Pith. sign in

REVIEW 3 major objections 4 minor 72 references

Beam single spin asymmetry $A_{LU}^{\sin \phi_R}$ of the dihadron production in SIDIS process

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read The longitudinal beam single-spin asymmetry in pion-pair SIDIS is dominated by the $e(x)\otimes H_1^{\sphericalangle}$ term, with the competing $f_1\otimes\widetilde{G}^{\sphericalangle}$ term negligible.

desk verdict A solid, transparent model-based estimate of the dihadron beam-spin asymmetry that deserves serious refereeing, but the Wandzura-Wilczek inference is only as strong as the spectator-model twist-3 DiFF with the quark mass set to zero. read the letter →

arxiv 2505.05963 v1 pith:YK74HONS submitted 2025-05-09 hep-ph

Yanli Li , Keyang She , Hui Li , Xiaoyu Wang , De-Min Li , Zhun Lu This is my paper · ORCID
classification hep-ph
keywords beamsingle-spinasymmetrydihadronfragmentationfunctiontwist-3PDFe(x)semi-inclusivedeepinelasticscatteringWandzura-WilczekapproximationspectatormodelDGLAPevolutionpion-pairproduction
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 establish that the longitudinal beam single-spin asymmetry $A_{LU}^{\sin \phi_R}$ measured in pion-pair production in semi-inclusive deep inelastic scattering is controlled by a single twist-3 term: the convolution of the quark distribution $e(x)$ with the chiral-odd dihadron fragmentation function $H_1^{\sphericalangle}$. Using spectator-model inputs for $e(x)$, the unpolarized dihadron fragmentation function $D_1$, the interference function $H_1^{\sphericalangle}$, and the twist-3 fragmentation function $\widetilde{G}^{\sphericalangle}$, the authors reproduce the $z$- and $M_h$-dependence of the CLAS data once DGLAP evolution of $e(x)$ is included. The second contribution, $f_1 \otimes \widetilde{G}^{\sphericalangle}$, comes out negligible in every kinematic region, which the authors take as support for the Wandzura-Wilczek approximation for this observable. If the claim holds, this asymmetry is a clean collinear access route to $e(x)$ -- a twist-3 distribution linked to the nucleon scalar charge and to the proton mass decomposition -- with testable predictions for COMPASS, EIC, and EicC.

What carries the argument

The load-bearing object is the ratio in Eq. (22): a kinematic factor times the charge-weighted sum $[x e(x)H_{1,ot}^{\sphericalangle}(z,M_h^2) + (M_h/(zM))f_1(x)\widetilde{G}_{ot}^{\sphericalangle}(z,M_h^2)]$ divided by the unpolarized sum $f_1(x)D_{1,oo}(z,M_h^2)$. The spectator model supplies each ingredient: $e(x)$ from scalar and axial-vector diquark channels, $D_{1,oo}$ and $H_{1,ot}^{\sphericalangle}$ from the two-hadron fragmentation correlator, and $\widetilde{G}_{ot}^{\sphericalangle}$ from the quark-gluon-quark correlator. With the fragmenting quark mass set to $m=0$, the imaginary part of $F_s^*F_p$ drops out of $\widetilde{G}_{ot}^{\sphericalangle}$, leaving only the real-part term; this is the step that makes the $f_1\otimes\widetilde{G}^{\sphericalangle}$ contribution numerically tiny. DGLAP evolution of $e(x)$ (implemented with HOPPET) changes the $x$- and $Q^2$-shape of the asymmetry but barely affects its $z$- and $M_h$-dependence. The Wandzura-Wilczek approximation invoked here is the statement that the genuine quark-gluon-quark piece of the twist-3 function can be neglected, leaving only the twist-2-derived part.

