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Relative Hadron Yields in HRG With Medium Modification

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Pith's one-line read This paper finds that NJL-based, temperature- and density-dependent baryon masses in an excluded-volume hadron resonance gas lower the fitted chemical freeze-out temperature to about 145 MeV at high collision energies, shifting the entire…

desk verdict Competent incremental HRG paper whose central freeze-out extraction is undermined by missing T,mu-dependent mass derivatives in the number-density formula. read the letter →

arxiv 2411.14826 v1 pith:WR5DCN7X submitted 2024-11-22 hep-ph nucl-th

Nasir Ahmad Rather , Sameer Ahmad Mir , Iqbal Mohi Ud Din , Saeed Uddin This is my paper · ORCID
classification hep-phnucl-th
keywords hadronresonancegaschemicalfreeze-outNJLmodelmedium-modifiedbaryonmassesexcludedvolumeparticleratioslineheavy-ioncollisions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the chemical freeze-out point of the hot hadronic matter produced in ultra-relativistic nucleus-nucleus collisions moves to lower temperatures and lower baryon chemical potentials when baryon masses are made temperature- and density-dependent through the SU(3) NJL constituent-quark model, an effective model that generates quark masses through chiral condensates. Inserting these medium-modified masses into an excluded-volume hadron resonance gas (a gas of hadrons with hard-core repulsion) still reproduces the measured antibaryon-to-baryon ratios, the kaon and pion ratios, and the correlation between $k^-/k^+$ and $\bar{p}/p$, with a fitted hard-core baryonic radius of $0.20$ fm. The central finding is that the chemical freeze-out temperature then saturates near $145$ MeV at high collision energies, well below the roughly $170$ MeV obtained with vacuum hadron masses in other fits. If the result is correct, the commonly quoted freeze-out line overestimates both $T$ and $\mu_B$, and the vacuum-mass 'hadron gas' temperature near $170$ MeV may actually belong to the quark-gluon phase.

What carries the argument

The load-bearing machinery is the SU(3) NJL gap equations (Eqs. 2–5) that produce constituent quark masses $m^*_u$, $m^*_d$, $m^*_s$ as functions of $T$ and $\mu$, combined with the constituent-quark-model mass formulas of Table II that assemble those quark masses into baryon masses. Those masses are inserted into the grand-canonical ideal-gas pressure (Eq. 8), and the standard excluded-volume prescription (Eqs. 11–19) converts the ideal pressure into a hard-core pressure with a baryonic radius $r$; the number density is the $\mu$-derivative of that pressure (Eq. 18). The model is closed by the freeze-out parameterization $T(\mu_B)=c-d\mu_B^2-e\mu_B^4$ and $\mu_B(\sqrt{s_{NN}})=f/(1+g\sqrt{s_{NN}})$, with $c,d,e,f,g,r$ fitted to the $\bar{p}/p$ data and checked against the other ratios. The decisive move is that the same $T$- and $\mu$-dependent masses appear inside the thermal integrals, which lowers the light-baryon masses and thereby systematically lowers the extracted freeze-out temperature.

What would settle it

Refit the $\bar{p}/p$ data using the full $\mu$-derivative of the NJL-modified pressure, including the $\partial m_B/\partial \mu$ terms from the gap equations, and compare the resulting $(T,\mu_B)$ to the paper's values ($c=145\pm1.3$ MeV, $r=0.20\pm0.03$ fm); if the shift exceeds the quoted uncertainties, the reported freeze-out line is an artifact of the neglected mass dependence.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that a thermodynamically consistent excluded-volume HRG with NJL-generated, $T$- and $\mu$-dependent baryon masses describes the energy dependence of $\bar{p}/p$, $\bar{\Lambda}/\Lambda$, $\bar{\Xi}/\Xi$, $\bar{\Omega}/\Omega$, $k^-/k^+$, and $\pi^-/\pi^+$ from AGS to LHC energies, and in doing so produces a chemical freeze-out line systematically lower than vacuum-mass models. The baryon masses all decrease with temperature: the proton mass drops by about 23\% from its vacuum value, $\Lambda$ by about 18\%, while decuplet baryons such as $\Omega$ change by only about 4\%. Because the freeze-out parameters are extracted from the $\bar{p}/p$ fit, the lower light-baryon masses push the fitted temperature down, giving $\chi^2/\mathrm{dof}=0.48$ for $\bar{p}/p$ with $T(\mu_B)$ saturating near $145$ MeV, $r=0.20$ fm, and correspondingly smaller $\mu_B$ values; the same parameter set then yields $\chi^2/\mathrm{dof}$ values of 2.02, 1.5, 0.9, 1.45, and 0.96 for the other listed ratios.

Load-bearing premise

The calculation assumes that the standard excluded-volume formulas remain valid when the baryon mass is a function of temperature and chemical potential, because the number density is obtained by differentiating the pressure with respect to $\mu$ while holding the mass fixed; the omitted $\partial m_B/\partial \mu$ terms are never written down or estimated.

