arxiv: 2512.02560 · v2 · submitted 2025-12-02 · ⚛️ nucl-th · hep-ph

Recognition: 2 theorem links

· Lean Theorem

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

Yan Huang , Matyas Molnar , Daniel Kincses , Mate Csanad

Authors on Pith no claims yet

Pith reviewed 2026-05-17 02:42 UTC · model grok-4.3

classification ⚛️ nucl-th hep-ph

keywords femtoscopyLévy sourcepion pairsheavy-ion collisionstransverse mass dependencecollision energy dependenceEPOS4STAR Beam Energy Scan

0 comments

The pith

EPOS4 simulations show pion Lévy source radii in side and long directions shrink with transverse mass but grow with collision energy from 7.7 to 200 GeV.

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

The paper applies the EPOS4 model to compute three-dimensional femtoscopic parameters for pion pairs produced in heavy-ion collisions. It extracts the Lévy index alpha, the correlation strength lambda, and the three radii Rout, Rside, and Rlong, then tracks how each quantity changes with transverse mass and with beam energy across the STAR Beam Energy Scan range. The central results are that Rside and Rlong fall as mT rises and rise gradually as collision energy increases, while Rout stays roughly flat with energy; alpha depends only mildly on both variables and lambda falls with rising energy. These trends supply a model baseline that can be compared directly to experimental data to test whether real sources exhibit non-monotonic behavior linked to the equation of state.

Core claim

Using EPOS4, the extracted Rside and Rlong decrease with increasing transverse mass and increase gradually with collision energy, while Rout shows little energy dependence. The Lévy index alpha exhibits only mild dependence on mT and collision energy, whereas the correlation strength lambda shows clear mT dependence and generally decreases with increasing collision energy. Derived quantities such as the out-side squared radius difference and the out/side ratio are also computed, and the EPOS4 results agree with EPOS3 within about 2 sigma except for a systematic downward shift in Rside.

What carries the argument

Three-dimensional Lévy source parametrization of pion-pair correlation functions, which fits separate radii in the out, side, and long directions together with the stability index alpha.

If this is right

Rside and Rlong increase gradually with collision energy while Rout remains roughly constant.
The Lévy index alpha changes only mildly across the studied mT and energy ranges.
The correlation strength lambda decreases with increasing collision energy and shows clear transverse-mass dependence.
The out-side squared radius difference and out/side ratio can be extracted and compared across energies.
EPOS4 results lie within approximately 2 sigma of EPOS3 results except for systematically smaller Rside values.

Where Pith is reading between the lines

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

If the same trends appear in real data, they would reduce the likelihood of observing a strong first-order phase-transition signal in the out-side difference within this energy range.
The mild alpha dependence suggests that the underlying source shape remains relatively stable across the Beam Energy Scan, which could be tested by repeating the analysis in other event generators.
These baseline trends offer a concrete reference for searching non-monotonic features in the equation of state once experimental Lévy parameters become available.
A direct comparison of the same quantities in upcoming higher-statistics runs could quantify any model-data discrepancy in Rside.

Load-bearing premise

The EPOS4 model reproduces the space-time structure and emission dynamics of the particle source without introducing systematic biases that would distort the extracted Lévy parameters.

What would settle it

An experimental measurement from STAR data showing strong energy dependence in Rout or strong mT dependence in alpha would contradict the EPOS4 predictions reported here.

Figures

Figures reproduced from arXiv: 2512.02560 by Daniel Kincses, Mate Csanad, Matyas Molnar, Yan Huang.

**Figure 1.** Figure 1: Lévy index α from EPOS4 calculations as a function of transverse mass mT at different energies. The bands show the systematical uncertainties. 10 1 10 2 sNN [GeV] 1.4 1.5 1.6 1.7 1.8 kT: 0.375-0.425 GeV/c kT: 0.425-0.475 GeV/c kT: 0.475-0.525 GeV/c [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 3.** Figure 3: Lévy radii from EPOS4 calculations as a function of transverse momentum [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Energy dependence of Lévy radii from EPOS4 calculations at [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: The radius difference R2 diff from EPOS4 calculations as a function of collision energy √ sNN in three kT bins. The bands show the systematical uncertainties. 10 1 10 2 sNN [GeV] 1.3 1.4 1.5 R o u t / R sid e kT: 0.375-0.425 GeV/c kT: 0.425-0.475 GeV/c kT: 0.475-0.525 GeV/c [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 7.** Figure 7: Correlation strength parameters λ from EPOS4 as a function of transverse momentum mT at √ sNN = 7.7 − 200 GeV . The bands show the systematical uncertainties. 10 1 10 2 sNN [GeV] 0.60 0.65 0.70 0.75 0.80 0.85 kT: 0.375-0.425 GeV/c kT: 0.425-0.475 GeV/c kT: 0.475-0.525 GeV/c [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 9.** Figure 9: Correlation strength parameters λ from EPOS4 for variotus choices of ρ max λ (lines of different colors with bands), compared to PHENIX data of Ref. [7] (black points), as a function of mT. The bands shows the systematical uncertainties of the EPOS4 calculations. The statistical and systematical uncertainties of the PHENIX data points are shown as error bars and boxes, respectively. 0.2 0.3 0.4 0.5 0.6 0… view at source ↗

