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arxiv: 2512.05019 · v2 · pith:D6ZLF7EFnew · submitted 2025-12-04 · ✦ hep-ph · nucl-th

Geometry of particle emission in UrQMD Ar+Sc collisions at SPS energies

Barnabas Porfy , Mate Csanad This is my paper

Pith reviewed 2026-05-17 01:22 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords femtoscopyLévy distributionstwo-pion correlationsUrQMDAr+Sc collisionsSPS energiessource geometryheavy-ion collisions
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The pith

Simulations of Ar+Sc collisions at SPS energies show two-pion pair sources follow Lévy-stable distributions whose parameters map to spatial scale, shape, and emission strength.

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

The paper uses the UrQMD Monte Carlo generator to produce three-dimensional two-pion pair source distributions in central 40Ar + 45Sc collisions at SPS energies. After confirming that the simulated hadronic spectra are realistic, the authors demonstrate that these sources are well described by Lévy-stable distributions. They then assign physical interpretations to the fitted parameters that quantify the source size, its deviation from Gaussian form, and the overall strength of particle emission. This work supplies a reference calculation for intermediate-mass collision systems where experimental femtoscopy data are still limited.

Core claim

In central 40Ar+45Sc collisions at SPS energies the Ultra-Relativistic Quantum Molecular Dynamics Monte-Carlo event generator, after validation against hadronic spectra, yields three-dimensional two-pion pair source distributions that are described by Lévy-stable distributions. The extracted Lévy parameters are interpreted as measures of the spatial scale, the shape, and the strength of the emitting source, establishing a baseline for future experimental measurements in intermediate systems.

What carries the argument

Three-dimensional two-pion pair source distributions extracted from UrQMD events and fitted to Lévy-stable distributions, with parameters interpreted for spatial scale, shape, and strength.

If this is right

  • Lévy parameters extracted from the simulations quantify the spatial extent, non-Gaussian shape, and emission intensity of the pion source in these collisions.
  • The same fitting procedure extends femtoscopy studies from large systems at RHIC and LHC energies to intermediate systems at SPS energies.
  • The calculated sources serve as a theoretical reference against which upcoming experimental measurements in Ar+Sc collisions can be compared.

Where Pith is reading between the lines

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

  • Confirmation by experiment would support the idea that Lévy distributions capture emission geometry across a wide range of collision sizes.
  • The same simulation-plus-fit approach could be applied to other intermediate systems or energies to map how source parameters evolve.
  • Direct comparison of the Lévy parameters with hydrodynamic or transport-model predictions for the emission zone could test the microscopic origin of the non-Gaussian shape.

Load-bearing premise

The UrQMD Monte Carlo generator, once validated against hadronic spectra, produces two-pion source distributions that can be directly compared to experimental femtoscopy measurements.

What would settle it

Experimental two-pion correlation data from Ar+Sc collisions at SPS energies whose extracted source shapes deviate significantly from Lévy-stable forms would falsify the description.

Figures

Figures reproduced from arXiv: 2512.05019 by Barnabas Porfy, Mate Csanad.

Figure 1
Figure 1. Figure 1: Example fit (red line) to projected D(ρ) distributions (blue points) in Ar+Sc 0-10% centrality at 40A GeV/c in KT range [0.15-0.18] GeV/c with 2500 events merged. The fit is marked with a solid line, while the dashed line is an extrapolation. is perpendicular to both directions. To access the pair source function, we follow the definition of Ref. [13] for the three-dimensional spatial distance vector (in c… view at source ↗
Figure 2
Figure 2. Figure 2: The L´evy index parameter α, for 0–10% central Ar+Sc. For all transverse mass mT a), for selected transverse mass mT intervals b), and the average of all transverse mass mT intervals at the given energies c). The given colored band shows systematic uncertainty. 0.2 0.4 0.6 (GeV) mT 0.6 0.8 1 *1.2 λ 150A GeV/c 75A GeV/c 40A GeV/c 30A GeV/c 19A GeV/c 13A GeV/c - π - π + π + UrQMD 3.4, Ar+Sc 0-10%, π [PITH_F… view at source ↗
Figure 3
Figure 3. Figure 3: The intercept parameter λ ∗ , for 0–10% central Ar+Sc at all beam momenta, as a function of transverse mass mT. The given colored band shows systematic uncertainty. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The L´evy-scale parameters Rout, side, long, for 0–10% central Ar+Sc at all beam momenta, as a function of transverse mass mT. The colored bands show the systematic uncertainty [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The averaged L´evy-scale parameter R¯, for 0–10% central Ar+Sc. For all transverse mass mT as a function of mT a) and for selected transverse mass mT intervals as a function of beam momentum b). The given colored band shows systematic uncertainty. References [1] G. Goldhaber, W. B. Fowler, S. Goldhaber, and T. F. Hoang. Pion-pion correlations in antiproton annihi￾lation events. Phys. Rev. Lett., 3:181, 195… view at source ↗
read the original abstract