What would settle it

A dedicated measurement of $A_{LU}^{\sin\phi_R}$ at COMPASS, EIC, or EicC that separates the $e\otimes H_1^{\sphericalangle}$ and $f_1\otimes\widetilde{G}^{\sphericalangle}$ contributions -- for instance by inspecting the $M_h$-dependence at low $M_h$ (below about 0.63 GeV), where the model's $\widetilde{G}_{ot}^{\sphericalangle}$ is largest -- would settle whether the second term is truly negligible. A non-negligible $f_1\otimes\widetilde{G}^{\sphericalangle}$ contribution would falsify the paper's Wandzura-Wilczek conclusion.

Watch

Extended reading notes

Core claim

The central claim is that the beam single-spin asymmetry $A_{LU}^{\sin \phi_R}$ for pion-pair production in SIDIS is dominated by the convolution of the twist-3 PDF $e(x)$ with the twist-2 chiral-odd dihadron fragmentation function (DiFF) $H_{1,ot}^{\sphericalangle}$, while the second term, involving $f_1(x)$ and the twist-3 DiFF $\widetilde{G}_{ot}^{\sphericalangle}$, is negligible. With spectator-model inputs for all four functions and DGLAP evolution applied to $e(x)$, Eq. (22) reproduces the $z$- and $M_h$-dependence of the CLAS measurement, although the $x$- and $Q^2$-dependence show discrepancies with both CLAS and CLAS12 data. In every kinematic region studied (CLAS, CLAS12, COMPASS, EIC, EicC), the $f_1 \otimes \widetilde{G}^{\sphericalangle}$ contribution is consistent with zero, which the authors read as evidence for the Wandzura-Wilczek approximation. They conclude that the asymmetry remains measurable at the future facilities, with its magnitude suppressed at higher $Q^2$, and that QCD evolution of $e(x)$ is essential for such twist-3 analyses.

Load-bearing premise

The paper's conclusion that the second term is negligible depends on a spectator-model calculation of the twist-3 fragmentation function with the fragmenting quark mass set to zero. If that calculation does not capture the real quark-gluon-quark correlation, the neglected term could be sizeable and the Wandzura-Wilczek conclusion would fail.

Editorial extensions

If this is right

  • Because the $e(x)\otimes H_1^{\sphericalangle}$ term alone reproduces the measured $z$- and $M_h$-dependence, this asymmetry is a viable collinear probe of $e(x)$ that does not require a model for the twist-3 fragmentation function.
  • The $f_1\otimes\widetilde{G}^{\sphericalangle}$ term is reported to be consistent with zero at all studied kinematics, so under the paper's assumptions the Wandzura-Wilczek approximation is valid for this observable and future extractions may drop this term.
  • DGLAP evolution of $e(x)$ changes the asymmetry by enhancing it at small $x$ and small $Q^2$ and suppressing it at large $x$ and large $Q^2$; analyses that ignore twist-3 evolution would misestimate $e(x)$.
  • The same $x$-, $z$-, and $M_h$-shapes appear at COMPASS, EIC, and EicC with reduced magnitude, and the asymmetries are large enough to be measured.
  • The remaining discrepancies in the $x$- and $Q^2$-dependence at CLAS and CLAS12 indicate that the model, the evolution treatment, or the scale dependence of the DiFFs needs refinement at higher scales.

