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arxiv: 2606.26326 · v1 · pith:MRROHMEWnew · submitted 2026-06-24 · ⚛️ nucl-th · hep-ph

Studying the QCD Matter produced in Heavy-Ion Collisions using the MUSES Calculation Engine

Johannes Jahan , Kevin P. Pala , Yumu Yang , Isabella Danhoni , Prachi Garella , Jonathan Gonzales , Joaquin Grefa , Mauricio Hippert
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Surkhab Kaur Virk Micheal Kahangirwe Musa R. Khan Feyisola Nana Mateus Reinke Pelicer Tulio E. Restrepo Hitansh Shah T. Andrew Manning Mark Alford Dekrayat Almaalol Ahmed Abuali Alexander Clevinger Nikolas Cruz-Camacho Carlos Conde-Ocazionez Francesco Di Clemente David Friedenberg Hosein Gholami Marco Hofmann Jeremy W. Holt Isaac Legred Jamie M. Karthein Toru Kojo Konstantin Maslov Paolo Parotto Leonardo Pena Gr\'egoire Pihan Christopher Plumberg Roman Poberezhniuk Romulo Rougemont Jordi Salinas San Mart\'in Rajesh Kumar Volodymyr Vovchenko Veronica Dexheimer Jorge Noronha Jacquelyn Noronha-Hostler Claudia Ratti Nicol\'as Yunes (MUSES Collaboration)
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Pith reviewed 2026-06-26 00:45 UTC · model grok-4.3

classification ⚛️ nucl-th hep-ph
keywords QCD equation of stateheavy-ion collisionscritical pointhydrodynamic simulationviscous hydrodynamicsphase diagramtransport coefficientsbaryon chemical potential
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The pith

MUSES Calculation Engine performs relativistic viscous hydrodynamic simulations of heavy-ion collisions with equations of state featuring a movable critical point.

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

The paper explores the capabilities of the MUSES Calculation Engine Calliope for computing equations of state and related properties relevant to heavy-ion collisions. It shows workflows that merge multiple equations of state in a thermodynamically consistent way and invert them to produce inputs for hydrodynamic codes. The framework is applied to run simulations at collision energies of 7.7, 19.6, and 39 GeV that incorporate an extended temperature and baryon chemical potential range, a movable critical point, and transport coefficients encoding phenomenological critical scaling. A sympathetic reader would care because these capabilities allow modeling of QCD matter across a wider portion of the phase diagram where a critical point may influence collision observables.

Core claim

The MUSES Calculation Engine Calliope supplies modules for equations of state from lattice QCD or phenomenological models with or without a critical point, spanning two to four dimensions in temperature and chemical potentials, plus modules for thermodynamic quantities such as pressure Hessian elements and transport coefficients. It supports workflows that merge equations of state consistently and feed results into an equation of state inverter for hydrodynamic use. This framework is applied to relativistic viscous hydrodynamic simulations at √s_NN = 7.7, 19.6, and 39 GeV using equations of state with extended T and μ_B coverage, a movable critical point, and transport coefficients that phen

What carries the argument

The MUSES Calculation Engine Calliope, which integrates equations of state modules, thermodynamic calculators, and an equation of state inverter to prepare inputs for hydrodynamic simulations.

If this is right

  • Hydrodynamic simulations become possible with equations of state that include a movable critical point at multiple collision energies.
  • Transport coefficients can include phenomenological encoding of critical scaling near the critical point.
  • Different equations of state can be merged to extend coverage in temperature and baryon chemical potential while maintaining thermodynamic consistency.
  • Inverted equations of state produce direct inputs ready for use in relativistic viscous hydrodynamic codes.

Where Pith is reading between the lines

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

  • This setup could allow direct tests of how shifting the critical point location alters predicted observables such as elliptic flow at the listed energies.
  • Inclusion of strangeness and electric charge chemical potentials in four-dimensional equations of state may reduce uncertainties when comparing to real collision data that involve net strangeness and charge.
  • The same merging and inversion workflow could be reused to incorporate future lattice QCD results with improved critical point constraints.

Load-bearing premise

The phenomenological transport coefficients accurately capture critical scaling behavior near the movable critical point without introducing uncontrolled artifacts.

What would settle it

A systematic mismatch between the simulated flow harmonics or particle yields at √s_NN = 7.7 GeV and experimental data that persists after varying the critical point location would indicate the setup does not correctly capture the relevant physics.

