Pith. sign in

REVIEW 4 major objections 4 minor 48 references

Single spin asymmetry $A _ { U L } ^ { \sin ( 3 \phi _ { h } - \phi_{ R } ) }$ in dihadron production in SIDIS

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper calculates the T-odd dihadron fragmentation function H⊥1,OT in the spectator model and shows that the sin(3ϕh−ϕR) single-longitudinal-spin asymmetry comes out near zero, matching the measured null signal.

desk verdict Plausible one-loop spectator-model calculation of the T-odd dihadron FF H_perp_1,OT, with a credible qualitative explanation of the small COMPASS asymmetry but an overclaimed quantitative comparison. read the letter →

arxiv 2509.04033 v1 pith:IKGNGXRD submitted 2025-09-04 hep-ph

Lei Tan , Gang Li , Mao Song , Xuan Luo This is my paper
classification hep-ph
keywords singlelongitudinalspinasymmetrydihadronfragmentationfunctionsTMDfactorizationspectatormodelT-oddfunctionsemi-inclusivedeepinelasticscatteringazimuthaltransversity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to explain why the azimuthal asymmetry A_UL^{sin(3ϕh−ϕR)} seen in two-hadron production in deep inelastic scattering is indistinguishable from zero. It computes the T-odd dihadron fragmentation function H⊥1,OT—the s-wave/p-wave interference piece of the two-hadron analogue of the Collins function—using a spectator model, and finds that only a one-loop gluon correction makes it nonzero. Feeding this function together with spectator-model parton distributions into the transverse-momentum-dependent factorization formula gives an asymmetry that is small over the measured x, z, and M_h ranges and tracks the null data. The authors also predict a similarly small asymmetry at lower beam energy. If the calculation is right, the null result is a quantitative consequence of the tiny size of H⊥1,OT rather than an accidental experimental outcome.

What carries the argument

The central object is H⊥1,OT, the s-wave/p-wave interference term in the partial-wave expansion of the T-odd dihadron fragmentation function H⊥1. The mechanism that gives it a nonzero value is the one-loop gluon correction: the phase needed for a T-odd function comes from the complex p-wave vertex built from ρ and ω resonance propagators, while the tree diagram has no such phase. The calculation projects H⊥1,OT out of the quark-quark correlator using the trace 4π Tr[Δ iσ^{α−}γ5], evaluates the loop integrals with on-shell Cutkosky cuts, and then places the result into the sin(3ϕh−ϕR) modulation of the cross section via a convolution with h⊥1L.

What would settle it

A high-statistics measurement of this asymmetry at √s=17.4 GeV with uncertainties below about 0.005 per M_h bin would falsify the prediction if it shows a clear nonzero signal outside the 0.5–1.0 GeV region, where the model predicts a zero crossing near 0.74 GeV. An independent extraction of H⊥1,OT from e+e− back-to-back dihadron data that gives it a magnitude comparable to D1,OO would also break the explanation.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the previously uncalculated T-odd dihadron fragmentation function H⊥1,OT is naturally small—roughly 10^-3 of the unpolarized D1,OO—and that this smallness is what makes the sin(3ϕh−ϕR) asymmetry vanish. The calculation starts from a spectator-model correlation function for q→π+π−X with s- and p-wave vertex couplings; the tree-level contribution to H⊥1,OT vanishes, so the one-loop diagrams must be evaluated using Cutkosky cuts. The resulting H⊥1,OT has a zero at M_h≈0.74 GeV and, after convolution with h⊥1L in the TMD cross section, yields an asymmetry consistent with the preliminary data at √s=17.4 GeV and near zero at √s=7.2 GeV. The paper

Load-bearing premise

The near-zero prediction rests on an unmeasured quark-spin distribution being as small as the model's estimate, and on sea-quark and evolution effects being negligible; if that distribution is much larger, the asymmetry would show up even though the computed fragmentation function is tiny.

Editorial extensions

If this is right

  • The measured null asymmetry is not just a statistical artifact; the model predicts it, with a magnitude set by H⊥1,OT being about a thousand times smaller than D1,OO.
  • The M_h distribution of the asymmetry has a zero crossing near 0.74 GeV, so data binned in M_h can directly test the s-wave/p-wave interference picture.
  • At a lower beam energy (√s=7.2 GeV), the same asymmetry is also expected to be near zero and slightly smaller than at √s=17.4 GeV.
  • Because QCD evolution and sea-quark contributions are neglected at the model scale, the asymmetry is carried by the valence combination 4h⊥u_1L − h⊥d_1L under isospin symmetry, which future data could constrain only if H⊥1,OT is known.

