Pith. sign in

REVIEW 5 major objections 6 minor 59 references

Unraveling the neutron skin thickness through jet charge in deep inelastic scattering

T0 review · 5 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read In deep inelastic electron-lead collisions, the distribution of electric charge inside jets is predicted to shift with collision centrality in a way that reveals the neutron skin thickness of the nucleus.

desk verdict Clever and clean proposal for EIC, but the predicted signal is an artifact of the assumed b-dependent factorization until proven otherwise. read the letter →

arxiv 2506.10694 v1 pith:6P7O3VDD submitted 2025-06-12 hep-ph hep-exnucl-exnucl-th

Shan-Liang Zhang , Enke Wang , Xin-Nian Wang , Hongxi Xing This is my paper
classification hep-phhep-exnucl-exnucl-th
keywords neutronskinthicknessjetchargedeepinelasticscatteringElectron-IonCollidernuclearpartondistributionfunctionsWoods-Saxondensitycentralityisobarcollisions
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 proposes that the jet charge distribution in deep inelastic electron-nucleus scattering is a hard probe of the neutron skin thickness. Jet charge tracks the electric charge of the hadrons in a jet, and because the sign of the charge leans toward the flavor of the struck quark, scattering off a neutron-rich surface should suppress positively charged jets and enhance negatively charged ones in peripheral collisions. The authors demonstrate this centrality-dependent sensitivity in e+Pb collisions at the upcoming Electron-Ion Collider, showing that a double ratio of peripheral to minimum-bias jet-charge distributions grows monotonically with skin thickness and can differ by up to 30% for the PREX-II value. They also show that e+Zr versus e+Ru isobar collisions can distinguish small skin differences. A clean measurement of the neutron skin would constrain the equation of state of neutron-star matter and help settle the tension between existing elastic-scattering and hadronic-probe results.

What carries the argument

The load-bearing object is jet charge, $Q_J=\sum_h (p_T^h/p_T^J)^\kappa Q_h$, the transverse-momentum-weighted electric charge of the hadrons in a jet, whose sign at leading order tracks the flavor of the initiating quark and thereby converts the proton-neutron flavor difference into a measurable distribution. The argument passes through a TMD factorization formula for the jet charge distribution in e+A DIS, an impact-parameter-dependent factorization of nuclear PDFs, Eq. (4), as thickness-weighted sums of proton and neutron PDFs built from Woods-Saxon densities, Eq. (5), and finally the double ratio $R = R_C(Q_J \le -Q_c)/R_C(Q_J \ge Q_c)$, which cancels nPDF uncertainties, centrality-selection bias, and charge-blind final-state cold-nuclear-matter effects. The Woods-Saxon neutron skin parameter $a_n$ is fixed from $\Delta R_{np}$ through the approximate relation $\langle r^2\rangle_n \approx \frac{3}{5}c_n^2 + \frac{7}{5}\pi^2 a_n^2$.

What would settle it

At the EIC, measure the double ratio $R$ in e+Pb at $\sqrt{s}=105$ GeV, $x=0.05$, with centrality classes and $Q_c=0.25$ as used in this paper. If $R$ stays close to unity in the 90-100% peripheral bin for a target whose neutron skin is near 0.28 fm, while the paper predicts up to 30% deviation from unity, the claimed sensitivity is falsified.

Watch

Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that the jet charge distribution in neutral-current deep inelastic scattering is sensitive to the neutron skin of the target nucleus in a way that has not been demonstrated before. In the transverse-momentum-dependent (TMD) factorization formula the final-state jet charge distribution is tied to the initial-state u- and d-quark densities of the nucleus, so the neutron-rich surface of a heavy nucleus leaves a measurable imprint on the charge of the jets it produces. Simulating with PYTHIA and impact-parameter-dependent nuclear parton densities built from Woods-Saxon proton and neutron densities, the authors predict that in peripheral e+Pb collisions the ratio of peripheral to minimum-bias jet-charge distributions is suppressed for positive jet charge and enhanced for negative jet charge. The effect grows with the skin value: the double ratio $R$ reaches about 30% deviation from unity in the most peripheral 90-100% collisions for the PREX-II value, while the smaller coherent-photoproduction skin still yields a distinguishable, smaller signal; in the isobars, e+Zr is predicted to differ from e+Ru by more than 10% in peripheral collisions.