read the original abstract

Three-dimensional (3D) femtoscopic source parameters of pions provide a sensitive probe of the space-time structure of particle-emitting sources in high-energy heavy-ion collisions. Compared to one-dimensional measurements, three-dimensional femtoscopy not only provides a valuable cross-check but also offers a more complete characterization of the source geometry and its dynamical evolution. Particularly, differences between the out and side directions are sensitive to signals of a strong first-order phase transition, while the collision-energy dependence of L\'evy radii may reveal non-monotonic features related to the equation of state. In this work, we systematically investigate the transverse mass (mT) and collision-energy (sqrt(sNN)) dependence of the three-dimensional femtoscopic parameters of pion pairs with L\'evy-type sources in the STAR Beam Energy Scan (BES) range from sqrt(sNN) = 7.7 to 200 GeV using the EPOS4 model. The analyzed parameters include the L\'evy index alpha, the correlation strength lambda, and the three-dimensional radii Rout, Rside and Rlong, corresponding to the outward, sideward, and longitudinal (beam) directions. Derived quantities such as the out-side squared radius difference and the out/side ratio are also investigated. The results show that the extracted radii Rside and Rlong decrease with increasing transverse mass and increase gradually with collision energy, while Rout shows little energy dependence. The L\'evy index alpha exhibits only a mild dependence on mT and collision energy, whereas the correlation strength lambda shows a clear mT dependence and generally decreases with increasing collision energy. A comparison with EPOS3 results indicates general agreement within approximately 2sigma, with the notable exception of Rside, which is systematically smaller in EPOS4.

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.

Desk Editor's Note private letter to a colleague

EPOS4 gives mostly consistent Lévy parameters with EPOS3 but smaller Rside in pion femtoscopy predictions.

read the letter

The punchline is that this paper gives new EPOS4 predictions for the excitation functions of three-dimensional Lévy source parameters in pion pairs, covering the STAR BES energies. It mostly aligns with prior EPOS3 results but finds Rside systematically smaller. The work does well by performing a full scan and extracting Rout, Rside, Rlong, alpha, and lambda as direct outputs from the generator. It also looks at the out-side squared difference and the ratio, which are relevant for spotting phase transition effects. The trends—Rside and Rlong falling with mT and rising with energy, Rout flat in energy, alpha nearly constant, lambda dropping with energy—are presented clearly. The 2 sigma agreement with EPOS3, aside from that one radius, suggests the model changes didn't overhaul the femtoscopy picture. The soft spot is the reliance on EPOS4's unverified accuracy for the space-time source. No data comparison is done here, so these are benchmarks rather than tests. The Rside difference is noted but not investigated further, which leaves a small loose end. For a model study this is minor, but it means the results are only as good as the generator's physics. This is for heavy-ion physicists who use femtoscopy to probe the source and want model predictions to guide data analysis or look for non-monotonic signals. A reader focused on the Beam Energy Scan would get concrete numbers to compare against. It deserves a serious referee to confirm the simulation setup and parameter extraction methods are sound. I recommend sending it for peer review.

Referee Report

0 major / 3 minor

Summary. The manuscript uses the EPOS4 event generator to compute three-dimensional Lévy femtoscopic parameters (Rout, Rside, Rlong, Lévy index α, and correlation strength λ) for pion pairs in Au+Au collisions over the STAR BES energy range √sNN = 7.7–200 GeV. It reports the mT and collision-energy dependence of these quantities, derived observables such as the out–side difference and ratio, and a comparison to corresponding EPOS3 results, finding general agreement within ~2σ except for a systematic offset in Rside.

Significance. If the EPOS4 space-time evolution is reliable, the direct simulation outputs supply clean, falsifiable benchmarks for experimental Lévy-source analyses and can help isolate potential non-monotonic signals linked to the QCD equation of state. The absence of post-hoc fitting to data and the explicit comparison to an earlier generator version are clear strengths that facilitate future model-to-data tests.

minor comments (3)

[Section 3] The extraction of Lévy parameters from the simulated two-particle correlation functions is described only at a high level; a short paragraph or appendix detailing the fitting range, functional form, and treatment of statistical uncertainties would improve reproducibility.
[Results and discussion] The statement of “general agreement within approximately 2σ” (abstract and results section) would be strengthened by quoting the actual χ² or pull values for each parameter and energy, or by adding a supplementary table of differences.
[Figures 2–5] Figure captions should explicitly state the number of events per energy point and whether the displayed error bars are statistical only or include systematic contributions from the generator.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript, the clear summary of its scope, and the recommendation for minor revision. We appreciate the recognition of the strengths of the work, including the absence of post-hoc fitting and the direct comparison to EPOS3. Below we provide point-by-point responses to the major comments raised in the report.