Reading between the lines

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

  • If an independent extraction of H⊥1,OT from e+e− back-to-back dihadron data finds it much larger than the model's 10^-3 ratio, the model's explanation of the null SIDIS asymmetry would fail; conversely, a small H⊥1,OT would make this channel a weak probe of h⊥1L.
  • The zero crossing near M_h≈0.74 GeV, in the ρ/ω resonance region, is a sharp model-specific signature that finer M_h bins could test and could discriminate between different hadronization mechanisms.
  • Extending the calculation with QCD evolution and sea-quark terms could change the small-x prediction; it remains an open check whether the omitted sea h⊥1L contributions cancel or enhance the valence effect.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper calculates the T-odd dihadron fragmentation function H⊥1,OT in the spectator model, retaining the transverse-momentum dependence, and uses it to predict the sin(3φh−φR) single-longitudinal-spin asymmetry A_UL in dihadron SIDIS. The model calculation is one-loop, with the imaginary phase supplied by the p-wave vertex. The asymmetry is evaluated at COMPASS kinematics and compared with preliminary COMPASS data, which are consistent with zero; the same asymmetry is also predicted at HERMES. The paper concludes that the smallness of H⊥1,OT is the main reason the measured COMPASS asymmetry is small.

Significance. If the calculation is correct, this is the first spectator-model estimate of this particular T-odd DiFF and it offers a specific dynamical explanation for a measured asymmetry that has so far been discussed mainly at the level of cross-section structure. The paper also has the merit of not tuning its parameters to the COMPASS asymmetry: the model parameters come from a PYTHIA fit at HERMES kinematics, so the data comparison is an external test. However, the central claim is not yet quantitatively robust: the agreement with data is stated qualitatively, the calculation relies on an unmeasured spectator-model PDF, and the acknowledged neglect of evolution and sea quarks is potentially important in the low-x bins used by COMPASS. These issues are addressable within the paper's scope, but they need to be addressed before the explanation of the small asymmetry can be considered established.

major comments (4)
  1. [Sec. V and Eq. (19)] The central comparison with COMPASS is contingent on the spectator-model input h⊥1L from Ref. [47], which is unmeasured and is used at a low model scale. The paper explicitly states that QCD evolution is ignored and that the sea-quark/antiquark PDFs are set to zero. This matters because COMPASS accepts x down to 0.003, where sea quarks and evolution are not negligible. The asymmetry is the ratio of (4h⊥u_1L−h⊥d_1L)⊗H⊥1,OT to (4f^u_1+f^d_1)⊗D1,OO; since h⊥1L/f1 is not measured, a factor-of-a-few change in this ratio can move A_UL to the percent level even if H⊥1,OT is computed correctly. Please provide a sensitivity test: vary the spectator-model parameters of h⊥1L (or use an alternative parametrization), include an estimate of TMD evolution, and quantify the effect on Fig. 4.
  2. [Sec. IV, Eqs. (31)–(45)] The one-loop result is the central new ingredient, but its derivation is not shown. Equations (26)–(29) list the diagrams, Eqs. (30)–(45) give the final integrals and coefficient functions, but the projection onto H⊥b1,OT and H⊥d1,OT, the evaluation of the Cutkosky cuts with the eikonal propagators, and the tensor decomposition leading to A0,…,E0 are all asserted rather than derived. Without an appendix, supplementary file, or a clearly referenced companion calculation, a referee cannot verify this core result. Please include the derivation or a detailed outline.
  3. [Sec. V, Fig. 4] The model prediction is presented as a single dashed curve with no uncertainty band, and no statistical measure (e.g., χ² per degree of freedom) is given for the comparison with the COMPASS data. The manuscript itself acknowledges that the model parameters were fitted under HERMES kinematics and that their uncertainty is neglected. Since the data are consistent with zero and have sizable errors, the statement that the predictions “describe the vanishing data very well” is not quantitatively supported. Add an uncertainty estimate (at least from the model parameters and from αs≈0.3) and a goodness-of-fit measure.
  4. [Sec. V, Eq. (46)] The flavor sum in the denominator uses only 4f^u_1+f^d_1, with sea quarks set to zero because evolution is ignored. Even if one accepts the model-scale choice, this is inconsistent with the COMPASS x range: at x≈0.003 the sea contribution to f1 is not negligible, and the same statement applies to the unknown h⊥1L sea contribution in the numerator. The paper should either restrict the comparison to kinematics where sea quarks are demonstrably small or implement a minimal evolution/sea model. This is part of the load-bearing issue in the first major comment, but it deserves to be stated separately for Eq. (46).
minor comments (4)
  1. [Fig. 4 caption] The caption says “preliminary COMPASS data [28]”, but Ref. [28] is a spectator-model paper, not a COMPASS data paper. The text cites [36] for these data; the figure caption should be corrected.
  2. [Figs. 3 and 5] There are small typos: the y-axis label of Fig. 3 says “spectator medel prediction” and the label/text in Fig. 5 says “HEMERS” instead of HERMES.
  3. [Sec. II] The notation “a four-dimensional vector ⃗a as [a−,a+,⃗aT]” is nonstandard: the light-cone components are not a vector arrow. Using an arrow for a 4-vector is confusing; use ordinary italics for aμ.
  4. [Sec. V] The model parameters (a_s, a_p, f_s, etc.) are listed without uncertainties. Since the paper later acknowledges that the parameters carry uncertainty from the PYTHIA fit, it would be helpful to quote at least a rough uncertainty or explain why the listed constants are treated as fixed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the H⊥1,OT calculation is a genuine model prediction compared with external COMPASS data.