Editorial extensions

If this is right

  • The chemical freeze-out line shifts downward in both $T$ and $\mu_B$ relative to vacuum-mass HRG fits, with $T$ saturating near $145$ MeV for $\sqrt{s_{NN}}\gtrsim 100$ GeV.
  • A single hard-core baryonic radius of $r=0.20$ fm, fixed from $\bar{p}/p$, simultaneously describes $\bar{\Lambda}/\Lambda$, $\bar{\Xi}/\Xi$, $\bar{\Omega}/\Omega$, $k^-/k^+$, and $\pi^-/\pi^+$ with the same parameter set.
  • The correlation $k^-/k^+ = (\bar{p}/p)^\alpha$ is reproduced with $\alpha\approx 0.23$, matching the experimental $\alpha\approx 0.21$ better than the light-quark-composition value $\alpha=1/3$.
  • If the $145$ MeV saturation is physical, the $\sim 170$ MeV freeze-out temperature obtained with vacuum masses may describe the quark-gluon phase rather than a hadron gas, as the paper itself suggests.
  • Since $\mu_B$ also comes out lower at each collision energy, the present freeze-out curve is flatter and sits below the point-like and Van der Waals freeze-out lines from earlier works.

Reading between the lines

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

  • A direct consistency test that goes beyond the paper is to recompute the number densities with the full $\mu$-derivative, keeping the $\partial m_B/\partial \mu$ terms from the NJL gap equations; if those terms move the fitted $(T,\mu_B)$ by more than the quoted uncertainties, the reported freeze-out line is an artifact of treating masses as constant during differentiation.
  • The predicted 23\% drop in the proton mass near freeze-out implies that baryon-number susceptibilities and mean transverse-momentum ratios, which are sensitive to the baryon mass, should show a corresponding medium effect; the paper does not examine these observables.
  • A natural extension would be to make the freeze-out fit fully self-consistent by evaluating the NJL masses at each trial $(T,\mu_B)$ and refitting iteratively, which would show whether the fit quality and the $145$ MeV plateau survive exact thermodynamics.
  • The near-power-law correlation between $k^-/k^+$ and $\bar{p}/p$ with $\alpha\approx 0.23$ could serve as a constraint on freeze-out parameterizations in future low-energy runs, independently of the absolute yields.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This paper combines an SU(3) NJL constituent-quark model, which supplies temperature- and chemical-potential-dependent baryon masses, with an excluded-volume hadron resonance gas (EVHRG) to analyze particle yield ratios over a wide range of heavy-ion collision energies. The authors fit the Cleymans-type freeze-out parametrization, Eqs. (21)-(22), together with a baryon hard-core radius, to the antiproton-to-proton ratio, obtaining chi2/dof = 0.48. They then use the same parameter set to compare with other antibaryon-to-baryon ratios, k-/k+, pi-/pi+, and the k-/k+ versus pbar/p correlation, reporting reasonable chi2/dof values. The central claim is that the chemical freeze-out temperature saturates near 145 MeV at high sqrt(s_NN), substantially lower than the ~170 MeV obtained in vacuum-mass HRG fits, with lower baryon masses and a freeze-out line shifted in the T-mu_B plane.

Significance. If the calculation is internally consistent, the paper offers a concrete mechanism for reconciling the relatively high chemical freeze-out temperatures of vacuum-mass HRG fits with a purely hadronic phase, and it provides a set of predictions for other particle ratios using parameters fixed only by pbar/p. The authors are transparent about which parameters are fitted, report chi2/dof values, and the NJL parameters are not tuned to the ratio data; the same-parameter test of the other ratios is a genuine consistency check rather than a circular fit. The main weakness is that the thermodynamic derivation of the number densities omits the mass-derivative terms that are required because the baryon masses are explicitly T- and mu-dependent; this omission affects the central freeze-out temperature claim and must be addressed before the numerical results can be accepted.

