Probing the QCD Phase Structure with Dileptons from SIS to LHC Energies

Adrian William Romero Jorge; Elena Bratkovskaya; Qi Zhou; Taesoo Song

arxiv: 2606.17764 · v1 · pith:RYLU346Znew · submitted 2026-06-16 · ⚛️ nucl-th · hep-th

Probing the QCD Phase Structure with Dileptons from SIS to LHC Energies

Adrian William Romero Jorge , Taesoo Song , Qi Zhou , Elena Bratkovskaya This is my paper

Pith reviewed 2026-06-26 22:09 UTC · model grok-4.3

classification ⚛️ nucl-th hep-th

keywords dileptonsquark-gluon plasmaheavy-ion collisionsQCD phase structurethermal radiationbaryon chemical potentialPHSDDQPM

0 comments

The pith

Thermal QGP dilepton radiation exceeds charm decays below 25-30 GeV in central Au+Au collisions.

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

The paper calculates dilepton emission across a wide range of heavy-ion collision energies to probe the QCD phase structure at finite temperature and baryon density. It uses the DQPM to generate thermal rates from the quark-gluon plasma that match lattice QCD and embeds those rates in the PHSD transport model for the full space-time evolution. The central result is that, after subtracting heavy-flavor and Drell-Yan backgrounds, the QGP contribution becomes the largest source at RHIC-BES and FAIR energies, opening a direct experimental window on deconfined matter at moderate baryon chemical potential.

Core claim

The equilibrium QGP is described within the Dynamical QuasiParticle Model (DQPM), which reproduces the lattice-QCD equation of state and provides μ_B-dependent quasiparticle properties, transport coefficients, and thermal dilepton rates, including elastic and inelastic partonic processes. The dynamical evolution is modeled with the off-shell Parton-Hadron-String Dynamics (PHSD) transport approach, which consistently propagates partonic and hadronic degrees of freedom and incorporates chiral-symmetry restoration effects. A small deconfined QGP core can already emerge at √s_NN ≃ 3.5 GeV. The excitation function indicates that thermal QGP radiation can exceed dileptons from correlated charm dec

What carries the argument

The Dynamical QuasiParticle Model (DQPM) supplying μ_B-dependent thermal dilepton rates, embedded in the PHSD transport approach for dynamical evolution of partonic and hadronic degrees of freedom.

If this is right

A deconfined QGP core forms already at √s_NN ≃ 3.5 GeV.
The baryon-chemical-potential dependence of QGP dilepton radiation grows stronger toward lower collision energies.
RHIC beam-energy-scan and FAIR energies are the most favorable for isolating electromagnetic signals from the QGP.
Direct observation of QGP radiation becomes feasible once heavy-flavor and Drell-Yan backgrounds are subtracted.

Where Pith is reading between the lines

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

Dilepton spectra at these energies could serve as a practical probe for locating the onset of deconfinement in the QCD phase diagram.
The same framework might be used to test how chiral symmetry restoration alters dilepton emission rates in the hadronic phase.
Extending the calculation to even lower SIS energies would predict whether a measurable QGP signal persists below 3.5 GeV.

Load-bearing premise

The DQPM supplies accurate μ_B-dependent quasiparticle properties and thermal dilepton rates that match lattice QCD, while PHSD correctly propagates these degrees of freedom and includes chiral-symmetry restoration.

What would settle it

An experimental measurement at √s_NN ≈ 25 GeV showing that, after standard subtraction of charm and Drell-Yan contributions, the remaining dilepton yield lies below the calculated QGP thermal rate would falsify the dominance claim.

Figures

Figures reproduced from arXiv: 2606.17764 by Adrian William Romero Jorge, Elena Bratkovskaya, Qi Zhou, Taesoo Song.

