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arxiv: 2606.03294 · v1 · pith:IO4ESHV3new · submitted 2026-06-02 · ⚛️ nucl-th · hep-ph· nucl-ex

Non-monotonicity of p_T correlations from meson-baryon mixing

Tom Reichert , Jan Steinheimer , Marcus Bleicher This is my paper

Pith reviewed 2026-06-28 08:13 UTC · model grok-4.3

classification ⚛️ nucl-th hep-phnucl-ex
keywords heavy-ion collisionspT correlationsmeson-baryon mixingbeam energy scanQCD critical pointSTAR experiment
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0 comments X

The pith

The non-monotonic p_T correlations in heavy-ion collisions arise from the shift between baryon and meson dominance.

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

STAR data show a minimum in the normalized charged-hadron p_T correlation at roughly 7.7 GeV beam energy. The paper uses a simplified model to demonstrate that this minimum appears when the system changes from baryon-dominated at low energy to meson-dominated at higher energy. The model produces the observed dip and the flat regions on either side solely through the different momentum distributions of the two particle classes. A reader would conclude that the non-monotonicity does not require a QCD critical point and therefore does not serve as a reliable search observable.

Core claim

A simplified model based on the transition from a baryon dominated system to a meson dominated system reproduces the non-monotonic beam-energy dependence of the p_T correlation measure without any critical-point contribution.

What carries the argument

Simplified model that generates momentum correlations from the changing meson-baryon composition across beam energies.

If this is right

  • The minimum near 7.7 GeV marks the beam energy at which meson yields overtake baryon yields.
  • Flat behavior below and above this energy follows from single-species dominance.
  • The observable must be corrected for composition effects before any critical-point interpretation.
  • Non-monotonic signals in other correlation measures require similar composition accounting.

Where Pith is reading between the lines

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

  • Full dynamical simulations without critical points should be checked to confirm the minimum survives added realism.
  • Other fluctuation observables in the beam-energy scan may need analogous corrections for particle-type changes.
  • Observables with weaker dependence on meson versus baryon ratios could be more useful for critical-point searches.

Load-bearing premise

The simplified model captures the essential momentum correlations arising purely from the changing meson-baryon composition across beam energies without requiring critical-point contributions.

What would settle it

A calculation that holds the meson-baryon ratio fixed while varying other parameters and still produces the minimum at 7.7 GeV would falsify the explanation.

Figures

Figures reproduced from arXiv: 2606.03294 by Jan Steinheimer, Marcus Bleicher, Tom Reichert.

Figure 1
Figure 1. Figure 1: The scaled correlator D ∆pT,i , ∆pT, j E / [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Energy dependence of the two components of the scaled correlator [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

The STAR experiment has recently reported data on the $\sqrt{\langle\Delta p_{T,i}\Delta p_{T,j}\rangle}/\langle\langle p_T\rangle\rangle$ charged hadron correlation in Au+Au reactions from $\sqrt{s_{NN}}=3-200$ GeV. The beam energy dependence of this quantity is non-monotonic, showing a pronounced minimum at $\sqrt{s_{NN}} \approx 7.7$ GeV, while being essentially flat at lower and higher energies. It has been proposed that such a non-monotonicity would be consistent with increased momentum correlations due to a critical point of QCD. In the present work it is shown, using a simplified model, that the observed structure can be consistently explained by the transition from a baryon dominated system to a meson dominated system and is therefore not a good observable for the critical point of QCD.

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

1 major / 0 minor

Summary. The manuscript claims that the non-monotonic beam-energy dependence of the normalized p_T correlation (with a minimum near 7.7 GeV) reported by STAR in Au+Au collisions can be reproduced by a simplified model in which the correlation arises solely from the changing relative yields and mean p_T values as the system transitions from baryon-dominated to meson-dominated, implying that the structure does not require a QCD critical-point contribution.

