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arxiv: 2606.27162 · v1 · pith:W5AD3EUYnew · submitted 2026-06-25 · ✦ hep-ph

StringSpinner 2.0: Enabling quark spin effects in PYTHIA for e^+e^- annihilation

A. Kerbizi , L. L\"onnblad This is my paper

Pith reviewed 2026-06-26 03:47 UTC · model grok-4.3

classification ✦ hep-ph
keywords StringSpinnerPYTHIAquark spin effectsstring fragmentationCollins asymmetrye+e- annihilation3P0 modelspin density matrix
0
0 comments X

The pith

StringSpinner 2.0 adds joint spin density matrices to PYTHIA so that quark spin correlations propagate through string fragmentation in e+e- annihilation.

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

The paper extends the StringSpinner package to handle the full leading-order process of electron-positron annihilation into hadrons inside the PYTHIA generator. It introduces a joint spin density matrix that encodes the initial correlations between the produced quark and antiquark, then applies the propagation rules of the string+3P0 model at each step of the fragmentation chain when pseudoscalar or vector mesons are formed. This machinery produces observable spin-dependent asymmetries such as the Collins and Artru-Collins effects. The authors demonstrate the package by computing the polar-angle dependence of the Collins asymmetry for back-to-back pions and comparing the result with existing data. A reader would care because the update turns an existing hadronization model into a practical tool for generating events that include quark spin information without changing the core PYTHIA framework.

Core claim

The updated package implements the string+3P0 model rules for propagating a user-defined joint spin density matrix of the q qbar pair along the fragmentation chain, allowing simulation of spin effects including Collins and Artru-Collins asymmetries for pseudoscalar and vector mesons produced in e+e- annihilation at leading order.

What carries the argument

The joint spin density matrix of the q qbar pair, whose elements are updated at each string break according to the string+3P0 model's production amplitudes for mesons.

If this is right

  • The package now generates events that exhibit the Collins asymmetry and the Artru-Collins asymmetry at leading order.
  • Any spin-dependent observable predicted by the string+3P0 model can be studied by supplying a custom joint density matrix for the q qbar pair.
  • The implementation covers both pseudoscalar and vector meson production during string fragmentation.

Where Pith is reading between the lines

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

  • The same machinery could be used to explore how initial spin correlations affect the transverse momentum distributions of hadrons in e+e- events.
  • If the density matrix is taken from a different production mechanism, the package would allow direct comparison of competing models of quark spin transfer.

Load-bearing premise

Spin correlations between the initial quark and antiquark can be completely captured by a single joint density matrix and then transferred step-by-step using only the local production rules of the string+3P0 model.

What would settle it

If the polar-angle dependence of the Collins asymmetry for back-to-back pions generated by the package deviates significantly from the measured data while all other inputs remain fixed, the propagation rules or the chosen density-matrix parametrization would be shown to be insufficient.

Figures

Figures reproduced from arXiv: 2606.27162 by A. Kerbizi, L. L\"onnblad.

Figure 1
Figure 1. Figure 1: Kinematics of the e + e − → qq¯ in the CMS. 2.2. The joint spin density matrix ρ(q, q¯) Once the qq¯ pair is generated, we set up the joint spin den￾sity matrix ρ(q, q¯), which implements the correlations between the spin states of q and ¯q. For unpolarized beams, including γ ∗ /Z 0 interference and neglecting the quark mass, the joint spin density matrix reads [15] ρ(q, q¯) = 1 4  Iq ⊗ Iq¯ + C qq¯ zz σ z… view at source ↗
Figure 2
Figure 2. Figure 2: Representation of the spin-dependent fragmentation in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Simulated A UL 12 (full circles) and A UC 12 (full squares) asymmetries as a function of sin2 θ/(1 + cos2 θ) obtained from 20 106 e + e − events at √ s = 10.6 GeV. The straight lines represent the linear fits to the asymmetries. The corresponding asymmetries measured by BABAR [20] are given by the open points. and A UC 12 asymmetries. Likewise to the experimental analysis we have applied the selection z1(2… view at source ↗
read the original abstract

The StringSpinner package, which implements quark spin effects in the PYTHIA event generator using the string+${}^3P_0$ model of hadronization, is extended to handle the process $e^+e^-\rightarrow q\bar{q} \rightarrow hadrons$ at leading order. The correlations between the spin states of the $q\bar{q}$ pair produced in the reaction are described by a joint spin density matrix. The spin correlations are propagated along the string fragmentation chain by using the rules of the string+${}^3P_0$ model and are implemented for the production of pseudoscalar and vector mesons. The new version of the package can be used to simulate spin effects in $e^+e^-$ annihilation like the Collins and the Artru-Collins asymmetries. It can also be applied to the study of other spin effects in hadronization predicted by the string+${}^3P_0$ model with a user-defined joint spin density matrix of the $q\bar{q}$ pair. To showcase the usage of the package the polar angle dependence of the Collins asymmetries for back-to-back pions is studied and compared with the available data.