major comments (2)
  1. [Section II, Eqs. (9) and (18)] The number density is defined as (∂p/∂μ)_T, but throughout the derivation the baryon mass m is treated as μ-independent, even though m is explicitly T- and μ-dependent through the NJL gap equations (2)-(5) and Table II. In Eq. (9), the derivative ∂P_id/∂μ should include a term (∂P_id/∂m)(∂m/∂μ); in Eq. (18), the ideal density n_id(T, μ*) is itself an implicit function of μ* through the mass, so the standard inversion identity n_excl = n_id/(1 + b n_id) is not the exact derivative of p_excl(T, μ). The omitted term is not negligible a priori: for the Boltzmann limit n ∝ m^2 T K_2(m/T), the logarithmic derivative with respect to m is of order m/T, which is 5-10 for the masses and temperatures used here, and the NJL masses drop by roughly 20-30% over the fitted μ_B range. The paper neither derives the correct derivative nor states and quantifies the approximation. Because the fitted freeze-out parameters are extracted from quantities computed with these densities, the central claim of a lower freeze-out temperature is not yet established.
  2. [Section III, first paragraph and Eq. (19)] The implementation of excluded volume is ambiguous with respect to antibaryons. The text states that hard-core repulsion is present for baryon-baryon and antibaryon-antibaryon pairs, while baryon-antibaryon interactions are only attractive. However, Eq. (19) sums over all species i in the denominator without distinguishing particles from antiparticles. If the sum includes both B and \bar B, the model includes B-\bar B repulsion; if the sum is meant to include only baryons, the restriction must be stated and the formula for the pbar/p ratio must be modified accordingly. Since the baryon hard-core radius r = 0.20 fm is fitted to pbar/p, this ambiguity directly affects the extracted freeze-out parameters.
minor comments (6)
  1. [Introduction] There are several typographical errors: 'quantam' should be 'quantum', 'langragian' should be 'Lagrangian', and 'Mev' should be 'MeV'.
  2. [Table II] The mass formulas contain apparent typos, e.g., the Ξ^0 row has '1/(m_v m*_s)' and the Λ^0 row uses 'M*_u' in one place. Please correct these and specify exactly which formulas were used in the numerical code, since the table is the link between the NJL input and the HRG densities.
  3. [Eq. (21)] The parameter e is reported as 0.015 ± 0.08 MeV^-3, i.e., consistent with zero. The paper should state whether the μ_B^4 term is statistically required and how the fit changes if e is fixed to zero.
  4. [Fig. 12 caption] The freeze-out lines from other works are shown but the corresponding references in the caption (Cleymans et al., Andronic et al., Poberezhnyuk et al.) are not given with year or journal; please add full references.
  5. [Abstract and title] The phrase 'like mass particle ratios' is used without definition; please clarify whether it refers to particle-antiparticle pairs of comparable mass.
  6. [Section III, paragraph after Eq. (22)] The electric chemical potential is said to be fixed by a charge-to-baryon ratio of about 0.4, but the relation and the resulting μ_Q values are not shown. Please provide the explicit condition used.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: freeze-out parameters fitted only to pbar/p; other ratios and NJL masses are independent inputs.

full rationale

The derivation chain is self-contained. The medium-modified baryon masses are obtained independently from the SU(3) NJL gap equations (2)-(5) with parameters fixed by external literature (Table I, Refs. [22,35]) and are not fitted to any measured particle ratio. The freeze-out parameters c, d, e, f, g and the hard-core radius r are fitted only to the pbar/p data (Sec. III, Eqs. (21)-(22)); the Lbar/L, Xibar/Xi, Obar/O, k-/k+, and pi-/pi+ ratios are computed with the same parameters and constitute genuine cross-checks, with quoted chi2/dof values. The excluded-volume formula (18)-(19) is the standard Rischke et al. result [37]; the self-citation [39] in Eq. (15) supports a standard Laplace-transform identity and is not load-bearing. The lower freeze-out temperature follows from the T,mu-dependent masses entering the partition function, not from any equation that reduces to the fitted data by construction. One internal-consistency concern, which is not circularity, is that Eq. (18) omits explicit partial-m/partial-mu terms even though the Table II baryon masses depend on mu through the NJL gap equations; this should be assessed as a thermodynamic-consistency and correctness issue rather than evidence of circular reasoning.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central result rests on the NJL constituent mass model (with literature parameters), the excluded-volume ansatz, the Cleymans freeze-out parametrization, and five fitted ansatz constants plus a fitted hard-core radius. No new particles or interactions are introduced.

free parameters (6)
  • c (freeze-out temperature offset) = 145 +/- 1.3 MeV
    Fitted to antiproton/proton ratio data across collision energies; sets the T scale at mu_B=0.
  • d (mu_B^2 coefficient) = 0.17 +/- 0.01 MeV^-1
    Fitted to antiproton/proton ratio data.
  • e (mu_B^4 coefficient) = 0.015 +/- 0.08 MeV^-3
    Fitted to antiproton/proton ratio data; the error is larger than the value, indicating poor constraint.
  • f (mu_B normalization) = 1180 +/- 16.0 MeV
    Fitted to antiproton/proton ratio data.
  • g (mu_B collision-energy scale) = 0.28 +/- 0.01 GeV^-1
    Fitted to antiproton/proton ratio data.
  • baryon hard-core radius r = 0.20 +/- 0.03 fm
    Fitted to antiproton/proton ratio data; determines the excluded volume b = 16*pi*r^3/3.
assumptions (5)
  • domain assumption SU(3) NJL model with the given parameters describes the quark condensates and constituent quark masses.
    Used to compute T,mu-dependent baryon masses; assumes the model is valid at the freeze-out conditions considered.
  • domain assumption Baryon masses are given by the constituent quark formulas in Table II with M0, a, b from [22].
    Assumes the baryon mass is a sum of constituent quark masses plus spin-splitting terms; no derivation is given in this paper.
  • domain assumption Strangeness conservation fixes mu_S; charge-to-baryon ratio of about 0.4 fixes mu_Q.
    Standard constraints; makes mu_B the only independent chemical potential.
  • domain assumption Boltzmann approximation is valid for all hadrons.
    Used for all particle species, despite bosons like pions; standard but approximate.
  • ad hoc to paper The Cleymans parametrization (Eqs. 21-22) is an adequate form for the freeze-out curve.
    Chosen as the fitting ansatz, not derived from the model.