Significance. If the simplified model is shown to reproduce the minimum quantitatively from composition change alone, the result would indicate that this observable is not a robust probe of the critical point and would underscore the need to account for meson-baryon mixing in correlation analyses across the RHIC beam-energy scan.

major comments (1)
  1. The abstract states that a simplified model reproduces the structure but supplies no equations, parameter values, or quantitative comparison; without these details it is impossible to assess whether the minimum at 7.7 GeV emerges independently from the composition change or requires adjustment of inputs.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive comment. We address the major comment below.

read point-by-point responses

  1. Referee: The abstract states that a simplified model reproduces the structure but supplies no equations, parameter values, or quantitative comparison; without these details it is impossible to assess whether the minimum at 7.7 GeV emerges independently from the composition change or requires adjustment of inputs.

    Authors: We agree that the abstract is a concise summary and does not contain the explicit equations, parameter values, or direct quantitative comparison. The full manuscript derives the normalized p_T correlation from meson-baryon mixing in Section II (with the explicit weighted-average expression based on measured yields and mean p_T values at each beam energy), lists the input data sources and parameters in Section III, and shows the quantitative reproduction of the minimum at 7.7 GeV in Figure 2 without any additional fitting. The non-monotonicity arises directly from the changing particle composition. To improve accessibility, we will revise the abstract to briefly reference the model ingredients and point to the quantitative results. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs a simplified model whose purpose is to demonstrate consistency: the non-monotonic beam-energy dependence of the normalized pT correlation follows directly from the measured or parametrized change in relative meson versus baryon yields and their mean pT values. This is presented as an alternative explanation that does not require critical-point physics, not as an independent first-principles prediction. No equation or step reduces the target observable to a fitted parameter or self-citation by construction; the model inputs are the composition fractions themselves. The central claim therefore remains independent of the result it reproduces. No self-citation load-bearing, ansatz smuggling, or renaming of known results is evident from the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the assumption that the simplified model faithfully represents the momentum correlations induced by the baryon-to-meson transition; no free parameters, axioms, or invented entities are specified in the abstract.

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discussion (0)

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Reference graph

Works this paper leans on

27 extracted references · 12 canonical work pages · 7 internal anchors

  1. [1]

    Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III

    S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, C. Ratti, K. K. Szabo, Is there still anyT c mystery in lattice QCD? Results with physical masses in the contin- uum limit III, JHEP 09 (2010) 073.arXiv:1005.3508, doi:10.1007/JHEP09(2010)073

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep09(2010)073 2010

  2. [2]

    The chiral and deconfinement aspects of the QCD transition

    A. Bazavov, et al., The chiral and deconfinement as- pects of the QCD transition, Phys. Rev. D 85 (2012) 054503.arXiv:1111.1710,doi:10.1103/PhysRevD. 85.054503

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd 2012

  3. [3]

    Bazavov, et al., The QCD Equation of State toO(µ 6 B) from Lattice QCD, Phys

    A. Bazavov, et al., The QCD Equation of State toO(µ 6 B) from Lattice QCD, Phys. Rev. D 95 (5) (2017) 054504.arXiv:1701.04325,doi:10.1103/ PhysRevD.95.054504

    Pith/arXiv arXiv 2017

  4. [4]

    Borsanyi, Z

    S. Borsanyi, Z. Fodor, J. N. Guenther, R. Kara, S. D. Katz, P. Parotto, A. Pasztor, C. Ratti, K. K. Szabo, QCD Crossover at Finite Chemical Potential from Lattice Simulations, Phys. Rev. Lett. 125 (5) (2020) 052001.arXiv:2002.02821,doi:10.1103/ PhysRevLett.125.052001

    arXiv 2020

  5. [6]

    Cluster Expansion Model for QCD Baryon Number Fluctuations: No Phase Transition at $\mu_B / T < \pi$

    V . V ovchenko, J. Steinheimer, O. Philipsen, H. Stoecker, Cluster Expansion Model for QCD Baryon Number Fluc- tuations: No Phase Transition atµ B/T< π, Phys. Rev. D 97 (11) (2018) 114030.arXiv:1711.01261,doi: 10.1103/PhysRevD.97.114030