Load-bearing premise

The prediction assumes that at a given collision centrality the nuclear quark content is just the thickness-weighted average of separate proton and neutron quark contents, with the neutron spatial profile fixed by the skin thickness; if that factorisation is inaccurate, the predicted suppression and enhancement could be a model artifact rather than a real observable signature.

Editorial extensions

If this is right

  • At the EIC, the double ratio $R$ in e+Pb should distinguish the PREX-II skin value from the smaller coherent-photoproduction value, because the predicted $R$ values for the two benchmark skins separate clearly in peripheral centralities.
  • Peripheral e+Zr and e+Ru collisions should show a larger-than-10% difference in $R$, providing a new handle on small neutron skins in isobars.
  • Because $R$ is designed to cancel nPDF uncertainties, centrality-selection bias, and final-state cold-nuclear-matter effects, the extracted skin thickness would be less model-dependent than inclusive nuclear-PDF fits.
  • The same flavor-tagging logic extends to photon- and Z-boson tagged jets in p+Pb at the LHC, where quark-initiated jets dominate, giving another channel for the neutron skin.
  • A precise measurement of $\Delta R_{np}$ through this hard probe would tighten constraints on the neutron-star equation of state, complementing low-energy elastic scattering and astrophysical observations.

Reading between the lines

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

  • Because $R_C$ is computed as a function of centrality, which maps to impact parameter through the thickness function, the same data could in principle be inverted to extract the radial neutron density profile rather than only the rms skin radius.
  • Varying the threshold $Q_c$ and the power $\kappa$ in the definition of jet charge would provide independent cross-checks and could expose contamination from heavier-flavor jets, which are not captured by the leading u/d flavor picture.
  • The centrality-classification bias that the paper worries about could be tested directly by comparing $R$ extracted with different centrality estimators, such as electron kinematics versus forward neutron multiplicity, a check the paper does not perform.
  • If the factorization of Eq. (4) is accurate, similar jet-charge ratios could be applied to other neutron-rich nuclei at the EIC, extending the method beyond Pb, Ru, and Zr.
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

5 major / 6 minor

Summary. The paper proposes measuring the neutron skin thickness of neutron-rich nuclei using the jet charge distribution in deep inelastic scattering (DIS) at the Electron-Ion Collider. The authors simulate e+Pb, e+Ru, and e+Zr collisions with PYTHIA 8.3 and CT14nlo/EPPS16 nPDFs, assuming that impact-parameter-dependent nuclear PDFs factorize as a thickness-weighted sum of proton and neutron PDFs with Woods-Saxon densities. They define a centrality-dependent nuclear modification factor RC and a double ratio R, and predict that peripheral collisions suppress positive jet charge and enhance negative jet charge, with effects up to 30% for the PREX-II neutron skin thickness. They also apply the idea to isobar collisions and suggest extensions to photon- and Z-tagged jet charge in p+Pb collisions at the LHC.

Significance. If the predicted sensitivity is genuine, the proposal provides a new hard-probe channel for neutron skin studies that is complementary to low-energy elastic scattering and could help discriminate between discrepant values of Delta Rnp, such as PREX-II versus coherent pion photoproduction. The double-ratio construction is a sensible attempt to cancel centrality-selection and final-state uncertainties, and the use of jet charge as a flavor tag is well motivated by previous work. The paper is not circular: it uses external measurements of Delta Rnp as inputs and computes the observable without fitting Delta Rnp from its own output. However, the central prediction rests on an unvalidated impact-parameter factorization in Eq. (4), and the paper does not demonstrate that the predicted centrality pattern is not an artifact of that model assumption.