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Cite this review

Pith. "Pith review of Relative Hadron Yields in HRG With Medium Modification." pith.science (2026). https://pith.science/paper/WR5DCN7X

@misc{pith2026241114826,
  author       = {Pith},
  title        = {Pith review of: Relative Hadron Yields in HRG With Medium Modification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WR5DCN7X}},
  note         = {Machine review of arXiv:2411.14826}
}
abstract

In the framework of a constituent quark mass model, the modified baryon masses are incorporated into the hadron resonance gas (HRG) based analysis of the like mass particle ratios in ultra relativistic nucleus-nucleus collisions (URNNC) over a wide range of collision energy. In addition we have incorporated an essential feature of the hadronic interaction at short distance, i.e. the hard-core repulsion by using the standard excluded volume type approach. We have extracted the chemical freeze-out conditions. The resulting freeze-out line in our case is compared with those obtained earlier using different model approaches. The correlation between $k^{-}/k^{+}$ and $\bar p/p$ ratios is also studied.

Figures

Figures reproduced from arXiv: 2411.14826 by the authors.

Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 1
Figure 1. FIG. 1: ¯p [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Correlation between [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8: The graph shows the variation of constituent quark [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10: The graph shows the variation of [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: The graph shows the dependence of Temperature [PITH_FULL_IMAGE:figures/full_fig_p007_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Chemical freeze-out line from different calculatio [PITH_FULL_IMAGE:figures/full_fig_p008_12.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

82 extracted references · 72 canonical work pages

  1. [1]

    which leads to three gap equations for the constituent quark mass of the following type: m∗ u =m0u − 4Gs⟨ ψ uψ u⟩ − 2Ks⟨ψ dψ d⟩⟨ψ sψ s⟩ (2) m∗ d =m0d − 4Gs⟨ ψ dψ d⟩ − 2Ks⟨ψ sψ s⟩⟨ψ uψ u⟩ (3) m∗ s =m0s − 4Gs⟨ ψ sψ s⟩ − 2Ks⟨ψ uψ u⟩⟨ψ dψ d⟩ (4) here (ψψ ) = α q (where q =u,d,s ) is the quark conden- sate and is given as: α q = − 2Nc 2π 3 ∫ Λ 0 m∗ qd3p Eq [1 ...

  2. [2]

    Interacting hadron resonance gas meets lattice QCD,

    A. Andronic, P. Braun-Munzinger, J. Stachel, and M. Winn, “Interacting hadron resonance gas meets lattice QCD,” Phys. Lett. B 718, 80-85 (2012)

    work page 2012

  3. [3]

    The QCD Equation of State from the Lattice,

    O. Philipsen, “The QCD Equation of State from the Lattice,” arXiv:1207.5999 [hep-lat] (2012). Prog. Part. Nucl. Phys. 70 (2013), 55-107

    arXiv 2012

  4. [4]

    Phases of QCD: Lattice Thermodynamics and a Field Theoretical Model,

    C. Ratti, M. A. Thaler, and W. Weise, “Phases of QCD: Lattice Thermodynamics and a Field Theoretical Model,” Phys. Rev. D 73 (2006), 014019

    work page 2006

  5. [5]

    Adams et al

    J. Adams et al. [STAR Collaboration], Nucl. Phys. A 757 (2005), 102-183

    work page 2005

  6. [6]

    one can get the pressure for the case of HRG phase as: P id(T,µ ) = lim V →∞ T ln Zid(T,µ,V ) V = T g 2π 2 ∫ ∞ 0 p2ln [ 1 ±e− (E− µ )/T ] dp (8) The number density of the point-like particles can be obtained in thermodynamically consistent manner as: nid(T,µ ) = ( ∂P id ∂µ ) T (9) In terms of the corresponding canonical partition func- tion one can also w...

  7. [7]

    16 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 µ B ✭●❡❱✮ TChe ✭●❡❱✮ Pr❡s❡♥t ❈❛❧❝✉❧❛t✐♦♥ P♦❜❡r❡③❤♥②✉❦ ❡t✳❛❧ ❈❧❡②♠❛♥s ❡t✳❛❧ ❆♥❞r♦♥✐❝ ❡t✳❛❧ FIG. 12: Chemical freeze-out line from different calculatio ns. ment with the earlier works based on effective hadron mass scaling calculations [ 74]. Moreover Hirsch et. al

    work page

  8. [8]

    Colloquium: Phase Diagram of Strongly Interacting Matter,

    P. Braun-Munzinger and J. Wambach, “Colloquium: Phase Diagram of Strongly Interacting Matter,” Rev. Mod. Phys. 81 (2009), 1031-1050

    work page 2009

Show all 82 references
  1. [9]

    To describe the dependence of the freeze- out parameters on the collision energy we have shown in Figs

    The relatively smaller values of chemical freeze-out temperature obtained in our case at higher col- lision energies ( ∼ 145 MeV) may even be a desired effect, since higher temperatures ∼ 170 MeV obtained in simple thermal models that rely on vacuum hadronic masses, may corresp...

