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Two-pion source analysis in small to large systems at SPS energies

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Barnabás Pórfy, Zsombor Marcell Rácz

High Energy Physics - Phenomenology · Submitted 12 Oct 2026 · 38 references

Pith's verdict: A competent UrQMD reference for SPS femtoscopy, but the 1D sphericity assumption needs validation before it can be reliably compared to 3D data.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on October 14, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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arXiv ID2610.16786 (version 1)
Pith IDFLWPJXLC, Pith's permanent record of this paper and its review
CitationBarnab\'as P\'orfy, Zsombor Marcell R\'acz. "Two-pion source analysis in small to large systems at SPS energies." arXiv:2610.16786 (2026). https://pith.science/paper/FLWPJXLC
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The paper

The paper claims

UrQMD cascade simulations produce Lévy-shaped pion sources across Be+Be and Xe+La collisions, consistent with experimental femtoscopy.

The reading

This paper uses the UrQMD hadronic cascade model to simulate central Be+Be and Xe+La collisions at SPS energies. The authors reconstruct the spatial distribution of pion pairs and fit it with a Lévy-stable function. They find that the simulated pair sources are well described by Lévy shapes, with parameters (α, R, λ) showing systematic trends with transverse mass, collision energy, and system size. The results provide a purely hadronic baseline for future experimental femtoscopy and for comparisons with hydrodynamic models.

What carries the argument

The central object is the Lévy‑stable distribution (Eqs. 3‑4) used to parametrize the angle‑averaged pair‑source function D(ρ). The machinery consists of the UrQMD event generator in cascade mode, which records the space‑time coordinates of final‑state pions, from which the pair‑source distribution is reconstructed directly. The analysis reduces the full three‑dimensional problem to a one‑dimensional angular average over the pair separation ρ (Eqs. 5‑7), justified by the expected spherical symmetry near mid‑rapidity. Systematic uncertainties are evaluated by varying the relative‑momentum cut (q_LCMS).

Extended reading notes

Core claim

The central discovery is that the UrQMD cascade model, without a hydrodynamic stage, generates pair-source distributions whose shape is accurately fit by a one‑dimensional Lévy function. This holds for both the small ⁷Be+⁹Be system and the large ¹²⁹Xe+¹³⁹La system, across a range of collision energies. The extracted Lévy index α increases with pair transverse mass and decreases with collision energy; the scale parameter R shows the steep m_T fall traditionally associated with radial flow; and the correlation strength λ is nearly energy‑independent. These findings unify the phenomenological description of the space‑time structure of pion emission from small to large systems at SPS energies.

Load-bearing premise

The analysis assumes that the pair source is spherically symmetric near mid‑rapidity, allowing a one‑dimensional angular average; if this symmetry breaks down, especially for the larger Xe+La system, the fitted Lévy parameters may differ from true three‑dimensional values.

Editorial extensions

If this is right

  • The observed steep m_T decrease of the scale parameter R, mimicking collective flow, is now shown to arise from a purely hadronic cascade, challenging the interpretation that only hydrodynamics can produce it.
  • The ordering of α by system size at the highest SPS energy (smallest in Be+Be, largest in Xe+La) provides a baseline for testing whether future hydrodynamic extensions or experimental data reproduce the same trend.
  • The results serve as a hadronic reference for the NA61/SHINE femtoscopy program; deviations of experimental parameters from the UrQMD values would indicate physics beyond the cascade, such as a quark‑gluon plasma phase.
  • The study demonstrates that the Lévy shape is universal across systems from Be+Be to Xe+La in the UrQMD cascade, supporting the Lévy‑walk mechanism as the dominant cause of the power‑law tail in the hadronic stage.