Over the past few decades, progress in femtoscopy has been driven by the interplay between experimental measurements and theoretical calculations. Measurements provide data to support the theory, while theoretical predictions guide new measurements. In the recent decade, several experiments have confirmed that the two-particle pion-emitting source is well described by L\'evy alpha-stable distributions. To enable theoretical interpretation, phenomenological simulations have been done at RHIC and LHC energies, in large systems such as Au+Au or Pb+Pb, using various available heavy-ion collision models. However, such simulations have not been done in intermediate systems. In this paper, we investigate three-dimensional two-pion pair source distributions from $^{40}$Ar+$^{45}$Sc central collisions at SPS energies, generated with the Ultra-Relativistic Quantum Molecular Dynamics Monte-Carlo event generator. Supplemented by a validation of the simulated hadronic spectra, we find that the pair source can be described with L\'evy-stable distributions. We subsequently interpret the physical meaning of the extracted L\'evy parameters corresponding to the spatial scale, shape, and strength of the source. Our results form a baseline for future experimental measurements in intermediate systems.

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 / 2 minor

Summary. The paper uses the UrQMD Monte Carlo generator to simulate central 40Ar+45Sc collisions at SPS energies. After validating the model against single-particle hadronic pT and rapidity spectra, the authors extract the three-dimensional two-pion pair source distribution from the simulated emission points and show that it is well described by Lévy-stable distributions. They then interpret the extracted Lévy parameters (spatial scale R, shape parameter α, and strength λ) and position the results as a baseline for future experimental femtoscopy studies in intermediate-mass systems.

Significance. If the central finding holds, the work supplies the first Lévy-parameter predictions for smaller collision systems at SPS energies, complementing existing RHIC/LHC studies in large systems. The reliance on a publicly documented event generator supports reproducibility, and the explicit extraction of source parameters from Monte Carlo output provides a concrete, falsifiable reference for experimental comparisons.

major comments (1)
  1. [Validation section] Validation section: The model is validated solely against one-body pT and rapidity distributions. These observables do not directly constrain the relative space-time separations that define the pair source function S(r). Resonance lifetimes, rescattering, and freeze-out choices in UrQMD can modify the source geometry without altering single-particle yields, so the physical interpretation of the Lévy parameters (scale, shape, strength) risks being specific to this generator rather than a general feature of the collision system. The manuscript should add a discussion of source-construction details and any sensitivity tests to these model ingredients.
minor comments (2)
  1. Figure captions and text should explicitly state the fitting range and goodness-of-fit metric (e.g., χ²/dof) used to establish the Lévy description of the source.
  2. Notation for the three-dimensional source function and the Lévy parametrization should be introduced consistently in the methods section before the results are presented.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation and the recommendation for minor revision. The single comment on validation and source construction is constructive, and we address it directly below while committing to appropriate revisions.

read point-by-point responses

  1. Referee: [Validation section] Validation section: The model is validated solely against one-body pT and rapidity distributions. These observables do not directly constrain the relative space-time separations that define the pair source function S(r). Resonance lifetimes, rescattering, and freeze-out choices in UrQMD can modify the source geometry without altering single-particle yields, so the physical interpretation of the Lévy parameters (scale, shape, strength) risks being specific to this generator rather than a general feature of the collision system. The manuscript should add a discussion of source-construction details and any sensitivity tests to these model ingredients.

    Authors: We agree that single-particle spectra alone do not fully constrain the space-time separations encoded in S(r). UrQMD incorporates resonance lifetimes, rescattering, and freeze-out through its established transport dynamics, yet the resulting source geometry remains model-specific. In the revised manuscript we will add a new subsection detailing the source-construction procedure: how emission points (space-time coordinates at last interaction) are recorded for each pion, the freeze-out criteria employed, and the binning used to obtain the three-dimensional pair source distribution. We will also include a concise discussion of potential sensitivities to key model ingredients (e.g., resonance lifetimes and rescattering cross sections) and explicitly note the model dependence as a limitation, framing the results as a reproducible baseline for the UrQMD description of intermediate-mass systems at SPS energies. A comprehensive sensitivity scan lies outside the scope of this baseline study but will be highlighted as a natural direction for follow-up work. revision: partial