  2. [10]

    RHIC and QCD: An Overview,

    T. D. Lee, “RHIC and QCD: An Overview,” Nucl. Phys. A 590 (1995), 11-27

    1995

  3. [11]

    Using Eqn

    one can obtain the pressure of the system: ˆZ excl GC (T,µ,ζ ) = ∫ ∞ 0 e− ζVZ excl GC (T,µ,V )dV (12) 4 for the finiteness of the integral we must have: ζ = lim V →∞ lnZ excl GC (T,µ,V ) V (13) which gives Tζ = pexcl(T,µ ). Using Eqn. ( 11) in Eqn. ( 12) we get: ˆZ excl GC (T,µ...

  4. [12]

    Canonical Partition Function and Fi- nite Density Phase Transition in Lattice QCD,

    S. Ejiri, “Canonical Partition Function and Fi- nite Density Phase Transition in Lattice QCD,” Phys. Rev. D 78 (2008), 074507

    2008

  5. [13]

    Lattice QCD at Finite Temperature,

    E. Laermann and O. Philipsen, “Lattice QCD at Finite Temperature,” Ann. Rev. Nucl. Part. Sci. 53 (2003)

    2003

  6. [14]

    The Condensed Matter Physics of QCD,

    K. Rajagopal and F. Wilczek, “The Condensed Matter Physics of QCD,” in At The Frontier of Particle Physics: Handbook of QCD , Vol. 3, (2001), pp. 2061-2151

    2001

  7. [15]

    Cosmic Separation of Phases,

    E. Witten, “Cosmic Separation of Phases,” Phys. Rev. D 30 (1984), 272

    1984

  8. [16]

    Equation of State for Two Flavor QCD at Nt = 6,

    C. Bernard, T. Blum, et al. , “Equation of State for Two Flavor QCD at Nt = 6,” Phys. Rev. D 55 (1997), 6861

    1997

  9. [17]

    Phase Transitions in Quantum Chromodynamics,

    H. Meyer-Ortmanns, “Phase Transitions in Quantum Chromodynamics,” Rev. Mod. Phys. 68 (1996), 473

    1996

  10. [18]

    The Order of the Quantum Chromody- namics Transition Predicted by the Standard Model of Particle Physics,

    Y. Aoki, G. Endr˝ odi, Z. Fodor, S. D. Katz, and K. K. Szab´ o, “The Order of the Quantum Chromody- namics Transition Predicted by the Standard Model of Particle Physics,” Nature 443 (2006), 675-678

    2006

  11. [19]

    Is There a Flavor Hierar- chy in the Deconfinement Transition of QCD?

    R. Bellwied, et al. “Is There a Flavor Hierar- chy in the Deconfinement Transition of QCD?” Phys. Rev. Lett. 111 (2013), 202302

    2013

  12. [20]

    Rapidity Dependence of Deuteron Production in Cen- tral Au+Au Collisions at s NN= 200 GeV,

    I. Arsene et al. [BRAHMS Collab], “Rapidity Dependence of Deuteron Production in Cen- tral Au+Au Collisions at s NN= 200 GeV,” Phys. Rev. C 83 (2011), 044906

    2011

  13. [21]

    and Eqn. (22), we have treated the hard-core baryonic radius also as a free parameter in order to obtain the best fit to the experimental data over a wide range of RHIC-STAR and ALICE-LHC energies. To calculate the other like mass anti-baryon to baryon ratios and relative meson...

  14. [22]

    Charged-Particle Multiplicity and Pseudorapidity Distributions Measured with the PHOBOS Detector in Au+Au, Cu+Cu, d+Au, and p+p Collisions at Ultrarelativistic Energies,

    B. Alver et al. , “Charged-Particle Multiplicity and Pseudorapidity Distributions Measured with the PHOBOS Detector in Au+Au, Cu+Cu, d+Au, and p+p Collisions at Ultrarelativistic Energies,” Phys. Rev. C 83 (2011), 024913

    2011

  15. [23]

    Fast hadronization of a quark gluon plasma and meson production,

    S. Saeed-uddin, “Fast hadronization of a quark gluon plasma and meson production,” doi:10.1016/S0370-2693(97)00679-5

    doi

  16. [24]

    Quark–Gluon Plasma and Color Glass Condensate at RHIC? The Perspective from the BRAHMS Experiment,

    I. Arsene, I. G. Bearden, D. Beavis, et al. , “Quark–Gluon Plasma and Color Glass Condensate at RHIC? The Perspective from the BRAHMS Experiment,” Nucl. Phys. A 757 (2005), 1-27

    2005

  17. [25]

    Equation of State in (2+1)-Flavor QCD,

    A. Bazavov, et al. [HotQCD Collaboration], “Equation of State in (2+1)-Flavor QCD,” 9 Phys. Rev. D 90 (2014), 094503

    2014

  18. [26]

    M. Lutz, S. Klimt, and W. Weise, Nucl. Phys. A 542, 521 (1992). doi:10.1016/0375-9474(92)90256-J

    1992 doi

  19. [27]

    Fluctuations and Correlations of Conserved Charges in an Excluded-Volume Hadron Resonance Gas Model,