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

1 major / 1 minor

Summary. The manuscript presents StringSpinner 2.0, an extension of the StringSpinner package that implements quark spin effects in PYTHIA for the process e⁺e⁻ → q q̄ → hadrons at leading order. Spin correlations are encoded in a user-defined joint spin density matrix for the initial q q̄ pair and propagated through the string fragmentation chain according to the rules of the string+³P₀ model, with explicit implementations for both pseudoscalar and vector meson production. The package is shown to enable simulation of spin asymmetries such as the Collins and Artru-Collins asymmetries; its usage is illustrated by a comparison of the polar-angle dependence of the Collins asymmetry for back-to-back pions against existing data.

Significance. If the implementation is correct, the work supplies a publicly released Monte Carlo tool that allows systematic exploration of spin-dependent hadronization effects in e⁺e⁻ annihilation with arbitrary initial q q̄ spin correlations. This is useful for phenomenology because it connects the string+³P₀ framework directly to observable asymmetries and supplies an external data anchor for at least the Collins case.

major comments (1)
  1. [Abstract] Abstract (final paragraph): the polar-angle dependence of the Collins asymmetry is compared with data, yet the manuscript supplies neither the numerical values chosen for the elements of the joint spin density matrix nor any quantitative measure (χ², pull distribution, or uncertainty band) of the agreement. Because this comparison is presented as the principal demonstration that the spin-propagation rules function correctly, the absence of these details is load-bearing for the central claim.
minor comments (1)
  1. The abstract refers to 'the new version of the package' while the title uses 'StringSpinner 2.0'; a single consistent versioning statement would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and positive recommendation. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (final paragraph): the polar-angle dependence of the Collins asymmetry is compared with data, yet the manuscript supplies neither the numerical values chosen for the elements of the joint spin density matrix nor any quantitative measure (χ², pull distribution, or uncertainty band) of the agreement. Because this comparison is presented as the principal demonstration that the spin-propagation rules function correctly, the absence of these details is load-bearing for the central claim.

    Authors: We agree that the specific numerical values of the joint spin density matrix elements used for the Collins asymmetry comparison, together with a quantitative measure of agreement, should be stated explicitly. In the revised manuscript we will add these values (taken from the string+³P₀ model parameters already employed in the code) to the results section and report a χ² per degree of freedom for the polar-angle dependence shown in the figure. This change will be reflected in an updated abstract as well. revision: yes

Circularity Check

0 steps flagged

No significant circularity: implementation of established model with external data anchor

full rationale

The manuscript extends an existing StringSpinner package by implementing propagation rules for a user-defined joint spin density matrix of the q qbar pair through the string+3P0 fragmentation chain, for both pseudoscalar and vector mesons. The central claim is the correctness of this software implementation for producing observables such as Collins and Artru-Collins asymmetries. A direct comparison of the resulting polar-angle dependence against existing data supplies an external benchmark. No derivation reduces by construction to fitted inputs, no self-definitional equations appear, and no load-bearing uniqueness theorem or ansatz is imported via self-citation. The work is self-contained as a released code package whose predictions are not forced by its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumptions of the string+3P0 model for spin propagation and the applicability of a joint spin density matrix description to the initial q qbar state in e+e- annihilation.

axioms (1)
  • domain assumption Rules of the string+3P0 model govern propagation of spin correlations along the fragmentation chain for pseudoscalar and vector mesons
    Invoked to implement spin effects in the e+e- process

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Reference graph

Works this paper leans on

29 extracted references · 22 canonical work pages · 11 internal anchors

  1. [1]

    Kerbizi, L

    A. Kerbizi, L. Lönnblad, StringSpinner - adding spin to the PYTHIA string fragmentation, Comput. Phys. Com- mun. 272 (2022) 108234.arXiv:2105.09730,doi: 10.1016/j.cpc.2021.108234

    work page doi:10.1016/j.cpc.2021.108234 2022

  2. [2]

    An equivalence between generalized Maxwell model and fractional Zener model, Mechanics of Materials 100:148-153 (2016)

    A. Kerbizi, L. Lönnblad, Extending StringSpinner to han- dle vector-meson spin, Comput. Phys. Commun. 292 (2023) 108886.arXiv:2305.05058,doi:10.1016/j. cpc.2023.108886

    work page doi:10.1016/j 2023

  3. [3]

    Kerbizi, X

    A. Kerbizi, X. Artru, A. Martin, Production of vector mesons in the String+ 3P0 model of polarized quark frag- mentation, Phys. Rev. D 104 (11) (2021) 114038.arXiv: 2109.06124,doi:10.1103/PhysRevD.104.114038

    work page doi:10.1103/physrevd.104.114038 2021

  4. [4]