major comments (5)
  1. [Eq. (4), 'Jet Charge and neutron skin'] The centrality dependence of the entire prediction is generated by Eq. (4), which assumes that the impact-parameter-dependent nPDF is a thickness-weighted sum of proton and neutron PDFs, with all b-dependence entering only through the Woods-Saxon geometry. This factorization is not validated against existing nuclear DIS data or against the EPPS16/CT14nlo baseline used in the simulation. Any b-dependent nuclear modification, such as stronger shadowing at small impact parameters or a b-dependent EMC effect, would enter RC through the same integral and could produce a similar peripheral suppression/enhancement pattern. Because the 30% effect shown in Fig. 4 is proportional to this factorization, the paper does not yet establish that the observed centrality signal is a genuine neutron-skin signature rather than a model artifact.
  2. [Eq. (6) and text near Fig. 3] The paper states that uncertainties from nPDFs are expected to be largely cancelled in the ratio RC, but this cancellation holds only for b-independent uncertainties that scale identically in the centrality and minimum-bias cross sections. The factorization in Eq. (4) is precisely an assumption about the b-dependence of nPDFs, and any b-dependent uncertainty in the nuclear modification factor enters RC directly and is not cancelled by the minimum-bias normalization. The argument for nPDF cancellation therefore does not remove the model dependence identified above, and the claim should be either substantiated with a demonstration or qualified accordingly.
  3. [Eq. (7) and Fig. 4] The double ratio R is proposed to mitigate centrality-classification bias, but the assertion that 'the centrality selection bias should be significantly reduced by the first ratio' is not quantitatively demonstrated. In e+A DIS, centrality is not a direct measurement of impact parameter; the mapping from experimental centrality classes to bmin and bmax values is not specified, and no study is given of how an imperfect b selection, or contamination between centrality classes, affects R. Without such a demonstration, the centrality-to-impact-parameter mapping remains a free model input, and the quantitative predictions for the most peripheral bin (e.g., the 30% effect in Fig. 4) are not robust to realistic centrality resolution.
  4. [Phenomenological results, EIC projections] The paper claims that statistical and systematic uncertainties at the EIC will be 'much smaller than the bands shown in Fig. 4' but provides no quantitative estimate of expected event counts, jet reconstruction efficiencies, or systematic errors. The most peripheral centrality bin (80-100% or 90-100%) is likely to contain only a small fraction of the total DIS sample, and without a statistical projection it is not established that the predicted 20-30% modifications are measurable with the EIC design luminosity. This is a load-bearing gap for the central proposal, which is framed as a future measurement.
  5. [Eq. (5) and the relation between Delta Rnp and a_n] The mapping from Delta Rnp to the neutron diffuseness parameter a_n uses the approximate relation <r^2>_n ~ (3/5)c_n^2 + (7/5)pi^2 a_n^2 with c_n fixed, interpreting Delta Rnp entirely as a change in surface diffuseness rather than half-density radius. While this follows Refs. [41,42], the paper does not discuss how sensitive the predicted RC and R are to this modeling choice, nor does it validate the approximation against realistic density distributions. The vertical and horizontal uncertainty bands in Figs. 4 and 5 inherit this model assumption, so the reported sensitivity to Delta Rnp is not a complete propagation of the experimental uncertainty.
minor comments (6)
  1. [Abstract and Introduction] The phrase 'has traditionally been measured using elastic fixed target electron-nucleus scattering since the 1970s' is imprecise: modern measurements include parity-violating electron scattering, which is also fixed-target but at low momentum transfer, and the sentence should distinguish elastic scattering from the DIS process used here.
  2. [Introduction, paragraph after Eq. (1)] There are several typographical errors: 'more challenge' should be 'more challenging', 'ab initial calculations' should be 'ab initio calculations', 'Relativisitic Heavy Ion Collider' should be 'Relativistic Heavy Ion Collider', and 'state-of-art' should be 'state-of-the-art'.
  3. [Fig. 4 caption] The caption contains a typo: 'collisons' should be 'collisions'.
  4. [Eq. (5)] The text refers to a 'deformed Woods-Saxon distribution', but Eq. (5) is spherically symmetric. If the intention is to allow deformation for Ru and Zr, the parameters and the deformed form should be specified; otherwise 'deformed' is misleading.
  5. [Eq. (4) and notation] The notation f_i^{p/A} and f_i^{n/A} is not defined explicitly. It should be stated whether these are the bound proton and neutron PDFs with nuclear modifications, and how they are extracted from EPPS16 and CT14nlo in the PYTHIA implementation.
  6. [Phenomenological results, Fig. 3] The paper does not show the statistical or systematic uncertainties on the PYTHIA results in Fig. 3, nor the event statistics used. Adding this information would help the reader judge the significance of the moderate centrality dependence observed in the 'All QJ' panel.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the neutron-skin inputs are external measurements, and the jet-charge double ratio is computed forward from them; the unvalidated impact-parameter factorization is a model assumption, not a circular step.