Figures

Figures reproduced from arXiv: 2606.26326 by Ahmed Abuali, Alexander Clevinger, Carlos Conde-Ocazionez, Christopher Plumberg, Claudia Ratti, David Friedenberg, Dekrayat Almaalol, Feyisola Nana, Francesco Di Clemente, Gr\'egoire Pihan, Hitansh Shah, Hosein Gholami, Isaac Legred, Isabella Danhoni, Jacquelyn Noronha-Hostler, Jamie M. Karthein, Jeremy W. Holt, Joaquin Grefa, Johannes Jahan, Jonathan Gonzales, Jordi Salinas San Mart\'in, Jorge Noronha, Kevin P. Pala, Konstantin Maslov, Leonardo Pena, Marco Hofmann, Mark Alford, Mateus Reinke Pelicer, Mauricio Hippert, Micheal Kahangirwe, Musa R. Khan, Nicol\'as Yunes (MUSES Collaboration), Nikolas Cruz-Camacho, Paolo Parotto, Prachi Garella, Rajesh Kumar, Roman Poberezhniuk, Romulo Rougemont, Surkhab Kaur Virk, T. Andrew Manning, Toru Kojo, Tulio E. Restrepo, Veronica Dexheimer, Volodymyr Vovchenko, Yumu Yang.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematics of the regions of validity for heavy-ion and some new EoS modules of MUSES [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Contours of the onset of instability or [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Normalized thermodynamic quantities: pressure, entropy, energy, baryon, electric charge, and strangeness [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Mapping of the critical point at ( [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Left: Normalized baryon density [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows the normalized partial pressure P101/T4 as a function of T. The red curve is the HRG model result, while the dots are lattice QCD results ob￾50 100 150 200 0 0.01 0.02 0.03 0.04 0.05 T [MeV] P101/T 4 HRG Lattice QCD FIG. 6: Normalized partial pressure P101/T4 as a function of the temperature at µX = 0. Results obtained through the ideal HRG model (red line) are compared to the ones from lattice QCD (… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Einstein–Maxwell–Dilaton holographic transport coefficients as functions of [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Workflow example that creates two EoSs which [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Pressure as a function of temperature for the merged EoS (continuous lines), QvdW-HRG (dashed lines), [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Pressure normalized by [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Illustration of the highly non-linear mapping between a fixed grid log [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Boundary of the range of validity (shaded in [PITH_FULL_IMAGE:figures/full_fig_p028_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Phase diagram (in the natural hydrodynamic [PITH_FULL_IMAGE:figures/full_fig_p029_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Points in entropy density and net-baryon [PITH_FULL_IMAGE:figures/full_fig_p030_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Simulation chain used in this work. The standard stages of heavy-ion collisions are shown, together with [PITH_FULL_IMAGE:figures/full_fig_p031_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Cartoon of dynamical SPH trajectories [PITH_FULL_IMAGE:figures/full_fig_p033_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: For a single central Au+Au event at [PITH_FULL_IMAGE:figures/full_fig_p034_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: For a fixed, single initial condition at [PITH_FULL_IMAGE:figures/full_fig_p035_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: For a fixed, single initial condition at each [PITH_FULL_IMAGE:figures/full_fig_p037_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20: Isentropic trajectories computed using the [PITH_FULL_IMAGE:figures/full_fig_p038_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: For a fixed, single initial condition at [PITH_FULL_IMAGE:figures/full_fig_p039_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: Probability distribution function (PDF) of [PITH_FULL_IMAGE:figures/full_fig_p040_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23: Spatial rapidity distribution of fluid cells that [PITH_FULL_IMAGE:figures/full_fig_p040_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24: Spatial rapidity distribution of fluid cells that [PITH_FULL_IMAGE:figures/full_fig_p041_24.png] view at source ↗
Figure 26
Figure 26. Figure 26: FIG. 26: Spatial rapidity distribution of fluid cells that are “near the critical point” (defined inside the ellipse with [PITH_FULL_IMAGE:figures/full_fig_p042_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: FIG. 27: Percentage of fluid cells that enter the [PITH_FULL_IMAGE:figures/full_fig_p043_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: FIG. 28: Collision energy dependence of the [PITH_FULL_IMAGE:figures/full_fig_p043_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: FIG. 29: Results for the [PITH_FULL_IMAGE:figures/full_fig_p044_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: FIG. 30: Display of the regions probed in the QCD phase diagram for a single Au+Au collision event at [PITH_FULL_IMAGE:figures/full_fig_p045_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: FIG. 31: Percentage of error due to backup EoS [PITH_FULL_IMAGE:figures/full_fig_p046_31.png] view at source ↗
read the original abstract