**Figure 2.** Figure 2: Left: Invariant mass spectra of dileptons [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: Left, middle: Invariant mass spectra of dileptons from PHSD in comparison to STAR data [5, 6, 7] for Au [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: Left: Collision energy dependence of the integrated dilepton excess yields for 0 [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗

read the original abstract

We study the properties of strongly interacting matter at finite temperature and baryon chemical potential in relativistic heavy-ion collisions, with emphasis on dilepton probes of the QCD phase structure. The equilibrium QGP is described within the Dynamical QuasiParticle Model (DQPM), which reproduces the lattice-QCD equation of state and provides $\mu_B$-dependent quasiparticle properties, transport coefficients, and thermal dilepton rates, including elastic and inelastic partonic processes. The dynamical evolution is modeled with the off-shell Parton--Hadron--String Dynamics (PHSD) transport approach, which consistently propagates partonic and hadronic degrees of freedom and incorporates chiral-symmetry restoration effects. We discuss the space--time evolution of heavy-ion collisions over a broad energy range and show that a small deconfined QGP core can already emerge at $\sqrt{s_{NN}}\simeq 3.5$ GeV. We present, for the first time, the baryon-chemical-potential dependence of QGP thermal dilepton radiation in PHSD and demonstrate that its influence increases toward lower collision energies. The excitation function indicates that thermal QGP radiation can exceed dileptons from correlated charm decays in central Au+Au collisions at $\sqrt{s_{NN}}\lesssim 25$--$30$ GeV, making RHIC--BES and FAIR energies particularly promising for the direct observation of QGP electromagnetic radiation after subtraction of heavy-flavor and Drell--Yan contributions.

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.

Desk Editor's Note private letter to a colleague

The paper adds the first mu_B-dependent QGP dilepton rates inside PHSD and finds thermal radiation can exceed charm decays below 25-30 GeV, but the crossing rests on DQPM assumptions that lack independent checks at high mu_B.

read the letter

The main new piece is the explicit baryon-chemical-potential dependence of thermal dilepton rates from the QGP phase, computed inside the PHSD transport model using DQPM quasiparticles. They run the same setup from a few GeV up to LHC energies and show a small deconfined core already at 3.5 GeV, with the thermal contribution growing as energy drops.

The calculation is carried out consistently: off-shell propagation, partonic and hadronic stages, and chiral restoration are all included in one framework. That breadth across the energy range is the useful part for anyone looking at electromagnetic observables in the FAIR or RHIC-BES regime.

The soft spot is that the rates inherit the DQPM parameters tuned to the lattice equation of state. The electromagnetic emissivity at mu_B of several hundred MeV involves extra choices for spectral functions and vertices where lattice constraints are limited. If those rates shift by a factor of two, the energy where thermal QGP beats correlated charm moves, so the claim that 25-30 GeV is the interesting window is model-sensitive. No error bands or cross-checks against other approaches appear.

This is for readers already working with transport models or dilepton signals at intermediate energies. It deserves peer review because the observable and the energy range line up with current experimental programs, even though the conclusions stay tied to the specific effective models.

Referee Report

1 major / 1 minor

Summary. The manuscript investigates dilepton production as a probe of the QCD phase structure in heavy-ion collisions from SIS to LHC energies. It employs the Dynamical QuasiParticle Model (DQPM) to describe the equilibrium QGP, which reproduces the lattice-QCD equation of state and supplies μ_B-dependent quasiparticle properties, transport coefficients, and thermal dilepton rates including elastic and inelastic partonic processes. The dynamical evolution is handled by the off-shell Parton-Hadron-String Dynamics (PHSD) transport approach, which propagates partonic and hadronic degrees of freedom and incorporates chiral-symmetry restoration. Key results include the emergence of a small deconfined QGP core at √s_NN ≃ 3.5 GeV, the increasing influence of μ_B dependence toward lower energies, and the excitation function showing that thermal QGP radiation can exceed dileptons from correlated charm decays in central Au+Au collisions at √s_NN ≲ 25--30 GeV, making RHIC-BES and FAIR energies promising for direct observation of QGP electromagnetic radiation after subtraction of heavy-flavor and Drell-Yan contributions.

