angular dependence is a direct consequence of the spin-dependent parton distribution. However, to provide stronger evidence, we will add explicit expressions for the hard kernel and preliminary numerical estimates of the asymmetry in the revised version of the paper. revision: yes

Circularity Check

0 steps flagged

No circularity: standard factorization applied to new observable

full rationale

The paper proposes the one-point energy correlator (OPEC) as a novel probe of transversity h_1^q via single-spin asymmetry in transversely polarized p↑p collisions, claiming a clean sin(φ_s - φ_n) dependence over wider θ_n range than j_⊥ measurements. This rests on applying established perturbative QCD factorization and TMD theorems to the new infrared-safe observable. No derivation step reduces by construction to a fitted parameter, self-defined quantity, or load-bearing self-citation chain; the central claim is an independent application of external factorization results to this observable rather than a tautological renaming or internal fit. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on perturbative QCD factorization for jet observables in polarized collisions and the infrared-collinear safety of the one-point energy correlator; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • standard math Standard QCD factorization theorems apply to one-point energy correlators in transversely polarized proton-proton collisions
    The proposal relies on existing factorization frameworks for jet substructure observables to isolate the transversity contribution.

pith-pipeline@v0.9.0 · 5653 in / 1289 out tokens · 43257 ms · 2026-05-18T15:57:20.743109+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 5 Pith papers

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

  1. Sivers Tomography from Charge and Angle Only

    hep-ph 2026-05 conditional novelty 8.0

    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...

  2. Energy Correlators Within Jets in Transversely Polarized Proton-Proton Collisions at $\sqrt{s} = 200$ GeV

    hep-ex 2026-04 unverdicted novelty 8.0

    First measurement of energy correlators in jets from transversely polarized pp collisions at 200 GeV shows sizable spin asymmetries for pions that provide sensitivity to nucleon transversity with reduced fragmentation...

  3. Simplified approach to extracting nucleon transversity in collinear factorization using near-side energy-energy correlators

    hep-ph 2026-04 unverdicted novelty 7.0

    A new method extracts the nucleon transversity PDF via near-side energy-energy correlators in dihadron fragmentation under collinear factorization, with leading-order results for SIDIS and e+e- annihilation that resem...

  4. Simplified approach to extracting nucleon transversity in collinear factorization using near-side energy-energy correlators

    hep-ph 2026-04 unverdicted novelty 7.0

    A new approach using near-side energy-energy correlators in dihadron fragmentation enables extraction of nucleon transversity PDF in collinear factorization without modeling intrinsic transverse momentum or dihadron r...

  5. Energy Correlators Resolving Proton Spin

    hep-ph 2025-09 unverdicted novelty 5.0

    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.

Reference graph

Works this paper leans on

103 extracted references · 103 canonical work pages · cited by 4 Pith papers · 35 internal anchors

  1. [1]

    distributions [1–3]. Whilef q 1 andg q 1 are well constrained [4], the transversity PDF remains poorly known because of its unique chiral- odd nature [2], which makes it inaccessible in inclusive scattering. Overcoming this experimental challenge is critical, as the first moment ofh q 1 defines the nucleon’s tensor charge,δq≡ R 1 0 dx[h q 1(x)−h ¯q 1(x)]....

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  2. [2]

    We also analyze the uncertain- ties originating from two key sources: the transversity PDFs and the Collins FFs

    yields systematically smaller asymmetries compared to the JAM3D-22 result. We also analyze the uncertain- ties originating from two key sources: the transversity PDFs and the Collins FFs. In both approaches, we ob- serve that the dominant source of uncertainty arises from the Collins function, while the transversity contribution plays a comparatively smal...

    work page

  3. [3]

    J. P. Ralston and D. E. Soper, Nucl. Phys.B152, 109 (1979)

    work page 1979

  4. [4]

    R. L. Jaffe and X.-D. Ji, Phys. Rev. Lett.67, 552 (1991)

    work page 1991

  5. [5]

    Transverse Polarisation of Quarks in Hadrons

    V. Barone, A. Drago, and P. G. Ratcliffe, Phys. Rept. 359, 1 (2002), hep-ph/0104283

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  6. [6]

    Parton distributions and lattice QCD calculations: a community white paper

    H.-W. Linet al., Prog. Part. Nucl. Phys.100, 107 (2018), arXiv:1711.07916 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  7. [7]

    J. D. Jackson, S. B. Treiman, and H. W. Wyld, Phys. Rev.106, 517 (1957)

    work page 1957

  8. [8]

    J. C. Collins, Nucl. Phys. B396, 161 (1993), arXiv:hep- ph/9208213

    work page arXiv 1993

  9. [9]