    A. Bhattacharyya, et al. “Fluctuations and Correlations of Conserved Charges in an Excluded-Volume Hadron Resonance Gas Model,” Phys. Rev. C 90 (2014), 034909

    2014

  20. [28]

    Criticality in a Hadron Resonance Gas Model with the van der Waals Interac- tion,

    S. Samanta and B. Mohanty, “Criticality in a Hadron Resonance Gas Model with the van der Waals Interac- tion,” Phys. Rev. C 97 (2018), 015201

    2018

  21. [29]

    QCD Phenomenol- ogy Based on a Chiral Effective Lagrangian,

    T. Hatsuda and T. Kunihiro, “QCD Phenomenol- ogy Based on a Chiral Effective Lagrangian,” Phys. Rep. 247 (1994), 221-367

    1994

  22. [30]

    A Nu- cleonic NJL model for finite nuclei: Dynamic mass generation and ground state observables,

    T. J. Burvenich and D. G. Madland, “A Nu- cleonic NJL model for finite nuclei: Dynamic mass generation and ground state observables,” doi:10.1016/j.nuclphysa.2003.10.002

    2003 doi

  23. [31]

    Flavo r Dependence of Baryon Melting Temperature in Effective Models of QCD,

    J. M. Torres-Rincon, B. Sintes, and J. Aichelin, “Flavo r Dependence of Baryon Melting Temperature in Effective Models of QCD,” Phys. Rev. C 91 (2015), 065206

    2015

  24. [32]

    Medium Modi- fication of Hadron Masses and the Thermody- namics of the Hadron Resonance Gas Model,

    G. P. Kadam and H. Mishra, “Medium Modi- fication of Hadron Masses and the Thermody- namics of the Hadron Resonance Gas Model,” Phys. Rev. C 93 (2016), 025205

    2016

  25. [33]

    Hadron–Quark Phase Transition in the SU (3) Local Nambu–Jona-Lasinio (NJL) Model with Vector Interaction,

    G. Alaverdyan, “Hadron–Quark Phase Transition in the SU (3) Local Nambu–Jona-Lasinio (NJL) Model with Vector Interaction,” doi:10.3390/sym13010124

    doi

  26. [34]

    The Phase Diagram of Dense QCD,

    K. Fukushima and T. Hatsuda, “The Phase Diagram of Dense QCD,” Rep. Prog. Phys. 74 (2010), 014001

    2010

  27. [35]

    Hadron production in central nu- cleus–nucleus collisions at chemical freeze-out,

    A. Andronic, P. Braun-Munzinger, and J. Stachel, “Hadron production in central nu- cleus–nucleus collisions at chemical freeze-out,” doi:10.1016/j.nuclphysa.2006.03.012

    2006 doi

  28. [36]

    Hadron production and phase changes in relativistic heavy-ion collisions,

    J. Letessier and J. Rafelski, “Hadron production and phase changes in relativistic heavy-ion collisions,” Eur. Phys. J. A 35, 221–242 (2008)

    2008

  29. [37]

    Decoding the phase structure of QCD via particle production at high energy,

    A. Andronic, P. Braun-Munzinger, K. Redlich, and J. Stachel, “Decoding the phase structure of QCD via particle production at high energy,” arXiv:1710.09425 [nucl-th] ,

    arXiv

  30. [38]

    Systematics of chemical freeze- out parameters in heavy-ion collision experiments,

    S. Bhattacharyya, D. Biswas, S. K. Ghosh, R. Ray, and P. Singha, “Systematics of chemical freeze- out parameters in heavy-ion collision experiments,” Phys. Rev. D 101, 054002 (2020)

    2020

  31. [39]

    Dynamical model of elementary particles based on an analogy with supercon- ductivity.1

    Y. Nambu and G. Jona-Lasinio, “Dynamical model of elementary particles based on an analogy with supercon- ductivity.1 ” doi:10.1103/PhysRev.122.345

    doi

  32. [40]

    Hadron resonance gas with van der Waals interactions,

    V. Vovchenko, “Hadron resonance gas with van der Waals interactions,” Int. J. Mod. Phys. E 29, 2040002 (2020)

    2020

  33. [41]

    The Nambu—Jona- Lasinio model of quantum chromodynamics,

    S. P. Klevansky, “The Nambu—Jona- Lasinio model of quantum chromodynamics,” doi:10.1103/RevModPhys.64.649

    doi

  34. [42]

    Baryonic Masses Based on the NJL Model,

    W. M. Alberico, et al. “Baryonic Masses Based on the NJL Model,” doi:10.1140/epja/i2002-10088-6

    doi

  35. [43]

    Particle Ratios in a Multicomponent Nonideal Hadron Resonance Gas,

    R. A. Parra, S. Uddin, W. Bashir, I. U. Bashir, “Particle Ratios in a Multicomponent Nonideal Hadron Resonance Gas,” Adv. High Energy Phys. 2023 (2023), 2012220

    2023

  36. [44]

    Excluded volume effect for the nuclear matter equation of state,

    D. H. Rischke, M. I. Gorenstein, H. St¨ ocker, and W. Greiner, “Excluded volume effect for the nuclear matter equation of state,” Z. Phys. C 51, 485-489 (1991)