Circularity Check

0 steps flagged

No significant circularity in UrQMD-generated Lévy source analysis

full rationale

The paper runs the external UrQMD Monte Carlo generator to produce Ar+Sc collision events, validates the output against single-particle pT and rapidity spectra, computes the three-dimensional two-pion emission-point source S(r) directly from the simulated space-time coordinates, and fits Lévy-stable distributions to that computed source. The extracted scale, shape (α), and strength parameters are then interpreted as properties of the model output. None of these steps reduces by construction to the inputs: the Lévy fit is a post-hoc description of independently generated data rather than a self-definition or a fitted quantity renamed as a prediction. No load-bearing self-citation chain or uniqueness theorem is invoked to force the result. The analysis is therefore self-contained as a characterization of publicly documented simulation output and receives a score of 0.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that UrQMD correctly generates the space-time emission geometry for pions in these collisions and that the extracted Lévy parameters have direct physical meaning for comparison with data.

free parameters (1)
  • Lévy alpha, R, lambda
    These parameters are fitted to the simulated pair-source distributions; their values are outputs of the analysis rather than inputs to the model.
axioms (1)
  • domain assumption UrQMD provides a sufficiently realistic description of particle production and correlations in Ar+Sc collisions at SPS energies
    Invoked when the authors validate hadronic spectra and then proceed to extract the source function from the same events.

pith-pipeline@v0.9.0 · 5504 in / 1349 out tokens · 48406 ms · 2026-05-17T01:22:18.168019+00:00 · methodology

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Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

  1. [1]

    Goldhaber, W

    G. Goldhaber, W. B. Fowler, S. Goldhaber, and T. F. Hoang. Pion-pion correlations in antiproton annihi- lation events.Phys. Rev. Lett., 3:181, 1959

    work page 1959

  2. [2]

    Goldhaber, S

    G. Goldhaber, S. Goldhaber, W.-Y. Lee, and A. Pais. Influence of Bose-Einstein statistics on the anti-proton proton annihilation process.Phys. Rev., 120:300, 1960

    work page 1960

  3. [3]

    D. A. Brown and P. Danielewicz. Imaging of sources in heavy ion reactions.Phys. Lett. B, 398:252–258, 1997

    work page 1997

  4. [4]

    S. S. Adler et al. Evidence for a long-range component in the pion emission source in Au + Au collisions at √sN N = 200 GeV.Phys. Rev. Lett., 98:132301, 2007

    work page 2007

  5. [5]

    Adare et al

    A. Adare et al. L´ evy-stable two-pion Bose-Einstein correlations in √sN N = 200 GeV Au+Au collisions. Phys. Rev. C, 97(6):064911, 2018. [Erratum: Phys.Rev.C 108, 049905 (2023)]

    work page 2018

  6. [6]

    Adhikary et al

    H. Adhikary et al. Two-pion femtoscopic correlations in Be+Be collisions at √sNN = 16.84 GeV measured by the NA61/SHINE at CERN.Eur. Phys. J. C, 83(10):919, 2023

    work page 2023

  7. [7]

    Tumasyan et al

    A. Tumasyan et al. Two-particle Bose-Einstein correlations and their L´ evy parameters in PbPb collisions at sNN=5.02 TeV.Phys. Rev. C, 109(2):024914, 2024

    work page 2024

  8. [8]

    D. Kincses. Pion Interferometry with L´ evy-Stable Sources in = 200 GeV Au + Au Collisions at STAR. Universe, 10(3):102, 2024

    work page 2024

  9. [9]

    N. J. Abdulameer et al. Centrality dependence of L´ evy-stable two-pion Bose-Einstein correlations in sNN=200 GeV Au+Au collisions.Phys. Rev. C, 110(6):064909, 2024

    work page 2024

  10. [10]

    Cs¨ org˝ o, B

    T. Cs¨ org˝ o, B. Lorstad, and J. Zim´ anyi. Quantum statistical correlations for slowly expanding systems. Phys. Lett. B, 338:134–140, 1994

    work page 1994

  11. [11]

    S. V. Akkelin and Yu. M. Sinyukov. The HBT interferometry of expanding sources.Phys. Lett. B, 356:525– 530, 1995

    work page 1995

  12. [12]

    Csan´ ad and D.l Kincses

    M. Csan´ ad and D.l Kincses. Femtoscopy with L´ evy Sources from SPS through RHIC to LHC.Universe, 10(2):54, 2024. 7

    work page 2024

  13. [13]

    L´ evy walk of pions in heavy-ion collisions.Commun

    D´ aniel Kincses, M´ arton Nagy, and M´ at´ e Csan´ ad. L´ evy walk of pions in heavy-ion collisions.Commun. Phys., 8(1):55, 2025

    work page 2025

  14. [14]

    Csorgo, S

    T. Csorgo, S. Hegyi, and W. A. Zajc. Bose-Einstein correlations for Levy stable source distributions.Eur. Phys. J. C, 36:67–78, 2004

    work page 2004

  15. [15]