Reading between the lines

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

  • The assumption of spherical symmetry (R_out ≈ R_side ≈ R_long) may be weakest for the large Xe+La system, so a future full 3D analysis could reveal azimuthal asymmetries not captured by the 1D fit.
  • The 1D analysis used for Be+Be and Xe+La versus the 3D analysis for Ar+Sc introduces an inconsistency in the comparison of R values; reconciling the two methods would strengthen the system‑size ordering.
  • If the Lévy index α from experiment [9] for Be+Be (≈1) differs from the UrQMD value (≈1.6 at top energy), it signals that the cascade model underestimates the power‑law tail, possibly requiring a hydrodynamical or anomalous‑diffusion component.
Original abstract

Over the past decade, femtoscopic measurements using L\'evy-stable source functions have been carried out in collision systems ranging from small to large at SPS, RHIC, and LHC energies. In recent years, these have been accompanied by a number of phenomenological studies of the same systems and energies. We contribute to this line of work by investigating the shape of two-pion pair-source distributions in central $^7$Be+$^9$Be and $^{129}$Xe+$^{139}$La collisions simulated with the UrQMD model in cascade mode. To make the comparison with measurements meaningful, kinematic selections similar to the experimental ones are applied to the simulated events and particles. One-dimensional L\'evy fits are performed, and the resulting source parameters are studied as functions of pair transverse mass, collision energy, and system size. We find that the simulated sources are well described by L\'evy distributions in all systems considered, which offers a common phenomenological picture of the space-time structure of pion emission. Finally, we compare our findings with results from an intermediate system, Ar+Sc. The results serve as a purely hadronic reference for past and upcoming femtoscopic measurements of the NA61/SHINE experiment.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-14: 1 request, 6,316 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.40 · human participants 0.01 · controlled comparison 0.31 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Over the past decade, femtoscopic measurements using L\'evy-stable source functions have been carried out in collision systems ranging from small to large at SPS, RHIC, and LHC energies. In recent years, these have been accompanied by a number of phenomenological studies of the same systems and energies. We contribute to this line of work by investigating the shape of two-pion pair-source distributions in central $^7$Be+$^9$Be and $^{129}$Xe+$^{139}$La collisions simulated with the UrQMD model in cascade mode. To make the comparison with measurements meaningful, kinematic selections similar to the experimental ones are applied to the simulated events and particles. One-dimensional L\'evy fits are performed, and the resulting source parameters are studied as functions of pair transverse mass, collision energy, and system size. We find that the simulated sources are well described by L\'evy distributions in all systems considered, which offers a common phenomenological picture of the space-time structure of pion emission. Finally, we compare our findings with results from an intermediate system, Ar+Sc. The results serve as a purely hadronic reference for past and upcoming femtoscopic measurements of the NA61/SHINE experiment.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Over the past decade, femtoscopic measurements using L\'evy-stable source functions have been carried out in collision systems ranging from small to large at SPS, RHIC, and LHC energies. background 1.00 0.05 0.02 asserted 1.00
s1 In recent years, these have been accompanied by a number of phenomenological studies of the same systems and energies. background 1.00 0.04 0.01 asserted 1.00
s2 We contribute to this line of work by investigating the shape of two-pion pair-source distributions in central $^7$Be+$^9$Be and $^{129}$Xe+$^{139}$La collisions simulated with the UrQMD model in cascade mode. contribution 1.00 0.95 0.03 asserted 0.95
s3 To make the comparison with measurements meaningful, kinematic selections similar to the experimental ones are applied to the simulated events and particles. method 1.00 0.89 0.02 asserted 0.97
s4 One-dimensional L\'evy fits are performed, and the resulting source parameters are studied as functions of pair transverse mass, collision energy, and system size. method 0.99 0.95 0.04 asserted 0.73
s5 We find that the simulated sources are well described by L\'evy distributions in all systems considered, which offers a common phenomenological picture of the space-time structure of pion emission. result 0.90 0.96 0.86 asserted 1.00
s6 Finally, we compare our findings with results from an intermediate system, Ar+Sc. contribution 0.47 0.85 0.03 asserted 0.81
s7 The results serve as a purely hadronic reference for past and upcoming femtoscopic measurements of the NA61/SHINE experiment. interpretation 0.88 0.34 0.08 asserted 1.00