Reading between the lines

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

  • A lattice QCD evaluation of the quark-gluon-quark correlator that defines $\widetilde{G}^{\sphericalangle}$ would test the key model assumption directly: if that correlator is not negligible at the relevant scales, the vanishing of the $f_1\otimes\widetilde{G}^{\sphericalangle}$ term is a spectator-model artifact rather than a property of QCD.
  • The same spectator-model machinery could be applied to other twist-3 dihadron observables, such as the asymmetry with a transversely polarized target; a similarly negligible $\widetilde{G}^{\sphericalangle}$ there would show the Wandzura-Wilczek approximation extends beyond this one beam-spin observable.
  • The paper assumes the DGLAP kernel for $e(x)$ is the same as for $f_1(x)$; a comparison of $A_{LU}^{\sin\phi_R}$ measurements at two well-separated $Q^2$ values, for example CLAS12 versus EIC, would test that assumption and could reveal a distinct twist-3 evolution kernel.
  • The near-zero $f_1\otimes\widetilde{G}^{\sphericalangle}$ prediction could itself be checked by isolating the low-$M_h$ region (below about 0.63 GeV) where the real-part term in $\widetilde{G}_{ot}^{\sphericalangle}$ is largest; a measurable contribution there would falsify the approximation.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies the longitudinal-beam single-spin asymmetry A_LU^{sin phi_R} for pion-pair (dihadron) production in SIDIS off an unpolarized proton. The theoretical basis is the collinear factorization formula Eq. (22), taken from Bacchetta and Radici, in which the asymmetry receives two contributions: a twist-3 PDF e(x) coupled to the twist-2 DiFF H_1^angle, and the unpolarized PDF f_1(x) coupled to a twist-3 DiFF G~^angle. The authors use spectator-model results for e(x), D_1, H_1^angle, and G~^angle, with f_1 from CT10, and evolve e(x) by assuming that its DGLAP kernel is the same as that of f_1. They compare the resulting asymmetry with CLAS and CLAS12 data, report good agreement for the z- and M_h-dependencies while acknowledging discrepancies in x and Q^2, and provide predictions for COMPASS, EIC, and EicC. The main physics conclusions are that the e(x) otimes H_1^angle term dominates, the f_1 otimes G~^angle contribution is consistent with zero and thereby supports the Wandzura-Wilczek approximation, and that QCD evolution of e(x) significantly affects the x- and Q^2-dependence.

Significance. If the results hold, the paper provides a complete model estimate of a twist-3 observable that can access e(x) through dihadron production, and it is apparently the first to include the twist-3 DiFF G~^angle in this asymmetry. The authors give explicit model expressions, parameter tables, and a clear enumeration of the input assumptions, and they produce falsifiable predictions for COMPASS, EIC, and EicC. The comparison with published CLAS and CLAS12 data is a useful benchmark, and the discussion of QCD evolution in a twist-3 PDF analysis is timely. The central numerical and phenomenological conclusions, however, are not yet supported at the level claimed: the agreement with data is qualitative, and the Wandzura-Wilczek conclusion rests on a single spectator-model term with the quark mass set to zero.

