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arxiv: 2602.15770 · v2 · pith:ZTRYKI3Rnew · submitted 2026-02-17 · ✦ hep-ph · nucl-ex· nucl-th

More uses for Thermal Models

Natasha Sharma , Lokesh Kumar , Sourendu Gupta This is my paper

Pith reviewed 2026-05-22 11:37 UTC · model grok-4.3

classification ✦ hep-ph nucl-exnucl-th
keywords thermal modelsheavy-ion collisionschemical potentialsparticle yieldsfreeze-out parametersRHICbaryon chemical potential
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0 comments X

The pith

Combinations of particle and anti-particle yields test thermal models without free parameters and extract chemical potentials directly from data.

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

The paper demonstrates that specific ratios of measured particle yields to their anti-particle counterparts can verify thermal models in heavy-ion collisions without fitting any parameters such as temperature or volume. These same ratios allow direct extraction of the ratios of chemical potentials to temperature for baryon number, strangeness, and electric charge. Applied to RHIC data for protons, lambdas, and cascades across beam energies from 7.7 to 39 GeV, the extracted values agree with previously published STAR freeze-out parameters. The method further predicts the corresponding ratios for omega particles and extends to estimating yields of light nuclei at energies where measurements are absent.

Core claim

Combinations of particle and anti-particle yields can be used to test thermal models in a parameter free way and to extract μ_B/T, μ_S/T and μ_Q/T from measured ratios for p, Λ, and Ξ at √s_NN = 7.7-39 GeV, which compare well with published STAR freeze-out parameters and predict similar combinations for Ω yields.

What carries the argument

Combinations of particle-to-anti-particle yield ratios that cancel the common temperature and volume factors in the thermal distribution formula, leaving only exponentials of the chemical potentials over temperature.

If this is right

  • The extracted μ_B/T, μ_S/T and μ_Q/T values match published STAR freeze-out parameters.
  • The same combinations predict the corresponding yield ratios for Ω particles.
  • The approach extends to predicting anti-nuclei yields at beam energies where they remain unmeasured.
  • Updated parametrizations are provided for the collision-energy dependence of T and μ_B, together with a new parametrization for μ_S.

Where Pith is reading between the lines

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

  • The method could reduce the number of free parameters needed when fitting thermal models to new data sets from other facilities.
  • Similar ratio combinations might be tested in smaller collision systems or at LHC energies to check consistency across different regimes.
  • If the predictions for nuclei hold, they could help constrain the thermal description of light cluster formation in the hadronic phase.

Load-bearing premise

Particle yields are produced according to a single common thermal distribution at chemical freeze-out with no significant non-thermal processes or feed-down that would invalidate the chosen ratios.

What would settle it

A significant mismatch between the predicted Ω or light-nuclei yield ratios and actual measurements at the same beam energies would show that the parameter-free extraction does not hold.

Figures

Figures reproduced from arXiv: 2602.15770 by Lokesh Kumar, Natasha Sharma, Sourendu Gupta.

Figure 1
Figure 1. Figure 1: Double ratios of various particles as given in Eq. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Extracted µB/T, µS/T, and µQ/T ratios as a function of number of participating nucleons ⟨Npart⟩ in various energies. Lines represent the linear fits to the data points. and the published fits from the STAR experiment is a val￾idation of the method used here. Due to the larger relative errors on µQ/T, its comparison does not add anything to this conclusion. 0 50 100 150 200 250 300 350 400 〉 part 〈 N 0.0 0.… view at source ↗
Figure 4
Figure 4. Figure 4: Verification of RΩ predicted by Eq. (9). The quantity is computed from experimentally measured Ω and Ω yields, while the cosh is obtained using the chemical potential ratios obtained using Eqs. (6–8). 5.2 Validation using RΩ As mentioned above, RΩ provides a validation of the method. The experimentally measured Ω− and Ω+ yields are used to estimate RΩ. Using the extracted values of µB/T, µS/T and µQ/T one … view at source ↗
Figure 6
Figure 6. Figure 6: Energy dependence of freeze-out parameters [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Top: Ratios Rp and Rd, and their comparison with model predictions using µB/T as per Eqs. (6) and (16). Bottom: Prediction of anti-nuclei p¯, ¯d, and t¯ using measurements of nuclei and Eqs. (6), (16), and (17) as explained in the text. Unfilled symbols represent the pre￾dictions while the solid symbols represent the published measured yields. For deuterons (Bd = 2) and tritons (Bt = 3), Eq. (5) can be wri… view at source ↗
read the original abstract

We explore combinations of particle and anti-particle yields which can be used to test thermal models in a parameter free way. We also explore combinations which can be used to extract $\mu_B/T$, $\mu_S/T$ and $\mu_Q/T$. We use experimentally measured particle-antiparticle specific ratios for proton $p$, Lambda $\Lambda$, and cascade $\Xi$, for $\sqrt{s_{NN}}=$ 7.7-39 GeV from RHIC BES phase-1 to extract the $\mu_{B,S,Q}/T$. These compared well with published STAR freeze-out parameters. These combinations are verified to predict a similar combination of $\Omega$ yields. We also extend this idea to predict (anti-)nuclei yields at energies where they are not measured. We also update parametrizations for the $\sqrt{s_{NN}}$ dependence of freeze-out parameters $T$ and $\mu_B$, and present for the first time a similar parametrization of $\mu_S$.