full rationale

The paper's main new result is the spectator-model calculation of the T-odd dihadron fragmentation function H⊥1,OT from one-loop diagrams, followed by a prediction of the sin(3φh−φR) asymmetry using Eq. (19). The model parameters are not fitted to the COMPASS asymmetry; they are taken from Ref. [28], where they were determined by comparing with PYTHIA event generation at HERMES kinematics. The comparison with COMPASS data is therefore an external test, not a fit renamed as a prediction. The use of the same spectator model for the PDFs f1 and h⊥1L (Ref. [47]) introduces model dependence, but it is not circular: h⊥1L is an independent input from a prior calculation, and the asymmetry is not constructed so that the output reproduces that input by definition. The paper explicitly acknowledges neglected QCD evolution and sea-quark contributions, and these are robustness/accuracy limitations rather than circular reasoning. No load-bearing step reduces to its own input by construction, and no self-citation chain is invoked to force the result. Hence the central derivation is self-contained against external benchmarks, and the circularity score is 0.

Assumptions & free parameters 12 free parameters · 6 assumptions · 0 invented entities

The prediction depends on a set of spectator-model parameters fitted to PYTHIA in Ref [28], on the spectator-model PDF h_perp_1L from Ref [47], and on the stated approximations (massless quark, no evolution, isospin). None of these are new free parameters introduced ad hoc in this paper, but the central claim inherits all of them.