major comments (3)
  1. [Sec. III.C, Figs. 5 and 6] The paper's central quantitative claim — "good agreement" with the CLAS z- and M_h-dependent asymmetries — is not supported by any numerical goodness-of-fit measure. The model curves have no uncertainty bands, no chi^2 or pull values are given, and the text itself concedes that the x- and Q^2-dependencies disagree. Since the x- and Q^2-shapes are precisely the observables that carry the e(x) input and its DGLAP evolution, a quantitative comparison (for example chi^2/ndf or bin-wise pulls) is required before the claim of agreement can be evaluated. Without this, the comparison in Figs. 5 and 6 is illustrative only and does not establish the model's ability to describe the data.
  2. [Sec. III.B, Eqs. (33)-(35) and (44)] The conclusion that the f_1 otimes G~^angle term is negligible and "supports the Wandzura-Wilczek approximation" depends entirely on the spectator-model expression for G~_ot. In Eq. (34) the Im(F_s^* F_p) term is multiplied by the coefficient C, and Eq. (35) shows that C is proportional to the fragmenting quark mass m; with m = 0.0 GeV fixed in Eq. (44), this term vanishes and only the Re(F_s^* F_p) contribution, proportional to m_s, remains. The quark-gluon-quark correlator in Eq. (18) is a general nonperturbative object, and the spectator-model replacement of the full final-state sum is a model assumption rather than a QCD result. If the true G~_ot had a different magnitude or sign, the second term in Eq. (22), with its explicit M_h/(zM) and 1/z prefactors, would change the z- and M_h-dependence of the asymmetry and the Wandzura-Wilczek conclusion would not follow. The manuscript should either provide a cross-check of G~_ot (for example, a nonzero m test, an alternative DiFF model, or a model-independent bound) or soften the Wandzura-Wilczek claim to a model-dependent statement.
  3. [Sec. III.A, DGLAP evolution of e(x)] The assumption that the DGLAP evolution kernel for the twist-3 PDF e(x) is identical to that of f_1 is stated but not justified. Twist-3 distributions generally mix with quark-gluon-quark correlation functions under evolution, and the evolution of e(x) is not in general identical to that of a twist-2 PDF. Because one of the paper's stated conclusions is that QCD evolution "plays an essential role" in these observables, the uncertainty introduced by this assumption should be quantified or checked against available LO twist-3 evolution results. As it stands, the x- and Q^2-dependence of the evolved predictions is not fully under control.
minor comments (4)
  1. [Eqs. (48)-(52)] The notation |M| appears where the nucleon mass M is meant, and the placement of the factors 1/x and |R| in the integrands of Eqs. (48)-(52) should be clarified; please ensure that all kinematic prefactors are defined consistently with Eq. (22).
  2. [Captions of Figs. 5-7] The captions use "dashed lines" for two different quantities — the e(x) H_1^angle term and the total asymmetry without QCD evolution — which makes the panels ambiguous. Please use distinct line styles and a clear legend in all three figures.
  3. [Sec. III.C, text before Eq. (53)] There is an incomplete sentence and a typo in the paragraph introducing the CLAS kinematics: "...scattered off an unpolarized proton the kinematical region" should be rewritten, and "dihadron production production" should be corrected.
  4. [Sec. II, Eq. (16) and surrounding text] Several typeset symbols are garbled, for example "H <)" should be H^{angle} throughout; please correct the encoding so that the partial-wave expansions are readable.

Circularity Check

0 steps flagged · score 2.0 of 10

No constructional circularity: the asymmetry is computed from independent spectator-model inputs and compared with un-fitted CLAS/CLAS12 data; the f1⊗G~ smallness is a model output, not an input. Minor self-citations and adjacent tuning keep the score at 2.

full rationale

The derivation is self-contained in the sense required for circularity: Eq. (22) is the standard factorized expression for A_LU^{sin φ_R} from Ref. [36], and none of its ingredients is defined in terms of the asymmetry it predicts. The e(x) input is the spectator model Set 2 of Ref. [50], whose parameter choice was validated against the one-hadron π+ beam SSA at CLAS12, not against the dihadron A_LU data compared in Figs. 5-6; the DiFF inputs D1 and H1^angle, together with the spectator parameters in Eq. (44), were tuned to PYTHIA in Ref. [40]; and the twist-3 DiFF G~^angle is taken from the independent spectator-model calculation of Ref. [49]. The z- and M_h-dependence of the prediction is governed by the DiFF ratios H1/D1 and G~/D1, so it is not forced by the e(x) tuning, while the x- and Q^2-dependence are genuine tests against the data. The statement that f1⊗G~ is 'consistent with zero' is a numerical model output, not an input: even with m=0 in Eq. (44), the Re(F_s^*F_p) term in Eq. (34) survives, so the smallness is not tautological. The main caveats are model dependence and self-citations: Refs. [49], [50], and [54] share authors with the present paper, and setting m=0 removes the Im(F_s^*F_p) contribution to G~^angle, so the Wandzura-Wilczek support is only as strong as the spectator-model qgq correlator. These are correctness risks rather than circular reductions, hence the score is 2 rather than 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central numerical results rest on a chain of model inputs: spectator model e(x) parameters from Refs. [50,56], DiFF parameters from Refs. [40,49], CT10 PDFs, and an assumed DGLAP kernel. None are derived in this paper, and all control the predicted asymmetry. The paper introduces no new physical entities. The most consequential assumptions are the f1-like evolution of e(x) and the spectator model for G~^angle_ot, because they shape the x/Q2 comparison and the WW conclusion.