Circularity Check

0 steps flagged

No significant circularity in simulation outputs

full rationale

The paper computes and reports Lévy parameters (R_out, R_side, R_long, alpha, lambda) as direct numerical outputs extracted from EPOS4-generated pion-pair events across the STAR BES energy range. These quantities are obtained by running the event generator and applying standard femtoscopic analysis to the simulated data; no algebraic reduction, parameter fitting to external experimental targets, or self-referential definitions appear in the derivation chain. The reported mT and sqrt(s_NN) trends, out-side differences, and EPOS3 comparisons are therefore independent computational results rather than quantities forced by construction from prior fits or self-citations. The study is self-contained as a model-based survey intended for later experimental comparison.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The study rests on the domain assumption that the EPOS4 transport/hydrodynamic model correctly generates the space-time emission profile of pions; no additional free parameters or invented entities are introduced in the reported analysis.

axioms (1)

domain assumption EPOS4 accurately models the space-time evolution and pion emission in heavy-ion collisions at BES energies.
All extracted Lévy parameters are obtained by running this model; any mismatch with reality would propagate directly into the reported trends.

pith-pipeline@v0.9.0 · 5636 in / 1353 out tokens · 62448 ms · 2026-05-17T02:42:46.922726+00:00 · methodology

discussion (0)

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Large amplification of the isospin-dependence of proton emitting source size in radioactive heavy-ion collisions: a signal of n-p correlation
nucl-ex 2026-04 unverdicted novelty 6.0

Proton emitting source size is amplified by 24% in neutron-rich versus neutron-deficient tin collisions, revealing a beyond-mean-field short-range n-p correlation effect.
A self-consistent calculation of non-spherical Bose-Einstein correlation functions with Coulomb final-state interaction
nucl-th 2026-01 unverdicted novelty 6.0

The authors generalize their prior spherical-source method to non-spherical sources with a self-consistent treatment of Coulomb interactions and provide software for three-dimensional correlation functions.

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages · cited by 2 Pith papers

[1]

Adhikary et al

H. Adhikary et al. Two-pion femtoscopic correlations in be+be collisions at√sN N = 16.84gev measured by the na61/shine at cern.Eur. Phys. J. C, 83:919, 2023

work page 2023
[2]

B. Pórfy. Femtoscopy at na61/shine using symmetric lévy sources in central40ar+45sc from 40agev/c to 150agev/c. In23rd Zimányi School Winter Workshop. World Scientific, 2024

work page 2024
[3]

B. Pórfy. Femtoscopy analysis in small systems at na61/shine.EPJ Web Conf., 296:06004, 2024

work page 2024
[4]

Adare et al

A. Adare et al. Lévy-stable two-pion bose-einstein correlations in√sN N = 200gev au+au collisions.Phys. Rev. C, 97:064911, 2018

work page 2018
[5]

L. Kovács. Charged kaon femtoscopy with lévy sources in√sN N = 200gev au+au collisions at phenix. Universe, 9:336, 2023

work page 2023
[6]

Mukherjee

A. Mukherjee. Kaon femtoscopy with lévy-stable sources from√sN N = 200gev au+au collisions at rhic. Universe, 9:300, 2023

work page 2023
[7]

N. J. Abdulameer et al. Centrality dependence of lévy-stable two-pion bose-einstein correlations in√sN N = 200gev au+au collisions.Phys. Rev. C, 110:064909, 2024

work page 2024
[8]

D. Kincses. Pion interferometry with lévy-stable sources in √sN N = 200gev au+au collisions at star. Universe, 10:102, 2024

work page 2024
[9]

Tumasyan et al

A. Tumasyan et al. Two-particle bose-einstein correlations and their lévy parameters in pbpb collisions at√sN N = 5.02tev.Phys. Rev. C, 109:024914, 2024

work page 2024
[10]

B. Kórodi. Centrality dependent lévy hbt analysis in√sN N = 5.02tev pbpb collisions at cms.Universe, 9:318, 2023

work page 2023
[11]

Csörgő, S

T. Csörgő, S. Hegyi, T. Novák, 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
[12]

Csanád, T

M. Csanád, T. Csörgő, and M. Nagy. Anomalous diffusion of pions at rhic.Braz. J. Phys., 37:1002, 2007

work page 2007
[13]