    1991

  37. [45]

    Particle Number Fluctuations for the Van der Waals Equation of State,

    V. Vovchenko, D. V. Anchishkin, and M. I. Gorenstein, “Particle Number Fluctuations for the Van der Waals Equation of State,” J. Phys. A 48 (2015), 305001

    2015

  38. [46]

    S. A. Mir, I. M. U. Din, N. A. Rather, S. Uddin arXiv:2406.11752[hep-ph] (2024)

    2024 arXiv

  39. [47]

    Centrality Dependence of Chemical Freeze- Out Parameters and Strangeness Equilibration in RHIC and LHC Energies,

    D. Biswas, “Centrality Dependence of Chemical Freeze- Out Parameters and Strangeness Equilibration in RHIC and LHC Energies,” doi:10.1155/2021/6611394

    2021 doi

  40. [48]

    Hagiwara, et al

    K. Hagiwara, et al. Phys. Rev. D 66 (2002), 01000

    2002

  41. [49]

    Statistical Model Predic- tions for Particle Ratios at √ sN N = 5 . 5 TeV,

    J. Cleymans, et al. “Statistical Model Predic- tions for Particle Ratios at √ sN N = 5 . 5 TeV,” Phys. Rev. C 74 (2006), 034903

    2006

  42. [50]

    Strangeness in Relativistic Heavy Ion Collisions,

    P. Koch, B. M¨ uller, and J. Rafelski, “Strangeness in Relativistic Heavy Ion Collisions,” doi:10.1016/0370-1573(86)90096-7

    doi

  43. [51]

    Comparison of Chemical Freeze-Out Criteria in Heavy- Ion Collisions,

    J. Cleymans, H. Oeschler, K. Redlich, and S. Wheaton, “Comparison of Chemical Freeze-Out Criteria in Heavy- Ion Collisions,” Phys. Rev. C 73 (2006), 034905

    2006

  44. [52]

    Particle multi- plicities and ratios in excluded volume models,

    M. Mishra and C. P. Singh, “Particle multi- plicities and ratios in excluded volume models,” doi:10.1103/PhysRevC.78.024910

    doi

  45. [53]

    Hadron Production and Phase Changes in Relativistic Heavy-Ion Collisions,

    J. Letessier and J. Rafelski, “Hadron Production and Phase Changes in Relativistic Heavy-Ion Collisions,” doi:10.1140/epja/i2007-10546-7

    doi

  46. [54]

    Identified Particle Produc- tion, Azimuthal Anisotropy, and Interferometry Mea- surements in Au+Au Collisions at √ sN N = 9 . 2 GeV,

    B. I. Abelev, et al. , “Identified Particle Produc- tion, Azimuthal Anisotropy, and Interferometry Mea- surements in Au+Au Collisions at √ sN N = 9 . 2 GeV,” Phys. Rev. C 81 (2010), 024911

    2010

  47. [55]

    Simple solution to the Strangeness Horn description puzzle,

    K. A. Bugaev et al. , “Simple solution to the Strangeness Horn description puzzle,” Eur. Phys. J. A 49 (2013), 30

    2013

  48. [56]

    Thermal description of par- ticle production in Au-Au collisions at STAR energies,

    A. Tawfik and E. Abbas, “Thermal description of par- ticle production in Au-Au collisions at STAR energies,” doi:10.1134/S154747711504024X

    doi

  49. [57]

    Net Pro- ton Flow and Nuclear Transparency Effects at RHIC: A Multiple Fireball Model approach,

    S. Uddin, M. Ali, J. Shabir, and M. F. Mir, “Net Pro- ton Flow and Nuclear Transparency Effects at RHIC: A Multiple Fireball Model approach,” arXiv:0901.1376, DOI: 10.48550/arXiv.0901.1376

    doi arXiv

  50. [58]

    Collision Energy Dependence of Particle Ratios and Freeze-out Parameters in Ultra Relativistic Nucleus Nucleus Collisions,

    I. M. U. Din, S. A. Mir, N. A. Rather, S. Uddin, R. A. Parra, “Collision Energy Dependence of Particle Ratios and Freeze-out Parameters in Ultra Relativistic Nucleus Nucleus Collisions,” arXiv:2408.07943 [hep-ph] (2024)

    2024 arXiv

  51. [59]

    Energy Dependence of Anti- Kaon-to-Kaon Ratio in High-Energy Collisions–A Simu- lated Study,

    S. Bhattacharyya, et al. “Energy Dependence of Anti- Kaon-to-Kaon Ratio in High-Energy Collisions–A Simu- lated Study,” Acta Phys. Pol. B 47, 2347 (2016)

    2016

  52. [60]

    Strangeness Production in the QGP,

    J. Rafelski and B. M¨ uller, “Strangeness Production in the QGP,” Phys. Rev. Lett. 48 (1982), 1066

    1982

  53. [61]

    Abbas et al

    E. Abbas et al. [The ALICE Collaboration], Eur. Phys. J. C 73, 2496 (2013)

    2013

  54. [62]