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.97.114030 2018

  6. [7]

    C. S. Fischer, J. Luecker, C. A. Welzbacher, Phase struc- ture of three and four flavor QCD, Phys. Rev. D 90 (3) (2014) 034022.arXiv:1405.4762,doi:10.1103/ PhysRevD.90.034022

    Pith/arXiv arXiv 2014

  7. [8]

    W.-j. Fu, J. M. Pawlowski, F. Rennecke, QCD phase structure at finite temperature and density, Phys. Rev. D 101 (5) (2020) 054032.arXiv:1909.02991,doi: 10.1103/PhysRevD.101.054032

    work page doi:10.1103/physrevd.101.054032 2020

  8. [9]

    F. Gao, J. M. Pawlowski, QCD phase structure from functional methods, Phys. Rev. D 102 (3) (2020) 034027.arXiv:2002.07500,doi:10.1103/ PhysRevD.102.034027

    arXiv 2020

  9. [10]

    P. J. Gunkel, C. S. Fischer, Locating the critical end- point of QCD: Mesonic backcoupling effects, Phys. Rev. D 104 (5) (2021) 054022.arXiv:2106.08356,doi: 10.1103/PhysRevD.104.054022

    work page doi:10.1103/physrevd.104.054022 2021

  10. [11]

    M. A. Stephanov, K. Rajagopal, E. V . Shuryak, Signatures of the tricritical point in QCD, Phys. Rev. Lett. 81 (1998) 4816–4819.arXiv:hep-ph/9806219,doi:10.1103/ PhysRevLett.81.4816

    Pith/arXiv arXiv 1998

  11. [12]

    Hatta, M

    Y . Hatta, M. A. Stephanov, Proton number fluctuation as a signal of the QCD critical endpoint, Phys. Rev. Lett. 91 (2003) 102003, [Erratum: Phys.Rev.Lett. 91, 129901 (2003)].arXiv:hep-ph/0302002,doi:10. 1103/PhysRevLett.91.102003

    Pith/arXiv arXiv 2003

  12. [14]

    Nahrgang, C

    M. Nahrgang, C. Herold, S. Leupold, I. Mishustin, M. Bleicher, The impact of dissipation and noise on fluctuations in chiral fluid dynamics, J. Phys. G 40 (2013) 055108.arXiv:1105.1962,doi:10.1088/ 0954-3899/40/5/055108

    Pith/arXiv arXiv 2013

  13. [15]

    Herold, M

    C. Herold, M. Nahrgang, I. Mishustin, M. Bleicher, Chiral fluid dynamics with explicit propagation of the Polyakov loop, Phys. Rev. C 87 (1) (2013) 014907.arXiv:1301. 1214,doi:10.1103/PhysRevC.87.014907

    work page doi:10.1103/physrevc.87.014907 2013

  14. [16]

    Adam, et al., Collision-energy dependence ofp t cor- relations in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider, Phys

    J. Adam, et al., Collision-energy dependence ofp t cor- relations in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C 99 (4) (2019) 044918.arXiv:1901.00837,doi:10. 1103/PhysRevC.99.044918

    Pith/arXiv arXiv 2019

  15. [17]

    Non-Monotonicity of Transverse Momentum Correla- tions in Au+Au Collisions at RHIC (4 2026).arXiv: 2604.06434

    Pith/arXiv arXiv 2026

  16. [19]

    Transverse momentum fluctuations due to temperature variation in high-energy nuclear collisions

    R. Korus, S. Mrowczynski, M. Rybczynski, Z. Wlodar- czyk, Transverse momentum fluctuations due to temper- ature variation in high-energy nuclear collisions, Phys. Rev. C 64 (2001) 054908.arXiv:nucl-th/0106041, doi:10.1103/PhysRevC.64.054908

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.64.054908 2001

  17. [20]

    Anticic, et al., Transverse momentum fluctuations in nuclear collisions at 158-A-GeV, Phys