    Csanad, T

    M. Csanad, T. Csorgo, and M. Nagy. Anomalous diffusion of pions at RHIC.Braz. J. Phys., 37:1002–1013, 2007

    work page 2007

  16. [16]

    Kincses, M

    D. Kincses, M. Stefaniak, and M. Csan´ ad. Event-by-Event Investigation of the Two-Particle Source Func- tion in Heavy-Ion Collisions with EPOS.Entropy, 24(3):308, 2022

    work page 2022

  17. [17]

    K´ orodi, D

    B. K´ orodi, D. Kincses, and M. Csan´ ad. Event-by-event investigation of the two-particle source function in sNN=2.76 TeV PbPb collisions with EPOS.Phys. Lett. B, 847:138295, 2023

    work page 2023

  18. [18]

    Kincses, E

    D. Kincses, E. ´Arp´ asi, L. Kov´ acs, M. Nagy, and M. Csan´ ad. Three-dimensional sizes and shapes of pion emission in heavy-ion collisions. 11 2025

    work page 2025

  19. [19]

    Cs¨ org˝ o, S

    T. Cs¨ org˝ o, S. Hegyi, T. Novak, and W. A. Zajc. Bose-Einstein or HBT correlations and the anomalous dimension of QCD.Acta Phys. Polon. B, 36:329–337, 2005

    work page 2005

  20. [20]

    Cs¨ org˝ o, S

    T. Cs¨ org˝ o, S. Hegyi, T. Nov´ ak, and W. A. Zajc. Bose-Einstein or HBT correlation signature of a second order QCD phase transition.AIP Conf. Proc., 828(1):525–532, 2006

    work page 2006

  21. [21]

    Bass et al

    S.A. Bass et al. Microscopic models for ultrarelativistic heavy ion collisions.Prog.Part.Nucl.Phys., 41:255– 369, 1998

    work page 1998

  22. [22]

    Bleicher et al

    M. Bleicher et al. Relativistic hadron hadron collisions in the ultrarelativistic quantum molecular dynamics model.J.Phys., G25:1859–1896, 1999

    work page 1999

  23. [23]

    Abgrall et al

    N. Abgrall et al. NA61/SHINE facility at the CERN SPS: beams and detector system.JINST, 9:P06005, 2014

    work page 2014

  24. [24]

    M. A. Lisa, S. Pratt, R. Soltz, and U. Wiedemann. Femtoscopy in relativistic heavy ion collisions.Ann. Rev. Nucl. Part. Sci., 55:357–402, 2005

    work page 2005

  25. [25]

    Cs¨ org˝ o

    T. Cs¨ org˝ o. Particle interferometry from 40-MeV to 40-TeV.Acta Phys. Hung. A, 15:1–80, 2002

    work page 2002

  26. [26]

    Bertsch, M

    G. Bertsch, M. Gong, and M. Tohyama. Pion Interferometry in Ultrarelativistic Heavy Ion Collisions. Phys. Rev. C, 37:1896–1900, 1988

    work page 1900

  27. [27]

    Pratt, T

    S. Pratt, T. Cs¨ org˝ o, and J. Zim´ anyi. Detailed predictions for two pion correlations in ultrarelativistic heavy ion collisions.Phys. Rev. C, 42:2646–2652, 1990

    work page 1990

  28. [28]

    Uzhinsky

    V. Uzhinsky. Toward UrQMD Model Description of pp and pC Interactions at High Energies. 8 2013

    work page 2013

  29. [29]

    Scott Chapman, Pierre Scotto, and Ulrich W. Heinz. A New cross term in the two particle HBT correlation function.Phys. Rev. Lett., 74:4400–4403, 1995

    work page 1995

  30. [30]

    S. S. Adler et al. Bose-Einstein correlations of charged pion pairs in Au + Au collisions at s(NN)**(1/2) = 200-GeV.Phys. Rev. Lett., 93:152302, 2004

    work page 2004

  31. [31]

    S. Pratt. Coherence and Coulomb Effects on Pion Interferometry.Phys. Rev. D, 33:72–79, 1986

    work page 1986

  32. [32]

    Excitation function of femtoscopic L´ evy source parameters of pion pairs in EPOS4

    Yan Huang, Matyas Molnar, Daniel Kincses, and Mate Csanad. Excitation function of femtoscopic L´ evy source parameters of pion pairs in EPOS4. 12 2025

    work page 2025

  33. [33]

    B. P´ orfy. Femtoscopy using L´ evy-type source at NA61/SHINE.PoS, ICHEP2024:603, 2025

    work page 2025

  34. [34]

    Cs¨ org˝ o and B

    T. Cs¨ org˝ o and B. L¨ orstad. Bose-Einstein correlations for three-dimensionally expanding, cylindrically symmetric, finite systems.Phys. Rev. C, 54:1390–1403, 1996. 8

    work page 1996