free parameters (4)
  • Spectator model parameters for e(x) (diquark masses, cutoffs, couplings) = M_s=0.6 GeV, M_v=0.8 GeV, Lambda=0.5 GeV, c_s^2=1.5, c_a^2=0.5, c_a'^2=1.0, N_s^2=6.525, N_v^2=28.716
    Adopted from Ref. [56]; they set the size and shape of e(x) and thereby the dominant eH_1^angle contribution.
  • DiFF spectator parameters = alpha_s=2.60 GeV^2, beta_s=-0.751, gamma_s=-0.193, alpha_p=7.07 GeV^2, beta_p=-0.038, gamma_p=-0.085, f_s=1197 GeV^-1…
    From Ref. [40], tuned to PYTHIA dihadron production; these control D_1, H_1^angle, and G~^angle_ot. The m=0 choice removes the Im(F_s*F_p) contribution to G~^angle_ot.
  • Strong coupling alpha_s = 0.3
    Used in the G~^angle_ot spectator calculation (after Eq. 44); the choice is not derived in this paper.
  • Initial scale for e(x) DGLAP evolution = Q^2 = 1 GeV^2
    The model e(x) is assigned to 1 GeV^2 and evolved with HOPPET; the physical scale of the spectator model is ambiguous.
assumptions (5)
  • domain assumption Twist-3 collinear factorization of the dihadron SIDIS cross section from Ref. [36] is valid.
    Eqs. (9)-(10) and Eq. (22) assume the Bacchetta-Radici factorization, including gauge invariance after kT integration. This is the standard framework, not proved here.
  • ad hoc to paper The DGLAP evolution kernel for the twist-3 PDF e(x) is the same as for f1(x).
    Stated in Sec. III A before Fig. 2 as an assumption. This approximation drives the x- and Q2-dependence results and the claim about the importance of QCD evolution.
  • domain assumption The spectator model for the quark-gluon-quark correlator in Eq. (33) correctly represents the twist-3 DiFF G~^angle_ot.
    Adopted from Ref. [49]; the model has no independent experimental validation and its m=0 limit removes the imaginary term.
  • domain assumption cos(theta)-dependent partial-wave terms in the DiFFs can be neglected.
    The paper argues these terms are higher order or cancel upon theta integration (Sec. II after Eq. 21), following Ref. [37].
  • domain assumption CT10 NLO PDF set gives the unpolarized f1 distribution.
    Adopted from Ref. [53] as an empirical input.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Beam single spin asymmetry $A_{LU}^{\sin \phi_R}$ of the dihadron production in SIDIS process." pith.science (2026). https://pith.science/paper/YK74HONS

@misc{pith2026250505963,
  author       = {Pith},
  title        = {Pith review of: Beam single spin asymmetry $A_LU^\sin \phi_R$ of the dihadron production in SIDIS process},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YK74HONS}},
  note         = {Machine review of arXiv:2505.05963}
}
abstract

We study the longitudinal beam single-spin asymmetry $A_{LU}^{\sin \phi_R}$ of dihadron production in semi-inclusive deep inelastic scattering process with a polarized electron beam scattering off an unpolarized proton target. The asymmetry arises from the convolutions of twist-3 PDF $e(x)$ and twist-2 DiFF $H_1^\sphericalangle$ as well as twist-2 PDF $f_1(x)$ and twist-3 DiFF $\widetilde{G}^{\sphericalangle}$. Using the spectator model calculations for the twist-3 PDF $e(x)$, the DiFFs $D_1 , H_1^\sphericalangle$, and $\widetilde{G}^{\sphericalangle}$, we estimate the BSA $A^{\sin \phi_R}_{LU}$ at the kinematical configuration of CLAS and CLAS12. We find good agreement with $z$- and $M_h$-dependencies data, though $x$- and $Q^2$- dependencies show discrepancies. We include DGLAP evolution of $e(x)$ and provide predictions for COMPASS, EIC, and EicC. The negligible contribution from $f_1(x) \otimes \widetilde{G}^{\sphericalangle}$ supports the Wandzura-Wilczek approximation, while our results highlight the importance of QCD evolution in twist-3 PDF analyses.