full rationale

The paper's input-output chain is not circular. The neutron skin thickness is taken from external measurements (PREX-II, coherent pion photoproduction) and from the isobar literature, and these values are converted to Woods-Saxon neutron diffuseness parameters via the external rms-radius relation of Ref. [41]. The jet-charge double ratio is then computed forward with PYTHIA using CT14nlo and EPPS16 nPDFs. No step uses the computed ratio to set the input neutron skin thickness, and no fitted parameter is renamed as a prediction: the 'prediction' is the centrality dependence of the ratio as a function of assumed input Delta Rnp. The impact-parameter factorization in Eq. (4) is an explicit ansatz; if it fails, the numerical signal would be a model artifact, but that is a correctness or validation concern, not circularity. The self-citations (nuclear TMD references and cold-nuclear-matter references) are not load-bearing for the claimed sensitivity: the simulation uses PYTHIA with CT14nlo/EPPS16, and the final-state effects are argued to cancel in the double ratio. The central claim therefore has independent content and does not reduce to its inputs by construction.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central prediction inherits most of its content from external inputs (PYTHIA, EPPS16, WS parameters). The paper's own modeling assumptions are the impact-parameter factorization and the mapping from Delta Rnp to diffuseness; the observable is then a deterministic function of the assumed density profile.

free parameters (3)
  • kappa (jet charge weighting power) = 0.3
    Controls shape of jet charge distribution; chosen from Ref. [29], not optimized in this paper.
  • Q_c (jet charge selection cut) = 0.25
    Sets separation between positive and negative jet charge regions in double ratio; chosen by hand.
  • neutron diffuseness parameter a_n = 0.566 fm and 0.654 fm for Pb; 0.505 fm for Ru; 0.574 fm for Zr
    Determined from external Delta Rnp values using the relation <r^2> ~ 3/5 c^2 + 7/5 pi^2 a^2; the mapping is a modeling choice that dictates the centrality dependence.
assumptions (6)
  • domain assumption Impact-parameter dependent nPDFs factorize as thickness-weighted sums of proton and neutron nPDFs (Eq. 4).
    The centrality dependence of the jet charge observable is entirely generated by this factorized form; no validation against nuclear DIS data is provided.
  • domain assumption Woods-Saxon density parametrization for proton and neutron distributions (Eq. 5).
    Used to construct thickness functions; proton parameters fixed from Ref. [23], neutron parameters from the Delta Rnp interpretation of Refs. [41,42].
  • standard math Relation <r^2> = 3/5 c^2 + 7/5 pi^2 a^2 for rms radius of Woods-Saxon distribution.
    Used to map Delta Rnp to a_n; standard approximate relation from Ref. [41].
  • domain assumption TMD QCD factorization for jet charge distribution in DIS (Eq. 2), as established in Ref. [29].
    The paper relies on this factorization to justify the flavor-jet charge correlation; it is not re-derived here.
  • domain assumption PYTHIA 8.3 with CT14nlo and EPPS16 nPDFs reproduces the TMD factorization results for jet charge.
    Simulations are used in place of a full analytical calculation; consistency argued from Ref. [29] but not quantified.
  • domain assumption Final-state cold nuclear matter effects are electric-charge blind and cancel in the double ratio R.
    Asserted in the text following Eq. (7); no simulation or calculation demonstrating the cancellation is provided.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Unraveling the neutron skin thickness through jet charge in deep inelastic scattering." pith.science (2026). https://pith.science/paper/6P7O3VDD

@misc{pith2026250610694,
  author       = {Pith},
  title        = {Pith review of: Unraveling the neutron skin thickness through jet charge in deep inelastic scattering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6P7O3VDD}},
  note         = {Machine review of arXiv:2506.10694}
}
abstract