The equation of state of hot and dense matter is essential for describing heavy-ion collisions at all collision energies. Here, we explore the capabilities of the latest version of the MUSES Calculation Engine, $\textit{Calliope}$, focusing on software modules and workflows that compute the equation of state and observable properties of the matter produced in heavy-ion collisions. These include several equations of state, ranging from first-principles lattice QCD to phenomenological approaches, with or without a critical point, and with phase-space dimensionality ranging from two dimensions defined by temperature $T$ and baryon chemical potential $\mu_B$, to four dimensions after the addition of strangeness and electric-charge chemical potentials $\mu_S$ and $\mu_Q$. We also discuss modules that provide additional thermodynamic quantities and observables relevant for heavy-ion modeling, including elements of the pressure Hessian matrix and transport coefficients. Workflow examples are constructed that merge two equations of state thermodynamically consistently to extend phase-diagram coverage, and feed the results into an equation of state inverter to produce inputs suitable for hydrodynamic simulations. Finally, we apply this framework to perform a relativistic viscous hydrodynamic simulation with equations of state with an extended $T$ and $\mu_B$ coverage and a movable critical point, including effects from transport coefficients that phenomenologically encode critical scaling, at collision energies $\sqrt{s_{NN}}=7.7, 19.6$, and $39$ GeV.

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

0 major / 3 minor

Summary. The manuscript presents the MUSES Calculation Engine (Calliope) and its software modules for generating equations of state (EOS) spanning lattice QCD results to phenomenological models with or without a critical point, in 2D (T, μ_B) to 4D (including μ_S, μ_Q) phase space. It describes workflows for thermodynamically consistent merging of EOS, computation of additional thermodynamic quantities including pressure Hessian elements and transport coefficients, EOS inversion for hydrodynamic use, and an application performing relativistic viscous hydrodynamic simulations at √s_NN = 7.7, 19.6, and 39 GeV that incorporate a movable critical point and transport coefficients encoding critical scaling.

Significance. If the described workflows function as outlined, the engine offers a practical integrated platform for heavy-ion collision modeling by combining first-principles and phenomenological inputs with consistent merging and hydro-ready outputs. The explicit support for movable critical points and phenomenological critical scaling in transport coefficients, together with the demonstrated merging and inversion steps, strengthens its utility for RHIC beam-energy-scan studies.

minor comments (3)
  1. [Abstract] Abstract: the phrase 'transport coefficients that phenomenologically encode critical scaling' is used without a reference to the explicit functional form or module name; adding a brief pointer to the relevant section or equation would improve traceability for readers.
  2. [Abstract] Abstract: the collision energies are given as √s_NN=7.7, 19.6, and 39 GeV; the manuscript should adopt a uniform notation (e.g., √s_{NN}) throughout and define the symbol on first use.
  3. The description of the hydrodynamic application states that the EOS have 'extended T and μ_B coverage' after merging, but does not quantify the extension (e.g., the new range in T or μ_B); a short statement or table entry would make the improvement concrete.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our work on the MUSES Calculation Engine (Calliope) and for recommending minor revision. No specific major comments were listed in the report, so we have no points to address point-by-point at this stage. We remain available to incorporate any additional feedback or clarifications that may arise.

Circularity Check

0 steps flagged

No significant circularity; software demonstration using external inputs

full rationale

The manuscript presents the MUSES Calliope engine as a modular workflow tool that ingests pre-existing lattice QCD and phenomenological EOS tables (with or without critical points), merges them thermodynamically, inverts for hydro variables, and feeds results into standard relativistic viscous hydro codes at fixed beam energies. No load-bearing derivation reduces a claimed prediction to a fitted parameter or self-citation by the paper's own equations. The transport-coefficient module is described as 'phenomenologically encode critical scaling' without asserting that the encoding is accurate or artifact-free; the central claim is simply that the framework can incorporate such modules. All cited EOS and hydro methods are external to the present work and are not redefined inside it. This is the expected 0-2 outcome for an engineering/software paper whose value lies in integration rather than novel first-principles reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard thermodynamic relations and hydrodynamics assumptions plus the choice of phenomenological critical scaling; no new physical entities are introduced.

free parameters (1)
  • critical point location parameters
    The critical point position in the T-μ_B plane is described as movable and is therefore a chosen parameter in the phenomenological EoS modules.
axioms (2)
  • domain assumption Thermodynamic consistency can be maintained when merging lattice QCD and phenomenological EoS
    The workflow examples assume matching at boundaries does not introduce discontinuities or thermodynamic violations.
  • domain assumption Relativistic viscous hydrodynamics remains applicable at the cited collision energies
    The simulation application presupposes hydrodynamics validity down to 7.7 GeV.

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