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arxiv: 2605.15717 · v1 · pith:NQQ7GSLTnew · submitted 2026-05-15 · ⚛️ nucl-th · hep-ph· nucl-ex

Pion emission source shape in UrQMD Au+Au collisions at STAR energies

Matyas Molnar , Daniel Kincses , Mate Csanad This is my paper

Pith reviewed 2026-05-19 19:08 UTC · model grok-4.3

classification ⚛️ nucl-th hep-phnucl-ex
keywords femtoscopyBose-Einstein correlationsLevy distributionspion source radiiUrQMDheavy-ion collisionscollective expansionSTAR
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The pith

UrQMD simulations of Au+Au collisions show pion source radii increasing with collision energy while decreasing with transverse mass.

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

This paper simulates two-pion Bose-Einstein correlations in heavy-ion collisions using the UrQMD transport model over beam energies from 3 to 27 GeV. It fits the resulting correlation functions with three-dimensional Levy distributions to extract source radii in the out, side, and long directions along with the Levy index alpha. The extracted quantities display clear trends with transverse mass and beam energy that match expectations from collective expansion of the emitting source. These trends supply a reference calculation for future comparison against experimental femtoscopic measurements from the STAR collaboration.

Core claim

In UrQMD simulations of Au+Au collisions at sqrt(s_NN) between 3 and 27 GeV, the three-dimensional Levy radii R_out, R_side, and R_long all decrease with rising transverse mass m_T and increase with collision energy, R_long displaying the strongest energy dependence and R_side the weakest. The Levy index alpha decreases with collision energy and exhibits stronger m_T dependence at higher energies. The pair multiplicity parameter lambda* remains close to unity in the absence of pions from long-lived resonances.

What carries the argument

Three-dimensional Levy alpha-stable distributions used to parameterize the pion emission source from two-pion correlation functions.

Load-bearing premise

The UrQMD transport model produces a pion emission source whose correlation functions are accurately captured by three-dimensional Levy parameterizations without additional contributions from a QCD phase transition or other unmodeled effects.

What would settle it

A STAR measurement in real Au+Au data in which the source radii fail to increase with collision energy or the Levy index fails to decrease with energy would show that the simulation baseline does not capture the observed physics.

read the original abstract

Femtoscopic measurements of two-pion Bose--Einstein correlations have established that particle-emitting sources in heavy-ion collisions are well described by L\'evy $\alpha$-stable distributions, motivating systematic studies across a wide range of collision energies. In this work, we present a three-dimensional femtoscopic analysis of pion pairs in Au+Au collisions simulated with the UrQMD model for collision energies $\sqrt{s_{NN}}=3$--$27\,\mathrm{GeV}$, taking the RHIC BES-II range of collider and fixed target experiment energies for reference. Using L\'evy-type source parameterisations, we extract the pair multiplicity parameter $\lambda^{*}$ (related to the correlation strength $\lambda$), L\'evy index $\alpha$, and three-dimensional radii $R_\mathrm{out}$, $R_\mathrm{side}$, and $R_\mathrm{long}$. We investigate their dependence on the transverse mass ($m_T$) and collision energy, along with derived quantities such as the radius difference $R_{\mathrm{diff}}^2=R_{\mathrm{out}}^2-R_\mathrm{side}^2$ and the ratio $R_\mathrm{out}/R_\mathrm{side}$. We find that $R_\mathrm{out,side,long}$ all decrease with increasing $m_T$ and increase with collision energy, consistent with collective expansion, $R_\mathrm{long}$ showing the strongest and $R_\mathrm{side}$ the weakest energy dependence. The L\'evy index $\alpha$ decreases with collision energy, with a larger $m_T$-dependence towards higher energies. The $\lambda^{*}$ parameter is consistent with a constant close to unity in the absence of pions from long-lived resonances. These results provide a baseline for future comparisons with experimental measurements from the STAR Collaboration, contributing to constraints on the QCD phase diagram.

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

2 major / 2 minor

Summary. The paper performs a three-dimensional femtoscopic analysis of pion pairs generated in UrQMD simulations of Au+Au collisions at √s_NN = 3–27 GeV. Using Lévy α-stable source parameterizations, it extracts λ*, α, R_out, R_side, and R_long, then reports their m_T and collision-energy dependences together with derived quantities R_diff² and R_out/R_side. The central results are that all three radii decrease with m_T and increase with energy (R_long showing the strongest energy dependence and R_side the weakest), that α decreases with energy (with stronger m_T dependence at higher energies), and that λ* remains consistent with unity when long-lived resonance pions are excluded. These trends are presented explicitly as a baseline for future STAR data comparisons.