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 manuscript proposes combinations of particle and anti-particle yields that cancel chemical-potential dependence, allowing parameter-free tests of thermal models and direct extraction of μ_B/T, μ_S/T, and μ_Q/T. Using measured ratios for p, Λ, and Ξ from RHIC BES phase-1 data at √s_NN = 7.7–39 GeV, the extracted values are compared to published STAR freeze-out parameters and shown to agree well; the same combinations are verified to predict Ω yields. The work also updates parametrizations of T and μ_B versus √s_NN, introduces a new parametrization for μ_S, and extends the method to predict (anti-)nuclei yields at energies where data are unavailable.

Significance. If the central claims hold, the parameter-free combinations provide a useful, low-model-dependence tool for testing thermalization and extracting freeze-out conditions directly from ratios. The reported agreement with independent STAR parameters and successful verification for Ω yields add credibility. The updated and new parametrizations of freeze-out quantities versus collision energy offer a convenient reference for future phenomenological studies. The approach could be extended to other particles, though its robustness depends on the validity of the single-freeze-out thermal assumption.

major comments (2)
  1. [Section describing the parameter-free combinations (near Eq. for the p-Λ-Ξ ratio)] The parameter-free combination (p/¯p)(Ξ/¯Ξ)/(Λ/¯Λ)² is presented as necessarily equal to unity once chemical potentials cancel. This holds only in the grand-canonical ensemble; at √s_NN = 7.7 GeV the small volume makes canonical suppression for strangeness non-negligible, and the suppression factors scale with strangeness content so they do not cancel in the ratio. A measured deviation from 1 could therefore reflect the ensemble choice rather than a failure of thermalization. This directly affects the central claim that the combination tests thermal models in a parameter-free way.
  2. [Section on extraction from p, Λ, Ξ data and comparison to STAR] The extraction of μ_B/T, μ_S/T, and μ_Q/T from the measured ratios is reported to agree with STAR parameters, yet the manuscript provides neither the explicit algebraic derivation of the inversion formulas nor tabulated input yields with uncertainties. Without these, independent verification of the numerical results and error propagation is not possible from the given information.
minor comments (2)
  1. [Throughout the manuscript] The notation for chemical potentials (μ_B, μ_S, μ_Q) and their ratios to T should be used consistently in all equations and text to avoid ambiguity.
  2. [Figures comparing extracted values to STAR parametrizations] Figures showing the extracted parameters versus √s_NN would benefit from explicit inclusion of the experimental uncertainties on the input ratios.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Section describing the parameter-free combinations (near Eq. for the p-Λ-Ξ ratio)] The parameter-free combination (p/¯p)(Ξ/¯Ξ)/(Λ/¯Λ)² is presented as necessarily equal to unity once chemical potentials cancel. This holds only in the grand-canonical ensemble; at √s_NN = 7.7 GeV the small volume makes canonical suppression for strangeness non-negligible, and the suppression factors scale with strangeness content so they do not cancel in the ratio. A measured deviation from 1 could therefore reflect the ensemble choice rather than a failure of thermalization. This directly affects the central claim that the combination tests thermal models in a parameter-free way.

    Authors: We agree that the exact cancellation to unity assumes the grand-canonical ensemble. In the canonical ensemble the strangeness suppression factors depend on the absolute strangeness content and therefore do not cancel in the ratio. This is a substantive point, especially at the lowest energies where the system volume is modest. In the revised manuscript we will explicitly state the grand-canonical assumption, add a short discussion of possible canonical corrections at √s_NN = 7.7 GeV, and note that any observed deviation from unity could arise either from incomplete thermalization or from the choice of ensemble. We will also indicate that the good agreement we find with independent STAR freeze-out parameters suggests the grand-canonical approximation remains useful across the BES range. revision: partial

  2. Referee: [Section on extraction from p, Λ, Ξ data and comparison to STAR] The extraction of μ_B/T, μ_S/T, and μ_Q/T from the measured ratios is reported to agree with STAR parameters, yet the manuscript provides neither the explicit algebraic derivation of the inversion formulas nor tabulated input yields with uncertainties. Without these, independent verification of the numerical results and error propagation is not possible from the given information.

    Authors: We thank the referee for highlighting this omission. In the revised version we will supply the explicit algebraic expressions that invert the measured ratios for μ_B/T, μ_S/T and μ_Q/T. We will also include a table of the input experimental yields (with uncertainties) for protons, Λ and Ξ (and their antiparticles) together with the extracted chemical-potential ratios and their propagated uncertainties. These additions will make the numerical results fully reproducible and allow independent verification of the error propagation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies thermal model to external data with independent validation

full rationale

The paper constructs combinations of particle-antiparticle yields from the thermal model assumptions to create a parameter-free test (expecting unity after cancellation of all μ/T terms) and separate combinations to extract μ_B/T, μ_S/T, μ_Q/T from measured p, Λ, Ξ ratios at RHIC BES energies. These extractions are compared directly to independently published STAR freeze-out parameters. Secondary updates to parametrizations of T, μ_B, and μ_S versus √s_NN are fits to the extracted values for descriptive purposes and for predicting Ω and nuclei yields, but do not make the central test or extraction claims reduce to the inputs by construction. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations are present. The chain is self-contained against external experimental benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that thermal models with a single freeze-out hypersurface describe the yields, plus fitted parametrizations for the energy dependence of T and chemical potentials.

free parameters (1)
  • parameters in √s_NN parametrizations of T, μ_B, and μ_S
    Updated functional forms for the energy dependence of freeze-out parameters are fitted to data.
axioms (1)
  • domain assumption Particle yields follow thermal distributions at common chemical freeze-out temperature and chemical potentials
    Invoked throughout the use of thermal models to relate yields to μ/T ratios.

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Reference graph

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