free parameters (12)
  • a_s = 2.60 GeV
    Spectator model s-wave Gaussian form-factor scale, fitted to PYTHIA at HERMES in Ref [28].
  • beta_s = -0.751
    z-exponent of s-wave Gaussian form factor, fit to PYTHIA in Ref [28].
  • gamma_s = -0.193
    (1-z) exponent of s-wave Gaussian form factor, fit to PYTHIA in Ref [28].
  • a_p = 7.07 GeV
    p-wave Gaussian form-factor scale, fit to PYTHIA in Ref [28].
  • beta_p = -0.038
    z-exponent of p-wave Gaussian form factor, fit to PYTHIA in Ref [28].
  • gamma_p = -0.085
    (1-z) exponent of p-wave Gaussian form factor, fit to PYTHIA in Ref [28].
  • f_s = 1197 GeV^-1
    s-wave vertex strength, fit to PYTHIA in Ref [28].
  • f_rho = 93.5
    rho-resonance p-wave vertex strength, fit to PYTHIA in Ref [28].
  • f_omega = 0.63
    omega-resonance p-wave vertex strength, fit to PYTHIA in Ref [28].
  • f'_omega = 75.2
    Additional omega vertex parameter, fit to PYTHIA in Ref [28].
  • M_s = 2.97 M_h
    Spectator mass relation, chosen in Ref [28]; enters the loop kinematics and the delta-function constraint.
  • alpha_s = 0.3
    Strong coupling fixed by hand in this work (Section V); no uncertainty is assigned.
assumptions (6)
  • domain assumption TMD factorization of the dihadron SIDIS cross section with the given convolution structure
    Required to write the asymmetry as a convolution of PDFs and DiFFs; standard in TMD phenomenology but not proven in this paper.
  • ad hoc to paper Spectator model with on-shell spectator delta function and Gaussian form factors independent of the loop momentum
    Stated after Eq. (29) following Refs [41-44]; directly shapes the one-loop result for H_perp_1,OT.
  • ad hoc to paper Quark mass set to zero in the tree and loop calculation
    Section IV: 'the mass of the input quark can be set to be zero GeV' and 'We have verified that even if the input quark is given a small mass...'; needed for the stated tree-level vanishing.
  • domain assumption One-loop order is sufficient for H_perp_1,OT; diagrams a and c and higher orders are negligible
    Only diagrams b and d are kept; the paper does not quantify higher-order corrections or the neglected diagrams beyond stating they vanish.
  • domain assumption Neglect of QCD evolution and vanishing sea-quark distributions
    Section V: 'we decide to ignore the QCD evolution which causes the antiquark PDFs f1 and h1L to take zero values.' This affects the small-x region of the COMPASS comparison.
  • domain assumption Isospin symmetry for the flavor dependence of the DiFFs
    Section V uses isospin symmetry to relate u, d, anti-u, anti-d fragmentation channels and to fix the sign of H_perp_1,OT.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Single spin asymmetry $A _ { U L } ^ { \sin ( 3 \phi _ { h } - \phi_{ R } ) }$ in dihadron production in SIDIS." pith.science (2026). https://pith.science/paper/IKGNGXRD

@misc{pith2026250904033,
  author       = {Pith},
  title        = {Pith review of: Single spin asymmetry $A _  U L  ^  \sin ( 3 \phi _  h  - \phi_ R  ) $ in dihadron production in SIDIS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IKGNGXRD}},
  note         = {Machine review of arXiv:2509.04033}
}
abstract

In the field of particle physics, the phenomenon of dihadron production in semi-inclusive deep inelastic scattering (SIDIS) process has always been a significant focus. This paper focuses on the single longitudinal spin asymmetry $A_{UL }^{\sin(3\phi_{h}-\phi_{R})}$ in the dihadron production during this process and combines the transverse-momentum-dependent dihadron fragmentation function (DiFF) $H_1^{\perp}$ to deeply analyze its underlying mechanism. Here, the involved DiFF $H_1^{\perp}$ is the analogue of the Collins function for single-hadron production and it describes the fragmentation of a transversely polarized quark at leading twist. Recent studies have shown that the azimuthal asymmetry signal observed by the COMPASS collaboration in the dihadron SIDIS is weak. To reveal the reason for this small signal and to study the asymmetry, we calculate the unknown T-odd DiFF $H_1^{\perp}$ using the spectator model. The spectator model, widely used in SIDIS, describes the internal structure of hadrons and the hadronization mechanism. This model has successfully explained dihadron production in unpolarized and single-polarized processes. During the research process, while maintaining the transverse momentum dependence of the hadron pair, we employ the transverse momentum dependent(TMD) factorization framework, using this method and the model, we first simulate the asymmetry in the COMPASS energy region and compare it with experimental data. Furthermore, we predict the same asymmetry at the HERMES, expecting to provide valuable theoretical references for relevant experimental studies.

Figures

Figures reproduced from arXiv: 2509.04033 by the authors.

Figure 1
Figure 1. FIG. 1: Angle definitions involved in the measurement [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: One loop order corrections to the fragmentation function of a quark into a meson pair in the spectator [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The DiFF [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The sin(3 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The sin(3 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

48 extracted references · 28 canonical work pages

  1. [47]

    Bacchetta, F

    A. Bacchetta, F. Conti, and M. Radici, Phys. Rev. D 78, 074010 (2008), arXiv:0807.0323 [hep-ph]

    arXiv 2008

  2. [28]

    Bacchetta and M

    A. Bacchetta and M. Radici, Phys. Rev. D 74, 114007 (2006), arXiv:hep-ph/0608037

    arXiv 2006

  3. [36]

    Azimuthal asymmetries in SIDIS di-hadron muoproduction off longitudinally polarized protons at COMPASS

    S. Sirtl, in 22nd International Symposium on Spin Physics (2017) arXiv:1702.07317 [hep-ex]

    work page Pith review arXiv 2017

  4. [1]