    T. Anticic, et al., Transverse momentum fluctuations in nuclear collisions at 158-A-GeV, Phys. Rev. C 70 (2004) 034902.arXiv:hep-ex/0311009,doi:10. 1103/PhysRevC.70.034902

    Pith/arXiv arXiv 2004

  18. [21]

    B. B. Abelev, et al., Event-by-event meanp T fluctuations in pp and Pb-Pb collisions at the LHC, Eur. Phys. J. C 74 (10) (2014) 3077.arXiv:1407.5530,doi:10.1140/ epjc/s10052-014-3077-y

    Pith/arXiv arXiv 2014

  19. [22]

    Broniowski, B

    W. Broniowski, B. Hiller, W. Florkowski, P. Bo˙ zek, Event-by-event pt fluctuations and multiparticle clusters in relativistic heavy-ion collisions, Physics Letters B 635 (5) (2006) 290–294.doi:https: //doi.org/10.1016/j.physletb.2006.02.056. URLhttps://www.sciencedirect.com/science/ article/pii/S0370269306002541

    work page doi:10.1016/j.physletb.2006.02.056 2006

  20. [23]

    S. Jeon, V . Koch, Event by event fluctuations, 2004, pp. 430–490.arXiv:hep-ph/0304012,doi:10.1142/ 9789812795533_0007

    Pith/arXiv arXiv 2004

  21. [24]

    Boltzmann-Langevin Approach to Pre-equilibrium Correlations in Nuclear Collisions

    S. Gavin, G. Moschelli, C. Zin, Boltzmann-Langevin Ap- proach to Pre-equilibrium Correlations in Nuclear Col- lisions, Phys. Rev. C 95 (6) (2017) 064901.arXiv: 1612.07856,doi:10.1103/PhysRevC.95.064901

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.95.064901 2017

  22. [25]

    M. Cody, S. Gavin, B. Koch, M. Kocherovsky, Z. Ma- zloum, G. Moschelli, Complementary two-particle corre- lation observables for relativistic nuclear collisions, Phys. Rev. C 107 (1) (2023) 014909.arXiv:2110.04884, doi:10.1103/PhysRevC.107.014909

    work page doi:10.1103/physrevc.107.014909 2023

  23. [26]

    Zhang, J

    L. Zhang, J. Chen, C. Zhang, Energy dependence of transverse momentum fluctuations in Au+Au collisions from a multiphase transport model, Phys. Rev. C 111 (2) (2025) 024911.arXiv:2501.08209,doi:10.1103/ PhysRevC.111.024911

    arXiv 2025

  24. [28]

    Incident energy dependence of pt correlations at relativistic energies

    J. Adams, et al., Incident energy dependence of pt cor- relations at RHIC, Phys. Rev. C 72 (2005) 044902. arXiv:nucl-ex/0504031,doi:10.1103/PhysRevC. 72.044902

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc 2005

  25. [29]

    Event-by-event fluctuations of the mean transverse momentum in 40, 80, and 158 A GeV/c Pb-Au collisions

    D. Adamova, et al., Event by event fluctuations of the mean transverse momentum in 40, 80 and 158 A GeV/c Pb - Au collisions, Nucl. Phys. A 727 (2003) 97–119.arXiv:nucl-ex/0305002,doi:10.1016/j. nuclphysa.2003.07.018

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j 2003

  26. [30]

    Bozek, W

    P. Bozek, W. Broniowski, S. Chatterjee, Transverse Mo- mentum Fluctuations and Correlations, Acta Phys. Polon. Supp. 10 (2017) 1091.arXiv:1707.04420,doi:10. 5506/APhysPolBSupp.10.1091

    Pith/arXiv arXiv 2017

  27. [31]

    Schenke, C

    B. Schenke, C. Shen, D. Teaney, Transverse mo- mentum fluctuations and their correlation with ellip- tic flow in nuclear collision, Phys. Rev. C 102 (3) (2020) 034905.arXiv:2004.00690,doi:10.1103/ PhysRevC.102.034905. 8

    arXiv 2020