    Thermal hadron pro- duction in high energy heavy ion collisions,

    J. Cleymans and H. Satz, “Thermal hadron pro- duction in high energy heavy ion collisions,” doi:10.1007/BF01555746

    doi

  55. [63]

    Particle Transverse Momentum Distri- butions in p-p Collisions at √ sN N= 0.9 TeV,

    I. u. Bashir, R. A. Parra, R. A. Bhat and S. Uddin, “Particle Transverse Momentum Distri- butions in p-p Collisions at √ sN N= 0.9 TeV,” Adv. High Energy Phys. 2019 (2019), 8219567

    2019

  56. [64]

    Adamczyk et al

    L. Adamczyk et al. [STAR Collaboration], Phys. Rev. C 96, 044904 (2017)

    2017

  57. [65]

    Rossi, et al

    A. Rossi, et al. doi:10.1016/0550-3213(75)90307-7

    doi

  58. [66]

    M. M. Aggarwal et al. [STAR Collaboration], Phys. Rev. C 83, 024901 (2011)

    2011

  59. [67]

    Adams et al

    J. Adams et al. (STAR Collaboration), doi:10.1103/PhysRevLett.91.072304

    doi

  60. [68]

    Identified particle production and freeze-out properties in heavy-ion collisions at RHIC Beam Energy Scan program,

    S. Das, “Identified particle production and freeze-out properties in heavy-ion collisions at RHIC Beam Energy Scan program,” Proceedings of the 2014 Conference

    2014

  61. [69]

    Ahle et al

    L. Ahle et al. [E802 Collaboration], Phys. Rev. C 60, 064901 (1999) . 10

    1999

  62. [70]

    B. I. Abelev et al. [STAR Collaboration], Phys. Rev. C 81, 024911 (2010)

    2010

  63. [71]

    Adam et al

    J. Adam et al. [STAR Collaboration], Phys. Rev. C 102, 034909 (2020)

    2020

  64. [72]

    Mischke et al

    A. Mischke et al. [NA49 Collaboration], doi:10.1088/0954-3899/28/7/330

    doi

  65. [73]

    Abelev et al

    B. Abelev et al. [ALICE Collaboration], Phys. Rev. C 88, 044910 (2013)

    2013

  66. [74]

    Limiting fragmenta- tion of chemical potentials in heavy ion collisions,

    L. A. Stiles and M. Murray, “Limiting fragmenta- tion of chemical potentials in heavy ion collisions,” arXiv:nucl-ex/0601039

    arXiv

  67. [75]

    in their work based on in-medium mass effect have also found a freeze-out temperature of ∼ 136 MeV at RHIC energy √sN N= 130 GeV which is somewhat close to our model calculation value of ∼ 142 MeV. IV. SUMMAR Y A number of URNNC experiments have been carried out at different ene...

  68. [76]

    Ra- pidity Dependence of Charged Antihadron to Hadron Ratios in Au+Au Collisions at √ sN N = 200 GeV,

    I. G. Bearden et al. [BRAHMS Collaboration], “Ra- pidity Dependence of Charged Antihadron to Hadron Ratios in Au+Au Collisions at √ sN N = 200 GeV,” Phys. Rev. Lett. 90, 102301 (2003)

    2003

  69. [77]

    Baryon-antibaryon produc- tion asymmetry in relativistic heavy ion collisions,

    J. Song and F. L. Shao, “Baryon-antibaryon produc- tion asymmetry in relativistic heavy ion collisions,” Phys. Rev. C 88, 027901 (2013)

    2013

  70. [78]

    Strange baryons in a hot and dense medium within the Nambu–Jona–Lasinio model,

    F. Gastineau and J. Aichelin, “Strange baryons in a hot and dense medium within the Nambu–Jona–Lasinio model,” J. Phys. G: Nucl. Part. Phys. 28, 2017 (2002)

    2002

  71. [79]

    Scaling of hadron masses and widths in thermal models for ultrarelativistic heavy-ion colli- sions,

    M. Michalec, et. al “Scaling of hadron masses and widths in thermal models for ultrarelativistic heavy-ion colli- sions,” Phys. Lett. B 520, 213-216 (2001)

    2001

  72. [80]

    Chemical Freezeout Condi- tions and Fluctuations of Conserved Charges in Heavy- Ion Collisions within the Van der Waals Model,

    R. Poberezhnyuk et al. , “Chemical Freezeout Condi- tions and Fluctuations of Conserved Charges in Heavy- Ion Collisions within the Van der Waals Model,” Phys. Rev. C 100 (2019), 054904

    2019

  73. [81]

    Particle Ratios at RHIC: Effective Hadron Masses and Chemical Freezeout,

    D. Zschiesche et al. , “Particle Ratios at RHIC: Effective Hadron Masses and Chemical Freezeout,” Nucl. Phys. A 715 (2003), 211-214

    2003

  74. [82]

    Hadron Production in a Thermal Model with Scaled Masses,

    L. R. Hirsch et al. , “Hadron Production in a Thermal Model with Scaled Masses,” Nucl. Phys. B 153 (2010), 150-154

    2010

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