    Konishi, A

    K. Konishi, A. Ukawa, and G. Veneziano, Nucl. Phys. B 157, 45 (1979)

    work page 1979

  5. [2]

    Vendramin, Nuovo Cim

    I. Vendramin, Nuovo Cim. A 62, 21 (1981)

    work page 1981

  6. [3]

    Vendramin, Nuovo Cim

    I. Vendramin, Nuovo Cim. A 66, 339 (1981)

    work page 1981

  7. [4]

    de Florian and L

    D. de Florian and L. Vanni, Physics Letters B 578, 139 (2004)

    work page 2004

  8. [5]

    Majumder, B

    A. Majumder, B. M¨ uller, and X.-N. Wang, Physical Re- view Letters 99 (2007), 10.1103/physrevlett.99.192301

    work page doi:10.1103/physrevlett.99.192301 2007

Show all 48 references
  1. [6]

    F. A. Ceccopieri, M. Radici, and A. Bacchetta, Physics Letters B 650, 81–89 (2007)

    2007

  2. [7]

    J. C. Collins and G. A. Ladinsky, (1994), arXiv:hep- ph/9411444

    1994

  3. [8]

    Bianconi, S

    A. Bianconi, S. Boffi, R. Jakob, and M. Radici, Physical Review D 62 (2000), 10.1103/physrevd.62.034008

    2000 doi

  4. [9]

    R. L. Jaffe, X. Jin, and J. Tang, Physical Review Letters 80, 1166–1169 (1998)

    1998

  5. [10]

    J. C. Collins, S. F. Heppelmann, and G. A. Ladinsky, Nuclear Physics B 420, 565–582 (1994)

    1994

  6. [11]

    Bacchetta and M

    A. Bacchetta and M. Radici, Physical Review D 67 (2003), 10.1103/physrevd.67.094002

    2003 doi

  7. [12]

    Bacchetta and M

    A. Bacchetta and M. Radici, Phys. Rev. D 69, 074026 (2004), arXiv:hep-ph/0311173

    2004 arXiv

  8. [13]

    Gliske, A

    S. Gliske, A. Bacchetta, and M. Radici, Phys. Rev. D 90, 114027 (2014), [Erratum: Phys.Rev.D 91, 019902 (2015)], arXiv:1408.5721 [hep-ph]

    2014 arXiv

  9. [14]

    J. C. Collins, Nucl. Phys. B 396, 161 (1993), arXiv:hep- ph/9208213

    1993

  10. [15]

    Anselmino, M

    M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, and S. Melis, Nucl. Phys. B Proc. Suppl. 191, 98 (2009), arXiv:0812.4366 [hep-ph]

    2009 arXiv

  11. [16]

    Number density interpretation of dihadron fragmentation functions,

    D. Pitonyak, C. Cocuzza, A. Metz, A. Prokudin, and N. Sato, “Number density interpretation of dihadron fragmentation functions,” (2023), arXiv:2305.11995 [hep-ph]

    2023 arXiv

  12. [17]

    Cocuzza, A

    C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl, Physical Review Letters 132 (2024), 10.1103/physrevlett.132.091901

    2024 doi

  13. [18]

    Cocuzza, A

    C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl (Jefferson Lab Angular Momentum (JAM)), Phys. Rev. D 109, 034024 (2024), arXiv:2308.14857 [hep- ph]

    2024 arXiv

  14. [19]

    Radici, R

    M. Radici, R. Jakob, and A. Bianconi, Phys. Rev. D 65, 074031 (2002), arXiv:hep-ph/0110252

    2002 arXiv

  15. [20]

    Vossen et al

    A. Vossen et al. (Belle), Physical Review Letters 107, 072004 (2011)

    2011

  16. [21]

    Courtoy, A

    A. Courtoy, A. Bacchetta, M. Radici, and A. Bianconi, Phys. Rev. D 85, 114023 (2012), arXiv:1202.0323 [hep- ph]

    2012 arXiv

  17. [22]

    Bacchetta, A

    A. Bacchetta, A. Courtoy, and M. Radici, Phys. Rev. Lett. 107, 012001 (2011), arXiv:1104.3855 [hep-ph]

    2011 arXiv

  18. [23]

    Bacchetta, A

    A. Bacchetta, A. Courtoy, and M. Radici, JHEP 03, 119 (2013), arXiv:1212.3568 [hep-ph]

    2013 arXiv

  19. [24]