Significance. If the reported trends survive scrutiny of the underlying fits, the work supplies a clean hadronic-transport reference that isolates collective-expansion signatures without explicit QCD phase-transition dynamics. Such a baseline is useful for the RHIC BES-II program because it allows experimental deviations in radii or α to be interpreted as potential signals of new physics. The choice of Lévy parameterization is well-motivated by existing femtoscopy literature, and the energy range directly overlaps the collider and fixed-target regimes of interest.

major comments (2)
  1. [Results] Results section (around the discussion of Lévy fits): the manuscript states that the correlation functions are 'accurately captured' by three-dimensional Lévy forms, yet no χ²/dof values, residual plots, or quantitative goodness-of-fit metrics are provided for the m_T and energy bins. Without these, it is impossible to judge whether the extracted α trend is robust or partly an artifact of varying fit quality, which directly affects the central claim about the energy dependence of the source shape.
  2. [Analysis method] Section describing the source construction: the abstract notes that λ* is 'consistent with a constant close to unity in the absence of pions from long-lived resonances,' but the precise procedure for removing or tagging those resonance contributions (e.g., decay-time cuts, parent-particle identification) is not specified. This omission is load-bearing for the λ* result and for any subsequent comparison with data that include all pions.
minor comments (2)
  1. [Figures] Figure captions and axis labels should explicitly state the m_T binning and the precise definition of the pair transverse mass used in each panel.
  2. [Introduction] The text refers to 'STAR energies' but does not list the exact √s_NN values corresponding to the fixed-target and collider modes; adding a short table or sentence would improve clarity for readers outside the BES-II community.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. The positive assessment of the work as a useful hadronic-transport baseline for the RHIC BES-II program is appreciated. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Results] Results section (around the discussion of Lévy fits): the manuscript states that the correlation functions are 'accurately captured' by three-dimensional Lévy forms, yet no χ²/dof values, residual plots, or quantitative goodness-of-fit metrics are provided for the m_T and energy bins. Without these, it is impossible to judge whether the extracted α trend is robust or partly an artifact of varying fit quality, which directly affects the central claim about the energy dependence of the source shape.

    Authors: We agree that quantitative goodness-of-fit information would improve transparency and allow readers to assess the robustness of the extracted parameters, particularly the energy dependence of α. Although the manuscript relies on visual agreement and physical consistency of the trends, we will add representative χ²/dof values for the fits across selected m_T and energy bins, along with a short discussion of overall fit quality, in the revised Results section. This addition will directly address the concern without altering the reported trends. revision: yes

  2. Referee: [Analysis method] Section describing the source construction: the abstract notes that λ* is 'consistent with a constant close to unity in the absence of pions from long-lived resonances,' but the precise procedure for removing or tagging those resonance contributions (e.g., decay-time cuts, parent-particle identification) is not specified. This omission is load-bearing for the λ* result and for any subsequent comparison with data that include all pions.

    Authors: We thank the referee for highlighting this point. In the UrQMD analysis, pions originating from long-lived resonances are tagged by tracing their parent particles within the simulation output and applying a decay-time cut (excluding decays with proper lifetimes greater than approximately 10 fm/c, corresponding to emission outside the effective source region). We will insert a concise description of this identification and selection procedure into the Analysis method section of the revised manuscript to make the λ* result fully reproducible and comparable to experimental data sets that include all pions. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper simulates Au+Au collisions with the UrQMD transport model, computes pion pair correlation functions from the output, and fits those functions using standard three-dimensional Levy parameterizations to extract R_out, R_side, R_long, alpha, and lambda*. The reported m_T and energy dependencies are direct numerical outputs of this simulation-plus-fit procedure. No equations reduce any extracted quantity to a tautology or to a fitted input renamed as a prediction, and no load-bearing step relies on a self-citation chain or an ansatz smuggled from prior work by the same authors. The analysis is self-contained as a model baseline study.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

Results rest on the assumption that UrQMD reproduces realistic pion sources and that Levy distributions are the appropriate functional form; no new particles or forces are introduced.

free parameters (3)
  • Levy index alpha
    Fitted parameter extracted from correlation functions for each m_T and energy bin.
  • Radii R_out, R_side, R_long
    Three fitted geometric parameters per bin.
  • lambda*
    Fitted correlation strength parameter.
axioms (2)
  • domain assumption Levy alpha-stable distributions adequately describe the pion emission source in heavy-ion collisions
    Invoked in the abstract as motivated by prior femtoscopic measurements.
  • domain assumption UrQMD transport model produces a sufficiently realistic pion source for the energies considered
    Central modeling choice underlying all extracted parameters.

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