    J. C. Collins, Fragmentation of transversely polarized quarks probed in transverse momentum distributions, Nucl. Phys. B 396 (1993) 161–182.arXiv:hep-ph/ 9208213,doi:10.1016/0550-3213(93)90262-N

    work page doi:10.1016/0550-3213(93)90262-n 1993

  5. [5]

    J. C. Collins, S. F. Heppelmann, G. A. Ladinsky, Mea- suring transversity densities in singly polarized hadron hadron and lepton - hadron collisions, Nucl. Phys. B 420 (1994) 565–582.arXiv:hep-ph/9305309,doi: 10.1016/0550-3213(94)90078-7

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/0550-3213(94)90078-7 1994

  6. [6]

    R. L. Jaffe, X.-m. Jin, J. Tang, Interference fragmentation functions and the nucleon’s transversity, Phys. Rev. Lett. 80 (1998) 1166–1169.arXiv:hep-ph/9709322,doi: 10.1103/PhysRevLett.80.1166

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.80.1166 1998

  7. [7]

    Bianconi, S

    A. Bianconi, S. Boffi, R. Jakob, M. Radici, Two hadron in- terference fragmentation functions. Part 1. General frame- work, Phys. Rev. D 62 (2000) 034008.arXiv:hep-ph/ 9907475,doi:10.1103/PhysRevD.62.034008

    work page doi:10.1103/physrevd.62.034008 2000

  8. [8]

    Recursive model for the fragmentation of polarized quarks

    A. Kerbizi, X. Artru, Z. Belghobsi, F. Bradamante, A. Martin, Recursive model for the frag- mentation of polarized quarks, Phys. Rev. D 97 (7) (2018) 074010.arXiv:1802.00962, doi:10.1103/PhysRevD.97.074010

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.97.074010 2018

  9. [9]

    Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised proton

    C. Adolph, et al., Collins and Sivers asymmetries in muonproduction of pions and kaons offtransversely polarised protons, Phys. Lett. B 744 (2015) 250–259. arXiv:1408.4405,doi:10.1016/j.physletb.2015. 03.056

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2015 2015

  10. [10]

    The COMPASS collaboration, Collins and Sivers transverse-spin asymmetries in inclusive muoproduction ofρ 0 mesons, CERN-EP-2022-234 .arXiv:2211. 00093

    2022

  11. [11]

    Airapetian, et al., Effects of transversity in deep- inelastic scattering by polarized protons, Phys

    A. Airapetian, et al., Effects of transversity in deep- inelastic scattering by polarized protons, Phys. Lett. B 693 (2010) 11–16.arXiv:1006.4221,doi:10.1016/ j.physletb.2010.08.012

    Pith/arXiv arXiv 2010

  12. [12]

    A high-statistics measurement of transverse spin effects in dihadron production from muon-proton semi-inclusive deep-inelastic scattering

    C. Adolph, et al., A high-statistics measurement of transverse spin effects in dihadron production from muon–proton semi-inclusive deep-inelastic scattering, Phys. Lett. B 736 (2014) 124–131.arXiv:1401.7873, doi:10.1016/j.physletb.2014.06.080

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2014.06.080 2014

  13. [13]

    T. B. Hayward, et al., Observation of Beam Spin Asym- metries in the Processep→e ′ π+π−Xwith CLAS12, Phys. Rev. Lett. 126 (2021) 152501.arXiv:2101. 04842,doi:10.1103/PhysRevLett.126.152501

    work page doi:10.1103/physrevlett.126.152501 2021

  14. [14]

    Kerbizi, X

    A. Kerbizi, X. Artru, Model for baryon production in spin-dependent string fragmentation, Phys. Rev. D 113 (3) (2026) 034007.arXiv:2507.06810,doi:10.1103/ 7dd2-61z8

    arXiv 2026

  15. [15]

    K. Chen, G. R. Goldstein, R. L. Jaffe, X.-D. Ji, Probing quark fragmentation functions for spin 1/2 baryon pro- duction in unpolarizede +e− annihilation, Nucl. Phys. B 445 (1995) 380–398.arXiv:hep-ph/9410337,doi: 10.1016/0550-3213(95)00193-V

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/0550-3213(95)00193-v 1995

  16. [16]

    Angular dependences in inclusive two-hadron production at BELLE

    D. Boer, Angular dependences in inclusive two-hadron production at BELLE, Nucl. Phys. B 806 (2009) 23– 67.arXiv:0804.2408,doi:10.1016/j.nuclphysb. 2008.06.011

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.nuclphysb 2009

  17. [17]

    Measuring transverse spin correlations by 4-particle correlations in $e^+ e^-\to 2 \ {\rm jets}$