The random walk’s guide to anomalous diffusion: a fractional dynamics approach.Physics Reports, 339(1):1–77, 2000

Ralf Metzler and Joseph Klafter. The random walk’s guide to anomalous diffusion: a fractional dynamics approach.Physics Reports, 339(1):1–77, 2000

work page 2000
[14]

Femtoscopy with lévy sources from sps through rhic to lhc.Universe, 10(2), 2024

Máté Csanád and Dániel Kincses. Femtoscopy with lévy sources from sps through rhic to lhc.Universe, 10(2), 2024

work page 2024
[15]

Lévy walk of pions in heavy-ion collisions.Communications Physics, 2025

Márton Nagy Dániel Kincses and Máté Csanád. Lévy walk of pions in heavy-ion collisions.Communications Physics, 2025

work page 2025
[16]

Investigating the excitation function of hbt radii for lévy-stable sources

Máté Csanád and Dániel Kincses. Investigating the excitation function of hbt radii for lévy-stable sources. Journal of Physics G: Nuclear and Particle Physics, 52(2):025102, jan 2025. 8

work page 2025
[17]

K. Werner. Revealing a deep connection between factorization and saturation: New insight into mod- eling high-energy proton-proton and nucleus-nucleus scattering in the epos4 framework.Phys. Rev. C, 108:064903, Dec 2023

work page 2023
[18]

Werner, J

K. Werner, J. Jahan, I. Karpenko, T. Pierog, M. Stefaniak, and D. Vintache. Heavy ion collisions from√sN N of 62.4 gev down to 7.7 gev in the epos4 framework.Phys. Rev. C, 111:014903, Jan 2025

work page 2025
[19]

J. P. Nolan. Multivariate elliptically contoured stable distributions: theory and estimation.Comput. Stat., 28:2067–2089, 2013

work page 2067
[20]

S. Pratt. Coherence and coulomb effects on pion interferometry.Phys. Rev. D, 33:72–79, 1986

work page 1986
[21]

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
[22]

Equation of state within the EPOS3 model.Phys

Maria Stefaniak, Klaus Werner, Johannes Jahan, and Hanna Paulina Zbroszczyk. Equation of state within the EPOS3 model.Phys. Rev. C, 108(1):014905, 2023

work page 2023
[23]

Werner, B

K. Werner, B. Guiot, Iu. Karpenko, and T. Pierog. Analyzing radial flow features inp-pb andp-pcollisions at several tev by studying identified-particle production with the event generator epos3.Phys. Rev. C, 89:064903, Jun 2014

work page 2014
[24]

Event-by-event investigation of the two-particle source function in snn=2.76 tev pbpb collisions with epos.Physics Letters B, 847:138295, 2023

Balázs Kórodi, Dániel Kincses, and Máté Csanád. Event-by-event investigation of the two-particle source function in snn=2.76 tev pbpb collisions with epos.Physics Letters B, 847:138295, 2023

work page 2023
[25]

Three-dimensional sizes and shapes of pion emission in heavy-ion collisions

Daniel Kincses, Emese Arpasi, Laszlo Kovacs, Marton Nagy, and Mate Csanad. Three-dimensional sizes and shapes of pion emission in heavy-ion collisions. 2025

work page 2025
[26]

Femtoscopic signatures of unique nuclear structures in relativistic collisions.Phys

Daniel Kincses. Femtoscopic signatures of unique nuclear structures in relativistic collisions.Phys. Rev. Res., 7(4):L042028, 2025

work page 2025
[27]

Adare and et al

A. Adare and et al. Lévy-stable two-pion bose-einstein correlations in√sN N = 200gev au+au collisions. Phys. Rev. C, 97:064911, 2018

work page 2018
[28]

Pratt, T

S. Pratt, T. Csörgő, and J. Zimányi. Detailed predictions for two-pion correlations in ultrarelativistic heavy ion collisions.Phys. Rev. C, 42:2646–2652, 1990

work page 1990
[29]

S. S. Adler and et al. Bose-einstein correlations of charged pion pairs in au+au collisions at√sN N = 200 gev.Phys. Rev. Lett., 93:152302, 2004

work page 2004
[30]

Csorgo, S

T. Csorgo, S. Hegyi, T. Novak, 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
[31]

Csorgo, B

T. Csorgo, B. Lorstad, and J. Zimanyi. Bose-Einstein correlations for systems with large halo.Z. Phys. C, 71:491–497, 1996

work page 1996
[32]

J. Bolz, U. Ornik, M. Plumer, B. R. Schlei, and R. M. Weiner. Resonance decays and partial coherence in Bose-Einstein correlations.Phys. Rev. D, 47:3860–3870, 1993. 9

work page 1993