    Radici, A

    M. Radici, A. Courtoy, A. Bacchetta, and M. Guagnelli, JHEP 05, 123 (2015), arXiv:1503.03495 [hep-ph]

    2015 arXiv

  20. [25]

    Radici, A

    M. Radici, A. M. Ricci, A. Bacchetta, and A. Mukherjee, Phys. Rev. D 94, 034012 (2016), arXiv:1604.06585 [hep- ph]

    2016 arXiv

  21. [26]

    Radici and A

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

    2018 arXiv

  22. [27]

    Bianconi, S

    A. Bianconi, S. Boffi, R. Jakob, and M. Radici, Phys. Rev. D 62, 034009 (2000), arXiv:hep-ph/9907488

    2000 arXiv

  23. [29]

    Bacchetta, F

    A. Bacchetta, F. A. Ceccopieri, A. Mukherjee, and M. Radici, Phys. Rev. D 79, 034029 (2009), arXiv:0812.0611 [hep-ph]

    2009 arXiv

  24. [30]

    H. H. Matevosyan, A. Kotzinian, and A. W. Thomas, Physics Letters B 731, 208–216 (2014). 11

    2014

  25. [31]

    H. H. Matevosyan, A. W. Thomas, and W. Bentz, Phys- ical Review D 88 (2013), 10.1103/physrevd.88.094022

    2013 doi

  26. [32]

    H. H. Matevosyan, A. Kotzinian, and A. W. Thomas, Phys. Rev. Lett. 120, 252001 (2018)

    2018

  27. [33]

    Airapetian et al

    A. Airapetian et al. (HERMES), JHEP 06, 017 (2008), arXiv:0803.2367 [hep-ex]

    2008 arXiv

  28. [34]

    Adolph et al

    C. Adolph et al. (COMPASS), Phys. Lett. B713, 10 (2012), arXiv:1202.6150 [hep-ex]

    2012 arXiv

  29. [35]

    Adolph et al

    C. Adolph et al. (COMPASS), Phys. Lett. B736, 124 (2014), arXiv:1401.7873 [hep-ex]

    2014 arXiv

  30. [37]

    X. Luo, H. Sun, J. Li, Y.-L. Xie, and Tichouk, Phys. Rev. D 100, 094036 (2019), arXiv:1906.05674 [hep-ph]

    2019 arXiv

  31. [38]

    Luo and H

    X. Luo and H. Sun, Phys. Rev. D 102, 014044 (2020), arXiv:2004.13507 [hep-ph]

    2020 arXiv

  32. [39]

    X. Luo, H. Sun, and Y.-L. Xie, Phys. Rev. D 101, 054020 (2020), arXiv:2003.03770 [hep-ph]

    2020 arXiv

  33. [40]

    Eidelman et al

    S. Eidelman et al. (Particle Data Group), Phys. Lett. B 592, 1 (2004)

    2004

  34. [41]

    Marcel et al., Astron

    G. Marcel et al., Astron. Astrophys. 659, A194 (2022), arXiv:2109.13592 [astro-ph.HE]

    2022 arXiv

  35. [42]

    Bacchetta, R

    A. Bacchetta, R. Kundu, A. Metz, and P. J. Mulders, Phys. Rev. D 65, 094021 (2002), arXiv:hep-ph/0201091

    2002 arXiv

  36. [43]

    Bacchetta, A

    A. Bacchetta, A. Metz, and J.-J. Yang, Phys. Lett. B 574, 225 (2003), arXiv:hep-ph/0307282

    2003 arXiv

  37. [44]

    Amrath, A

    D. Amrath, A. Bacchetta, and A. Metz, Phys. Rev. D 71, 114018 (2005), arXiv:hep-ph/0504124

    2005 arXiv

  38. [45]

    Lu and I

    Z. Lu and I. Schmidt, Phys. Lett. B 747, 357 (2015), arXiv:1501.04379 [hep-ph]

    2015 arXiv

  39. [46]

    Sjostrand, P

    T. Sjostrand, P. Eden, C. Friberg, L. Lonnblad, G. Miu, S. Mrenna, and E. Norrbin, Comput. Phys. Commun. 135, 238 (2001), arXiv:hep-ph/0010017

    2001 arXiv

  40. [48]

    Airapetian et al

    A. Airapetian et al. (HERMES Collaboration), Phys. Rev. Lett. 103, 152002 (2009)

    2009

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.