    J. C. Collins, S. F. Heppelmann, and G. A. Ladinsky, Nucl. Phys. B420, 565 (1994), arXiv:hep-ph/9305309

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  10. [10]

    Z.-B. Kang, A. Prokudin, P. Sun, and F. Yuan, Phys. Rev. D93, 014009 (2016), arXiv:1505.05589 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  11. [11]

    Cammarota, L

    J. Cammarota, L. Gamberg, Z.-B. Kang, J. A. Miller, D. Pitonyak, A. Prokudin, T. C. Rogers, and N. Sato (Jefferson Lab Angular Momentum), Phys. Rev. D102, 054002 (2020), arXiv:2002.08384 [hep-ph]

    work page arXiv 2020

  12. [12]

    Gamberg et al.,Transversity distributions and tensor charges of the nucleon from a global analysis,Phys

    L. Gamberg, M. Malda, J. A. Miller, D. Pitonyak, A. Prokudin, and N. Sato (Jefferson Lab Angular Mo- mentum (JAM), Jefferson Lab Angular Momentum), Phys. Rev. D106, 034014 (2022), arXiv:2205.00999 [hep-ph]

    work page arXiv 2022

  13. [13]

    First Extraction of Transversity from a Global Analysis of Electron-Proton and Proton-Proton Data

    M. Radici and A. Bacchetta, Phys. Rev. Lett.120, 192001 (2018), arXiv:1802.05212 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  14. [14]

    Cocuzza, A

    C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl (JAM), Phys. Rev. Lett.132, 091901 (2024), arXiv:2306.12998 [hep-ph]

    work page arXiv 2024

  15. [15]

    Cocuzza, A

    C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl (Jefferson Lab Angular Mo- mentum (JAM)), Phys. Rev. D109, 034024 (2024), arXiv:2308.14857 [hep-ph]

    work page arXiv 2024

  16. [16]

    X. Gao, A. D. Hanlon, S. Mukherjee, P. Petreczky, Q. Shi, S. Syritsyn, and Y. Zhao, Phys. Rev. D109, 054506 (2024), arXiv:2310.19047 [hep-lat]

    work page arXiv 2024

  17. [17]

    H.-W. Lin, W. Melnitchouk, A. Prokudin, N. Sato, and H. Shows, Phys. Rev. Lett.120, 152502 (2018), arXiv:1710.09858 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  18. [18]

    D’Alesio, C

    U. D’Alesio, C. Flore, and A. Prokudin, Phys. Lett. B 803, 135347 (2020), arXiv:2001.01573 [hep-ph]

    work page arXiv 2020

  19. [19]

    Benel, A

    J. Benel, A. Courtoy, and R. Ferro-Hernandez, Eur. Phys. J. C80, 465 (2020), arXiv:1912.03289 [hep-ph]

    work page arXiv 2020

  20. [20]

    C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. Lett.41, 1585 (1978)

    work page 1978

  21. [21]

    C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. D19, 2018 (1979)

    work page 2018

  22. [22]

    Kinoshita, J

    T. Kinoshita, J. Math. Phys.3, 650 (1962)

    work page 1962

  23. [23]

    T. D. Lee and M. Nauenberg, Phys. Rev.133, B1549 (1964)

    work page 1964

  24. [24]

    Measurement of alpha_s(M_Z^2) from Hadronic Event Observables at the Z^0 Resonance

    K. Abeet al.(SLD), Phys. Rev. D51, 962 (1995), arXiv:hep-ex/9501003

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  25. [25]

    Adrianet al.(L3), Phys

    O. Adrianet al.(L3), Phys. Lett. B284, 471 (1992)

    work page 1992

  26. [26]

    P. D. Actonet al.(OPAL), Phys. Lett. B276, 547 (1992)

    work page 1992

  27. [27]

    Adachiet al.(TOPAZ), Phys

    I. Adachiet al.(TOPAZ), Phys. Lett. B227, 495 (1989)

    work page 1989

  28. [28]

    Braunschweiget al.(TASSO), Z

    W. Braunschweiget al.(TASSO), Z. Phys. C36, 349 (1987)

    work page 1987

  29. [29]

    Bartelet al.(JADE), Z

    W. Bartelet al.(JADE), Z. Phys. C25, 231 (1984)

    work page 1984

  30. [30]

    Fernandezet al., Phys

    E. Fernandezet al., Phys. Rev. D31, 2724 (1985)

    work page 1985

  31. [31]

    D. R. Woodet al., Phys. Rev. D37, 3091 (1988)

    work page 1988

  32. [32]

    H. J. Behrendet al.(CELLO), Z. Phys. C14, 95 (1982)

    work page 1982

  33. [33]

    Bergeret al.(PLUTO), Z

    C. Bergeret al.(PLUTO), Z. Phys. C28, 365 (1985)

    work page 1985

  34. [34]