The neutron skin thickness in neutron-rich nuclei has traditionally been measured using elastic fixed target electron-nucleus scattering since the 1970s. In this paper, we propose a novel probe of the neutron skin thickness through deep inelastic scattering in electron-ion collisions, leveraging the intrinsic correlation between final-state jet charge distribution and initial-state partonic distributions in nucleons. Specifically, we demonstrate the sensitivity of jet charge distribution to the neutron skin thickness in $e$+Pb collisions with varying centralities, and in isobar collisions of $e$+Ru and $e$+Zr. We predict a strong suppression of positive jet charge distribution and an enhancement for negative jet charge distribution in peripheral electron-ion collisions, revealing the neutron skin effect. This proposal can also be extended to photon and Z-boson tagged jet charge distribution in proton-nucleus collisions at the Large Hadron Collider, providing an alternative access to neutron skin thickness.

Figures

Figures reproduced from arXiv: 2506.10694 by the authors.

Figure 1
Figure 1. FIG. 1. (Color online) An illustration depicting negative jet [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (Color online) Jet charge distribution of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (Color online) The nuclear modification factor [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (Color online) The double ratio of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (Color online) The double ratio [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

59 extracted references · 19 canonical work pages

  1. [1]

    Roy and R

    P. Roy and R. Kanungo, DAE Symp. Nucl. Phys. 67, 23 (2024)

    work page 2024

  2. [2]

    Sammarruca, Symmetry 16, 34 (2024), arXiv:2311.02539

    F. Sammarruca, Symmetry 16, 34 (2024), arXiv:2311.02539

    arXiv 2024

  3. [3]

    Ma and S

    Y.-G. Ma and S. Zhang, Influence of Nuclear Structure 6 in Relativistic Heavy-Ion Collisions (, 2022), pp. 1–30, arXiv:2206.08218

    arXiv 2022

  4. [4]

    Frois et al

    B. Frois et al. , Phys. Rev. Lett. 38, 152 (1977)

    work page 1977

  5. [5]

    B. C. Clark, L. J. Kerr, and S. Hama, Phys. Rev. C 67, 054605 (2003), arXiv:nucl-th/0209052

    arXiv 2003

  6. [6]

    Neutron skins of $^{208}$Pb and $^{48}$Ca from pionic probes

    E. Friedman, Nucl. Phys. A 896, 46 (2012), arXiv:1209.6168

    work page Pith review arXiv 2012

  7. [7]

    C. M. Tarbert et al., Phys. Rev. Lett. 112, 242502 (2014), arXiv:1311.0168

    arXiv 2014

  8. [8]

    B. A. Brown, G. Shen, G. C. Hillhouse, J. Meng, and A. Trzcinska, Phys. Rev. C 76, 034305 (2007)

    work page 2007

Show all 59 references
  1. [9]

    Roca-Maza et al

    X. Roca-Maza et al. , Phys. Rev. C 92, 064304 (2015), arXiv:1510.01874

    2015 arXiv

  2. [10]

    Adhikari et al., Phys

    PREX, D. Adhikari et al., Phys. Rev. Lett. 126, 172502 (2021), arXiv:2102.10767

    2021 arXiv

  3. [11]

    Abrahamyan et al

    S. Abrahamyan et al. , Phys. Rev. Lett. 108, 112502 (2012), arXiv:1201.2568

    2012 arXiv

  4. [12]

    Hu et al

    B. Hu et al. , Nature Phys. 18, 1196 (2022), arXiv:2112.01125

    2022 arXiv

  5. [13]

    B. T. Reed, F. J. Fattoyev, C. J. Horowitz, and J. Piekarewicz, Phys. Rev. Lett. 126, 172503 (2021), arXiv:2101.03193

    2021 arXiv

  6. [14]

    Li et al

    H. Li et al. , Phys. Rev. Lett. 125, 222301 (2020), arXiv:1910.06170

    2020 arXiv

  7. [15]

    Q. Liu, S. Zhao, H.-j. Xu, and H. Song, Phys. Rev. C 109, 034912 (2024), arXiv:2311.01747

    2024 arXiv

  8. [16]

    Guo, B.-A

    W.-M. Guo, B.-A. Li, and G.-C. Yong, Phys. Rev. C 108, 034617 (2023), arXiv:2307.05135