Figures

Figures reproduced from arXiv: 2505.05963 by the authors.

Figure 1
Figure 1. FIG. 1: The angle definitions used to measure the beam single s [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: A diagram of the spectator model’s correlation funct [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4: A diagram of the correlation function [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The sin [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

72 extracted references · 65 canonical work pages

  1. [28]

    Courtoy, A

    A. Courtoy, A. S. Miramontes and H. Avakian, et al. Phys. Rev. D 106, 014027 (2022)

    work page 2022

  2. [1]

    Metz and A

    A. Metz and A. Vossen, Prog. Part. Nucl. Phys. 91, 136-202 (2016)

    work page 2016

  3. [2]

    X. K. Wen, B. Yan, Z. Yu and C. P. Yuan, (2024), arXiv:2408. 07255 [hep-ph]

    work page 2024

  4. [3]

    Boussarie, M

    R. Boussarie, M. Burkardt and M. Constantinou, et al. , (2023), arXiv:2304.03302 [hep-ph]

    arXiv 2023

  5. [4]

    Sharma, N

    S. Sharma, N. Kumar and H. Dahiya, Nucl. Phys. B 992, 116247 (2023)

    work page 2023

  6. [5]

    R. L. Jaffe and X. D. Ji, Nucl. Phys. B 375 , 527-560 (1992)

    work page 1992

  7. [6]

    Wakamatsu, Phys

    M. Wakamatsu, Phys. Lett. B 509, 59-68 (2001)

    work page 2001

  8. [7]

    Wakamatsu and Y

    M. Wakamatsu and Y. Ohnishi, Phys. Rev. D 67, 114011 (2003). 15

    work page 2003

Show all 72 references
  1. [8]

    Schweitzer, Phys

    P. Schweitzer, Phys. Rev. D 67, 114010 (2003)

    2003

  2. [9]

    Mukherjee, Phys

    A. Mukherjee, Phys. Lett. B 687, 180-183 (2010)

    2010

  3. [10]

    Avakian, A

    H. Avakian, A. V. Efremov, P. Schweitzer and F. Yuan, Phy s. Rev. D 81, 074035 (2010)

    2010

  4. [11]

    Lorc´ e, B

    C. Lorc´ e, B. Pasquini and P. Schweitzer, JHEP 01, 103 (2015)

    2015

  5. [12]

    Pasquini and S

    B. Pasquini and S. Rodini, Phys. Lett. B 788, 414-424 (2019)

    2019

  6. [13]

    Bastami, A

    S. Bastami, A. V. Efremov and P. Schweitzer, et al. Phys. Rev. D 103, 014024 (2021)

    2021

  7. [14]

    Ji, Nucl

    X. Ji, Nucl. Phys. B, 115181 (2020)

    2020

  8. [15]

    X. D. Ji, Phys. Rev. Lett. 74, 1071-1074 (1995)

    1995

  9. [16]

    Ji, Front

    X. Ji, Front. Phys. (Beijing) 16, 64601 (2021)

    2021

  10. [17]

    Lorc´ e, Eur

    C. Lorc´ e, Eur. Phys. J. C 78, 120 (2018)

    2018

  11. [18]

    Lorc´ e, A

    C. Lorc´ e, A. Metz, B. Pasquini and S. Rodini, JHEP 11, 121 (2021)

    2021

  12. [19]

    Abdul Khalek, A

    R. Abdul Khalek, A. Accardi and J. Adam, et al. Nucl. Phys. A 1026 , 122447 (2022)

    2022

  13. [20]

    Burkardt, Phys

    M. Burkardt, Phys. Rev. D 88, 114502 (2013)

    2013

  14. [21]

