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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

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