    2023 arXiv

  9. [17]

    L.-M. Liu, J. Xu, and G.-X. Peng, Phys. Lett. B 838, 137701 (2023), arXiv:2301.07893

    2023 arXiv

  10. [18]

    Cheng, S

    Y.-L. Cheng, S. Shi, Y.-G. Ma, H. St¨ ocker, and K. Zhou, Phys. Rev. C 107, 064909 (2023), arXiv:2301.03910

    2023 arXiv

  11. [19]

    Liu, C.-J

    L.-M. Liu, C.-J. Zhang, J. Xu, J. Jia, and G.-X. Peng, Phys. Rev. C 106, 034913 (2022), arXiv:2209.03106

    2022 arXiv

  12. [20]

    Liu et al

    L.-M. Liu et al. , Phys. Lett. B 834, 137441 (2022), arXiv:2203.09924

    2022 arXiv

  13. [21]

    Xu et al

    H.-j. Xu et al. , Phys. Rev. C 108, L011902 (2023), arXiv:2111.14812

    2023 arXiv

  14. [22]

    H.-j. Xu, H. Li, X. Wang, C. Shen, and F. Wang, Phys. Lett. B 819, 136453 (2021), arXiv:2103.05595

    2021 arXiv

  15. [23]

    Giacalone, G

    G. Giacalone, G. Nijs, and W. van der Schee, Phys. Rev. Lett. 131, 202302 (2023), arXiv:2305.00015

    2023 arXiv

  16. [24]

    Paukkunen, Phys

    H. Paukkunen, Phys. Lett. B 745, 73 (2015), arXiv:1503.02448

    2015 arXiv

  17. [25]

    Helenius, H

    I. Helenius, H. Paukkunen, and K. J. Eskola, Eur. Phys. J. C 77, 148 (2017), arXiv:1606.06910

    2017 arXiv

  18. [26]

    Aad et al

    ATLAS, G. Aad et al. , Eur. Phys. J. C 79, 935 (2019), arXiv:1907.10414

    2019 arXiv

  19. [27]

    van der Schee, Y.-J

    W. van der Schee, Y.-J. Lee, G. Nijs, and Y. Chen, (2023), arXiv:2307.11836

    2023 arXiv

  20. [28]

    Krohn, M

    D. Krohn, M. D. Schwartz, T. Lin, and W. J. Waalewijn, Phys. Rev. Lett. 110, 212001 (2013), arXiv:1209.2421

    2013 arXiv

  21. [29]

    Z.-B. Kang, X. Liu, S. Mantry, and D. Y. Shao, Phys. Rev. Lett. 125, 242003 (2020), arXiv:2008.00655

    2020 arXiv

  22. [30]

    Aad et al., Phys

    ATLAS, G. Aad et al., Phys. Rev. D 93, 052003 (2016), arXiv:1509.05190

    2016 arXiv

  23. [31]

    CMS, A. M. Sirunyan et al. , JHEP 10, 131 (2017), arXiv:1706.05868

    2017 arXiv

  24. [32]

    CMS, A. M. Sirunyan et al. , JHEP 07, 115 (2020), arXiv:2004.00602

    2020 arXiv

  25. [33]

    Chen, B.-W

    S.-Y. Chen, B.-W. Zhang, and E.-K. Wang, Chin. Phys. C 44, 024103 (2020), arXiv:1908.01518

    2020 arXiv

  26. [34]

    Abdul Khalek et al

    R. Abdul Khalek et al. , Nucl. Phys. A 1026, 122447 (2022), arXiv:2103.05419

    2022 arXiv

  27. [35]

    R. D. Field and R. P. Feynman, Nucl. Phys. B 136, 1 (1978)

    1978

  28. [36]

    W. J. Waalewijn, Phys. Rev. D 86, 094030 (2012), arXiv:1209.3019

    2012 arXiv

  29. [37]

    X. Liu, F. Ringer, W. Vogelsang, and F. Yuan, Phys. Rev. Lett. 122, 192003 (2019), arXiv:1812.08077

    2019 arXiv

  30. [38]