    L. P. Gamberg, D. S. Hwang and K. A. Oganessyan, Phys. Let t. B 584, 276-284 (2004)

    2004

  15. [22]

    Jakob, P

    R. Jakob, P. J. Mulders and J. Rodrigues, Nucl. Phys. A 626 , 937-965 (1997)

    1997

  16. [23]

    Airapetian et al

    A. Airapetian et al. [HERMES], Phys. Lett. B 648, 164-170 (2007)

    2007

  17. [24]

    Gohn et al

    W. Gohn et al. [CLAS], Phys. Rev. D 89, 072011 (2014)

    2014

  18. [25]

    Moretti [COMPASS], PoS SPIN2018, 052 (2019)

    A. Moretti [COMPASS], PoS SPIN2018, 052 (2019)

    2019

  19. [26]

    A. V. Efremov, K. Goeke and P. Schweitzer, Phys. Rev. D 67, 114014 (2003)

    2003

  20. [27]

    Avakian et al

    H. Avakian et al. [CLAS], Phys. Rev. D 69, 112004 (2004)

    2004

  21. [29]

    Konishi, A

    K. Konishi, A. Ukawa and G. Veneziano, Phys. Lett. B 78, 243-248 (1978)

    1978

  22. [30]

    Vendramin, Nuovo Cim

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

    1981

  23. [31]

    Vendramin, Nuovo Cim

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

    1981

  24. [32]

    F. A. Ceccopieri, M. Radici and A. Bacchetta, Phys. Lett . B 650, 81-89 (2007)

    2007

  25. [33]

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

    1994

  26. [34]

    As for the strong coupling, we choose αs ≈ 0.3

    numerically, as the Im( F s∗F p) term is proportional to the quark mass m. As for the strong coupling, we choose αs ≈ 0.3. In our analysis, we make the following assumptions (valid only for π+π− pairs) based on the isospin symmetry and charge conjugation [ 28, 40, 66] for twis...

  27. [35]

    Bianconi, S

    A. Bianconi, S. Boffi, R. Jakob and M. Radici, Phys. Rev. D 62, 034008 (2000)

    2000

  28. [36]

    Radici, R

    M. Radici, R. Jakob and A. Bianconi, Phys. Rev. D 65, 074031 (2002)

    2002

  29. [37]

    Bacchetta and M

    A. Bacchetta and M. Radici, Phys. Rev. D 69, 074026 (2004)

    2004

  30. [38]

    Bacchetta and M

    A. Bacchetta and M. Radici, Phys. Rev. D 67, 094002 (2003)

    2003

  31. [39]

    Courtoy, A

    A. Courtoy, A. Bacchetta, M. Radici and A. Bianconi, Phy s. Rev. D 85, 114023 (2012)

    2012

  32. [40]

    Bianconi, S

    A. Bianconi, S. Boffi, R. Jakob and M. Radici, Phys. Rev. D 62, 034009 (2000)

    2000

  33. [41]

    Bacchetta and M

    A. Bacchetta and M. Radici, Phys. Rev. D 74, 114007 (2006)

    2006

  34. [42]

    Bacchetta, F

    A. Bacchetta, F. A. Ceccopieri, A. Mukherjee and M. Radi ci, Phys. Rev. D 79, 034029 (2009)

    2009

  35. [43]

    H. H. Matevosyan, A. W. Thomas and W. Bentz, Phys. Rev. D 88, 094022 (2013)

    2013

  36. [44]

    H. H. Matevosyan, A. Kotzinian and A. W. Thomas, Phys. Le tt. B 731, 208-216 (2014)

    2014

  37. [45]

    H. H. Matevosyan, A. Kotzinian and A. W. Thomas, Phys. Re v. D 96, 074010 (2017)

    2017

  38. [46]

    H. H. Matevosyan, A. Kotzinian and A. W. Thomas, Phys. Re v. D 97, 014019 (2018)

    2018

  39. [47]

    Diehl, Prog

    S. Diehl, Prog. Part. Nucl. Phys. 133, 104069 (2023)

    2023

  40. [48]