    X. Artru, J. C. Collins, Measuring transverse spin cor- relations by 4 particle correlations ine +e− →2jets, Z. Phys. C 69 (1996) 277–286.arXiv:hep-ph/9504220, doi:10.1007/s002880050028

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s002880050028 1996

  18. [18]

    Seidl, et al., Measurement of Azimuthal Asymmetries in Inclusive Production of Hadron Pairs ine +e− Annihila- tion at √s=10.58-GeV, Phys

    R. Seidl, et al., Measurement of Azimuthal Asymmetries in Inclusive Production of Hadron Pairs ine +e− Annihila- tion at √s=10.58-GeV, Phys. Rev. D 78 (2008) 032011, [Erratum: Phys.Rev.D 86, 039905 (2012)].arXiv:0805. 2975,doi:10.1103/PhysRevD.78.032011. 8

    work page doi:10.1103/physrevd.78.032011 2008

  19. [19]

    Li, et al., Azimuthal asymmetries of back-to-back π± −(π 0, η, π±) pairs ine +e− annihilation, Phys

    H. Li, et al., Azimuthal asymmetries of back-to-back π± −(π 0, η, π±) pairs ine +e− annihilation, Phys. Rev. D 100 (9) (2019) 092008.arXiv:1909.01857,doi: 10.1103/PhysRevD.100.092008

    work page doi:10.1103/physrevd.100.092008 2019

  20. [20]

    J. P. Lees, et al., Measurement of Collins asymmetries in inclusive production of charged pion pairs ine +e− annihilation at BABAR, Phys. Rev. D 90 (5) (2014) 052003.arXiv:1309.5278,doi:10.1103/PhysRevD. 90.052003

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd 2014

  21. [21]

    J. P. Lees, et al., Collins asymmetries in inclusive charged KKandKπpairs produced ine +e− annihilation, Phys. Rev. D 92 (11) (2015) 111101.arXiv:1506.05864, doi:10.1103/PhysRevD.92.111101

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.92.111101 2015

  22. [22]

    Ablikim, et al., Measurement of azimuthal asymme- tries in inclusive charged dipion production ine +e− an- nihilations at √s=3.65 GeV, Phys

    M. Ablikim, et al., Measurement of azimuthal asymme- tries in inclusive charged dipion production ine +e− an- nihilations at √s=3.65 GeV, Phys. Rev. Lett. 116 (4) (2016) 042001.arXiv:1507.06824,doi:10.1103/ PhysRevLett.116.042001

    Pith/arXiv arXiv 2016

  23. [23]

    V ossen, et al., Observation of transverse polariza- tion asymmetries of charged pion pairs ine +e− anni- hilation near √s=10.58 GeV, Phys

    A. V ossen, et al., Observation of transverse polariza- tion asymmetries of charged pion pairs ine +e− anni- hilation near √s=10.58 GeV, Phys. Rev. Lett. 107 (2011) 072004.arXiv:1104.2425,doi:10.1103/ PhysRevLett.107.072004

    Pith/arXiv arXiv 2011

  24. [24]

    Kerbizi, X

    A. Kerbizi, X. Artru, String fragmentation of a quark pair with entangled spin states: Application toe +e− annihi- lation, Phys. Rev. D 109 (5) (2024) 054029.arXiv: 2312.14694,doi:10.1103/PhysRevD.109.054029

    work page doi:10.1103/physrevd.109.054029 2024

  25. [25]

    Kerbizi, L

    A. Kerbizi, L. Lönnblad, A. Martin, Quark spin effects ine +e− annihilation: A Monte Carlo event generator study, Phys. Rev. D 110 (7) (2024) 074029.arXiv: 2407.07706,doi:10.1103/PhysRevD.110.074029

    work page doi:10.1103/physrevd.110.074029 2024

  26. [26]

    J. C. Collins, Spin Correlations in Monte Carlo Event Generators, Nucl. Phys. B 304 (1988) 794–804.doi: 10.1016/0550-3213(88)90654-2

    work page doi:10.1016/0550-3213(88)90654-2 1988

  27. [27]

    I. G. Knowles, Spin Correlations in Parton - Parton Scat- tering, Nucl. Phys. B 310 (1988) 571–588.doi:10. 1016/0550-3213(88)90092-2

    1988

  28. [28]

    Systematic event generator tuning for the LHC

    A. Buckley, H. Hoeth, H. Lacker, H. Schulz, J. E. von Seggern, Systematic event generator tuning for the LHC, Eur. Phys. J. C 65 (2010) 331–357.arXiv:0907.2973, doi:10.1140/epjc/s10052-009-1196-7

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-009-1196-7 2010

  29. [29]

    Buckley, C

    A. Buckley, C. Gutchov, A. Kerbizi, L. Lönnblad, in preparation. 9