    Alrashed, D

    M. Alrashed, D. Anderle, Z.-B. Kang, J. Terry, and H. Xing, Phys. Rev. Lett. 129, 242001 (2022), arXiv:2107.12401

    2022 arXiv

  31. [39]

    Alrashed, Z.-B

    M. Alrashed, Z.-B. Kang, J. Terry, H. Xing, and C. Zhang, (2023), arXiv:2312.09226

    2023 arXiv

  32. [40]

    M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, Ann. Rev. Nucl. Part. Sci. 57, 205 (2007), arXiv:nucl- ex/0701025

    2007

  33. [41]

    Trzcinska et al

    A. Trzcinska et al. , Phys. Rev. Lett. 87, 082501 (2001)

    2001

  34. [42]

    Zenihiro et al

    J. Zenihiro et al. , Phys. Rev. C 82, 044611 (2010)

    2010

  35. [43]

    Sjostrand, S

    T. Sjostrand, S. Mrenna, and P. Z. Skands, Comput. Phys. Commun. 178, 852 (2008), arXiv:0710.3820

    2008 arXiv

  36. [44]

    Dulat et al

    S. Dulat et al. , Phys. Rev. D 93, 033006 (2016), arXiv:1506.07443

    2016 arXiv

  37. [45]

    K. J. Eskola, P. Paakkinen, H. Paukkunen, and C. A. Sal- gado, Eur. Phys. J. C 77, 163 (2017), arXiv:1612.05741

    2017 arXiv

  38. [46]

    Cacciari, G

    M. Cacciari, G. P. Salam, and G. Soyez, JHEP 04, 063 (2008), arXiv:0802.1189

    2008 arXiv

  39. [47]

    Cacciari, G

    M. Cacciari, G. P. Salam, and G. Soyez, Eur. Phys. J. C 72, 1896 (2012), arXiv:1111.6097

    2012 arXiv

  40. [48]

    Z.-B. Kang, X. Liu, S. Mantry, M. C. Spraker, and T. Wilson, Phys. Rev. D 103, 074028 (2021), arXiv:2101.04304

    2021 arXiv

  41. [49]

    Z.-B. Kang, A. J. Larkoski, and J. Yang, Phys. Rev. Lett. 130, 151901 (2023), arXiv:2301.09649

    2023 arXiv

  42. [50]

    Z.-B. Kang, X. Liu, S. Mantry, and J.-W. Qiu, Phys. Rev. D 88, 074020 (2013), arXiv:1303.3063

    2013 arXiv

  43. [51]

    D. P. Anderle et al. , Front. Phys. (Beijing) 16, 64701 (2021), arXiv:2102.09222

    2021 arXiv

  44. [52]

    Guo, Phys

    X.-f. Guo, Phys. Rev. D 58, 114033 (1998), arXiv:hep- ph/9804234

    1998

  45. [53]

    Z.-B. Kang, E. Wang, X.-N. Wang, and H. Xing, Phys. Rev. Lett. 112, 102001 (2014), arXiv:1310.6759

    2014 arXiv

  46. [54]

    Ru, Z.-B

    P. Ru, Z.-B. Kang, E. Wang, H. Xing, and B.-W. Zhang, Phys. Rev. D 103, L031901 (2021), arXiv:1907.11808

    2021 arXiv

  47. [55]

    Ru, Z.-B

    P. Ru, Z.-B. Kang, E. Wang, H. Xing, and B.-W. Zhang, (2023), arXiv:2302.02329

    2023 arXiv

  48. [56]

    Guo and X.-N

    X.-f. Guo and X.-N. Wang, Phys. Rev. Lett. 85, 3591 (2000), arXiv:hep-ph/0005044

    2000 arXiv

  49. [57]

    Wang and X.-N

    E. Wang and X.-N. Wang, Phys. Rev. Lett. 89, 162301 (2002), arXiv:hep-ph/0202105

    2002 arXiv

  50. [58]

    H. T. Li and I. Vitev, Phys. Rev. Lett. 126, 252001 (2021), arXiv:2010.05912

    2021 arXiv

  51. [59]

    Zhang, X.-N

    S.-L. Zhang, X.-N. Wang, and B.-W. Zhang, Phys. Rev. C 105, 054902 (2022), arXiv:2103.07836

    2022 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.