    Mirazita et al

    M. Mirazita et al. [CLAS], Phys. Rev. Lett. 126, 062002 (2021)

    2021

  41. [49]

    T. B. Hayward, C. Dilks, A. Vossen and H. Avakian, et al. Phys. Rev. Lett. 126, 152501 (2021)

    2021

  42. [50]

    W. Yang, X. Wang, Y. Yang and Z. Lu, Phys. Rev. D 99, 054003 (2019)

    2019

  43. [51]

    Mao and Z

    W. Mao and Z. Lu, Eur. Phys. J. C 73, 2557 (2013)

    2013

  44. [52]

    D. Boer, P. J. Mulders and F. Pijlman, Nucl. Phys. B 667 , 201-241 (2003)

    2003

  45. [53]

    Lu and I

    Z. Lu and I. Schmidt, Phys. Lett. B 747, 357-364 (2015)

    2015

  46. [54]

    H. L. Lai, M. Guzzi and J. Huston, et al. Phys. Rev. D 82, 074024 (2010)

    2010

  47. [55]

    Mao and Z

    W. Mao and Z. Lu, Phys. Rev. D 87, 014012 (2013)

    2013

  48. [56]

    Diehl et al

    S. Diehl et al. [CLAS], Phys. Rev. Lett. 128, 062005 (2022)

    2022

  49. [57]

    Bacchetta, A

    A. Bacchetta, A. Schaefer and J. J. Yang, Phys. Lett. B 578, 109-118 (2004)

    2004

  50. [58]

    Bacchetta, F

    A. Bacchetta, F. Conti and M. Radici, Phys. Rev. D 78, 074010 (2008)

    2008

  51. [59]

    G. P. Salam and J. Rojo, Comput. Phys. Commun. 180, 120-156 (2009)

    2009

  52. [60]

    L. P. Gamberg, G. R. Goldstein and K. A. Oganessyan, Phys . Rev. D 68, 051501 (2003)

    2003

  53. [61]

    Bacchetta, R

    A. Bacchetta, R. Kundu, A. Metz and P. J. Mulders, Phys. R ev. D 65, 094021 (2002)

    2002

  54. [62]

    Y. Yang, Z. Lu and I. Schmidt, Phys. Rev. D 96, 034010 (2017)

    2017

  55. [63]

    A. V. Belitsky, X. Ji and F. Yuan, Nucl. Phys. B 656 , 165-198 (2003)

    2003

  56. [64]

    Y. Yang, Z. Lu and I. Schmidt, Phys. Lett. B 761, 333-339 (2016)

    2016

  57. [65]

    Amrath, A

    D. Amrath, A. Bacchetta and A. Metz, Phys. Rev. D 71, 114018 (2005)

    2005

  58. [66]

    Singh, Nucl

    B. Singh, Nucl. Data Sheets 106, 601-618 (2005)

    2005

  59. [67]

    Courtoy, (2014), arXiv:1405.7659 [hep-ph]

    A. Courtoy, (2014), arXiv:1405.7659 [hep-ph]

    2014 arXiv

  60. [68]

    Sirtl, (2017), arXiv:1702.07317 [hep-ex]

    S. Sirtl, (2017), arXiv:1702.07317 [hep-ex]

    2017 arXiv

  61. [69]

    G. D. Alexeev et al. [COMPASS], Phys. Lett. B 845, 138155 (2023)

    2023

  62. [70]

    J. Song, Y. Li, S. C. Xue, H. Li and X. Wang, Universe 10, 280 (2024)

    2024

  63. [71]

    H. H. Matevosyan, A. Kotzinian and E. C. Aschenauer, et al. Phys. Rev. D 92, 054028 (2015)

    2015

  64. [72]

    Accardi, J

    A. Accardi, J. L. Albacete, M. Anselmino, et al. Eur. Phys. J. A 52, 268 (2016)

    2016

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.