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. L´evy stability index α versus mT in 0–10% central Be+Be and Xe+La collisions. Bands show the systematic uncertainties. reduce the parameter value. The absence of these decays leads to an overesti￾mated value, denoted as λ ∗ to distinguish it from the experimentally measured λ. An estimate based on the branching ratios of the above mentioned decays into pions suggests that the physical λ would be approximately 92–93% of the values shown. 5 Summary and outlook We have analyzed two-pion pair-source distributions in central Be+Be and Xe+La collisions at SPS energies (√ sNN ≈ 5–17 GeV)
Figure 2. L´evy stability index α versus √ sNN in 0–10% central Be+Be, Ar+Sc, and Xe+La collisions, averaged over all KT. Bands show the systematic uncer￾tainties. The single Be+Be point is drawn with an artificial horizontal width for visibility. both. Finally, the next step is extending the model with a hydrodynamic stage, and the present results provide the baseline against which such extensions and future measurements can be compared. Acknowledgments This work was supported by the NKFIH grant NKKP ADVANCED 152097. Furthermore, Barnab´as P´orfy was supported by the DKOP-23 Doctoral Excel-
Figure 3. L´evy scale parameter R versus mT in 0–10% central Be+Be and Xe+La collisions. Bands show the systematic uncertainties. 06/P06005. [2] G. Goldhaber, W. B. Fowler, S. Goldhaber and T. F. Hoang, Phys. Rev. Lett. 3, 181 (1959), doi:10.1103/PhysRevLett.3.181. [3] G. Goldhaber, S. Goldhaber, W.-Y. Lee and A. Pais, Phys. Rev. 120, 300 (1960), doi:10.1103/PhysRev.120.300. [4] M. A. Lisa, S. Pratt, R. Soltz and U. Wiedemann, Ann. Rev. Nucl. Part. Sci. 55, 357 (2005), arXiv:nucl-ex/0505014, doi:10.1146/annurev.nucl. 55.090704.151533. [5] T. Cs¨org˝o, Acta Phys. Hung. A 15, 1 (2002), arXiv:he
Figure 4. L´evy scale parameter R versus √ sNN for KT = 0.10–0.20 GeV/c in 0– 10% central Be+Be, Ar+Sc, and Xe+La collisions. Bands show the systematic uncertainties. The single Be+Be point is drawn with an artificial horizontal width for visibility. The systematic uncertainties for Xe+La were artifically increased 10 times, and 5 times for Be+Be, to enhance visibility. For Ar+Sc, the direction-averaged R¯ = q (R2 out + R2 side + R2 long)/3 is shown. [8] PHENIX Collaboration (A. Adare et al.), Phys. Rev. C 97, 064911 (2018), arXiv:1709.05649 [nucl-ex], doi:10.1103/PhysRevC.97.064911. [9]
Figure 5. Correlation strength λ ∗ versus mT in 0–10% central Be+Be and Xe+La collisions. Bands show the systematic uncertainties. [13] T. Cs¨org˝o, S. Hegyi and W. A. Zajc, Eur. Phys. J. C 36, 67 (2004), arXiv:nucl-th/0310042, doi:10.1140/epjc/s2004-01870-9. [14] M. Csan´ad, T. Cs¨org˝o and M. Nagy, Braz. J. Phys. 37, 1002 (2007), arXiv:hep-ph/0702032, doi:10.1590/S0103-97332007000600018. [15] T. Cs¨org˝o, S. Hegyi, T. Nov´ak and W. A. Zajc, Acta Phys. Polon. B 36, 329 (2005), arXiv:hep-ph/0412243. [16] T. Cs¨org˝o, S. Hegyi, T. Nov´ak and W. A. Zajc, AIP Conf. Proc. 828, 525 (2006), arXiv:n

Figures reproduced from arXiv:2610.16786 by the authors.

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