    M. Z. Akrawyet al.(OPAL), Phys. Lett. B252, 159 (1990)

    work page 1990

  35. [35]

    Decampet al.(ALEPH), Phys

    D. Decampet al.(ALEPH), Phys. Lett. B257, 479 (1991)

    work page 1991

  36. [36]

    Adevaet al.(L3), Phys

    B. Adevaet al.(L3), Phys. Lett. B257, 469 (1991)

    work page 1991

  37. [37]

    Measurement of alpha-s from energy-energy correlations at the Z0 resonance

    K. Abeet al.(SLD), Phys. Rev. D50, 5580 (1994), arXiv:hep-ex/9405006

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  38. [38]

    Measurement of transverse energy-energy correlations in multi-jet events in $pp$ collisions at $\sqrt{s} = 7$ TeV using the ATLAS detector and determination of the strong coupling constant $\alpha_{\mathrm{s}}(m_Z)$

    G. Aadet al.(ATLAS), Phys. Lett. B750, 427 (2015), arXiv:1508.01579 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  39. [39]

    Determination of the strong coupling constant $\alpha_s$ from transverse energy-energy correlations in multijet events at $\sqrt{s} = 8$ TeV using the ATLAS detector

    M. Aaboudet al.(ATLAS), Eur. Phys. J. C77, 872 (2017), arXiv:1707.02562 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  40. [40]

    Acharyaet al.(ALICE), (2024), arXiv:2409.12687 [hep-ex]

    S. Acharyaet al.(ALICE), (2024), arXiv:2409.12687 [hep-ex]

    work page arXiv 2024

  41. [41]

    Hayrapetyanet al.(CMS), Phys

    A. Hayrapetyanet al.(CMS), Phys. Rev. Lett.133, 071903 (2024), arXiv:2402.13864 [hep-ex]

    work page arXiv 2024

  42. [42]

    Chekhovskyet al.(CMS), Phys

    V. Chekhovskyet al.(CMS), Phys. Lett. B866, 139556 6 (2025), arXiv:2503.19993 [nucl-ex]

    work page arXiv 2025

  43. [43]

    Acharyaet al.(ALICE), (2025), arXiv:2504.03431 [hep-ex]

    S. Acharyaet al.(ALICE), (2025), arXiv:2504.03431 [hep-ex]

    work page arXiv 2025

  44. [44]

    Aadet al.(ATLAS), JHEP07, 085, arXiv:2301.09351 [hep-ex]

    G. Aadet al.(ATLAS), JHEP07, 085, arXiv:2301.09351 [hep-ex]

    work page arXiv

  45. [45]

    H. T. Li, Y. Makris, and I. Vitev, Phys. Rev. D103, 094005 (2021), arXiv:2102.05669 [hep-ph]

    work page arXiv 2021

  46. [46]

    Neill, G

    D. Neill, G. Vita, I. Vitev, and H. X. Zhu, inSnowmass 2021(2022) arXiv:2203.07113 [hep-ph]

    work page arXiv 2021

  47. [47]

    Z.-B. Kang, J. Penttala, F. Zhao, and Y. Zhou, Phys. Rev. D109, 094012 (2024), arXiv:2311.17142 [hep-ph]

    work page arXiv 2024

  48. [48]

    Electron Ion Collider: The Next QCD Frontier - Understanding the glue that binds us all

    A. Accardiet al., Eur. Phys. J. A52, 268 (2016), arXiv:1212.1701 [nucl-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  49. [49]

    Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report

    R. Abdul Khaleket al., Nucl. Phys. A1026, 122447 (2022), arXiv:2103.05419 [physics.ins-det]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  50. [50]

    Liu and H

    X. Liu and H. X. Zhu, Phys. Rev. Lett.130, 091901 (2023), arXiv:2209.02080 [hep-ph]

    work page arXiv 2023

  51. [51]

    H.-Y. Liu, X. Liu, J.-C. Pan, F. Yuan, and H. X. Zhu, Phys. Rev. Lett.130, 181901 (2023), arXiv:2301.01788 [hep-ph]

    work page arXiv 2023

  52. [52]

    H. Cao, X. Liu, and H. X. Zhu, Phys. Rev. D107, 114008 (2023), arXiv:2303.01530 [hep-ph]

    work page arXiv 2023

  53. [53]

    X. L. Li, X. Liu, F. Yuan, and H. X. Zhu, (2023), arXiv:2308.10942 [hep-ph]

    work page arXiv 2023

  54. [54]

    Z.-B. Kang, K. Lee, D. Y. Shao, and F. Zhao, JHEP 03, 153, arXiv:2310.15159 [hep-ph]

    work page arXiv

  55. [55]

    Bhattacharya, Z.-B

    S. Bhattacharya, Z.-B. Kang, D. Padilla, and J. Pent- tala, (2025), arXiv:2504.10475 [hep-ph]

    work page arXiv 2025

  56. [56]

    Z.-B. Kang, J. Penttala, and C. Zhang, (2024), arXiv:2410.21435 [hep-ph]

    work page arXiv 2024

  57. [57]

    A. B. Cuerpo, I. Scimemi, and A. Vladimirov, (2025), arXiv:2507.17478 [hep-ph]

    work page arXiv 2025

  58. [58]

    Song, S.-Y

    Y.-K. Song, S.-Y. Wei, L. Yang, and J. Zhou, (2025), arXiv:2509.14960 [hep-ph]

    work page arXiv 2025

  59. [59]

    Moult and H

    I. Moult and H. X. Zhu, (2025), arXiv:2506.09119 [hep- ph]

    work page arXiv 2025

  60. [60]

    Riembau and M

    M. Riembau and M. Son, Phys. Rev. D111, 014004 (2025), arXiv:2407.12082 [hep-ph]

    work page arXiv 2025

  61. [61]

    Mi and Z

    Z. Mi and Z. Wang, (2025), arXiv:2507.21613 [hep-ph]

    work page arXiv 2025

  62. [62]

    Riembau and M

    M. Riembau and M. Son, (2025), arXiv:2509.02669 [hep-ph]

    work page arXiv 2025

  63. [63]

    Y. J. Zhu, (2025), arXiv:2509.01652 [hep-ph]

    work page arXiv 2025

  64. [64]

    TMD Handbook,

    R. Boussarieet al., (2023), arXiv:2304.03302 [hep-ph]

    work page arXiv 2023

  65. [65]

    Azimuthal Asymmetric Distribution of Hadrons Inside a Jet at Hadron Collider

    F. Yuan, Phys.Rev.Lett.100, 032003 (2008), arXiv:0709.3272 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  66. [66]

    Testing the process dependence of the Sivers function via hadron distributions inside a jet

    U. D’Alesio, L. Gamberg, Z.-B. Kang, F. Mur- gia, and C. Pisano, Phys.Lett.B704, 637 (2011), arXiv:1108.0827 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  67. [67]

    Testing the universality of the Collins function in pion-jet production at RHIC

    U. D’Alesio, F. Murgia, and C. Pisano, Phys. Lett. B 773, 300 (2017), arXiv:1707.00914 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  68. [68]

    Z.-B. Kang, A. Prokudin, F. Ringer, and F. Yuan, Phys. Lett. B774, 635 (2017), arXiv:1707.00913 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  69. [69]

    Z.-B. Kang, X. Liu, F. Ringer, and H. Xing, JHEP11, 068, arXiv:1705.08443 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  70. [70]

    Azimuthal transverse single-spin asymmetries of inclusive jets and charged pions within jets from polarized-proton collisions at $\sqrt{s} = 500$ GeV

    L. Adamczyket al.(STAR), Phys. Rev. D97, 032004 (2018), arXiv:1708.07080 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  71. [71]

    Abdallahet al.(STAR), Phys

    M. Abdallahet al.(STAR), Phys. Rev. D106, 072010 (2022), arXiv:2205.11800 [hep-ex]

    work page arXiv 2022

  72. [72]

    Zhang (STAR), PoSSPIN2023, 059 (2024)

    Y. Zhang (STAR), PoSSPIN2023, 059 (2024)

    work page 2024

  73. [73]

    (2025), arXiv:2507.16355 [hep-ex]

    work page arXiv 2025

  74. [74]

    Nakagawa (sPHENIX), Ukr

    I. Nakagawa (sPHENIX), Ukr. J. Phys.69, 799 (2024)

    work page 2024

  75. [75]

    Quark Fragmentation within an Identified Jet

    M. Procura and I. W. Stewart, Phys. Rev. D81, 074009 (2010), [Erratum: Phys.Rev.D 83, 039902 (2011)], arXiv:0911.4980 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  76. [76]

    Z.-B. Kang, F. Ringer, and I. Vitev, JHEP11, 155, arXiv:1606.07063 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  77. [77]

    C. W. Bauer, S. Fleming, and M. E. Luke, Phys. Rev. D63, 014006 (2000), arXiv:hep-ph/0005275

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  78. [78]

    C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, Phys. Rev.D63, 114020 (2001), arXiv:hep-ph/0011336 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  79. [79]

    C. W. Bauer and I. W. Stewart, Phys. Lett.B516, 134 (2001), arXiv:hep-ph/0107001 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  80. [80]

    C. W. Bauer, D. Pirjol, and I. W. Stewart, Phys. Rev. D65, 054022 (2002), arXiv:hep-ph/0109045 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

Showing first 80 references.