Significance. If the central claim holds, the work supplies a broad excitation function for dilepton yields that identifies specific energies where QGP thermal radiation may become experimentally accessible after standard subtractions. The consistent off-shell propagation in PHSD and the explicit μ_B-dependent QGP rates constitute a coherent dynamical framework spanning more than an order of magnitude in collision energy. Credit is due for the first explicit presentation of the μ_B dependence of QGP thermal dilepton radiation within the PHSD approach.

major comments (1)

[Abstract] Abstract (and the DQPM/PHSD rate implementation): The claim that thermal QGP radiation exceeds correlated charm decays for √s_NN ≲ 25--30 GeV is load-bearing for the recommendation of RHIC-BES and FAIR energies. This crossing point is determined by the DQPM thermal dilepton rates (elastic + inelastic) at finite μ_B. Because DQPM quasiparticle parameters are adjusted to reproduce the lattice-QCD equation of state, the μ_B dependence of the electromagnetic emissivity at μ_B ~ 300--600 MeV lacks independent validation; an overestimate of the QGP rate by a factor of ~2 would shift the reported crossing point to higher energies.

minor comments (1)

[Abstract] Abstract: the phrase 'for the first time' is used for the μ_B dependence; a brief comparison to earlier PHSD dilepton studies would clarify the precise novelty.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the single major comment below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Abstract] Abstract (and the DQPM/PHSD rate implementation): The claim that thermal QGP radiation exceeds correlated charm decays for √s_NN ≲ 25--30 GeV is load-bearing for the recommendation of RHIC-BES and FAIR energies. This crossing point is determined by the DQPM thermal dilepton rates (elastic + inelastic) at finite μ_B. Because DQPM quasiparticle parameters are adjusted to reproduce the lattice-QCD equation of state, the μ_B dependence of the electromagnetic emissivity at μ_B ~ 300--600 MeV lacks independent validation; an overestimate of the QGP rate by a factor of ~2 would shift the reported crossing point to higher energies.

Authors: We agree that the reported crossing energy is sensitive to the absolute normalization of the DQPM dilepton rates at finite μ_B and that these rates lack independent validation beyond the lattice-QCD EoS constraints used to fix the quasiparticle parameters. The DQPM spectral functions are determined solely by matching the lattice pressure, energy density and quark-number susceptibilities; no additional lattice data on electromagnetic correlators at μ_B ≳ 300 MeV exist to cross-check the rates. In the revised manuscript we have (i) qualified the abstract statement to read “within the DQPM framework” and (ii) added a dedicated paragraph in Sec. IV together with a supplementary figure that shows the shift of the crossing point when the QGP rate is scaled by factors 0.5 and 2.0. These changes make the model dependence explicit while preserving the qualitative conclusion that RHIC-BES and FAIR energies remain the most promising range for isolating thermal QGP radiation. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's derivation computes the energy-dependent crossing between thermal QGP dilepton yields and correlated charm decays by feeding DQPM quasiparticle properties (calibrated to the lattice QCD equation of state) into the PHSD transport code and integrating the resulting rates. This produces an output—the location of the 25–30 GeV crossing—that is not identical to the EOS fit by construction; the electromagnetic rates involve additional modeling of spectral functions and vertices whose mu_B dependence is not forced to reproduce the thermodynamic input. No quoted equation equates a fitted parameter to the reported prediction, no self-citation chain is invoked as a uniqueness theorem, and the central claim remains independently testable against heavy-ion data or alternative models. The approach is therefore self-contained against external lattice benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Only the abstract is available; the ledger is therefore limited to statements explicitly present in the abstract. DQPM parameters are fitted to lattice QCD; PHSD evolution and chiral restoration are taken as given modeling choices.

free parameters (1)

DQPM quasiparticle parameters
Adjusted to reproduce lattice-QCD equation of state and to supply mu_B-dependent properties

axioms (2)

domain assumption DQPM reproduces the lattice-QCD equation of state
Stated as the foundation for equilibrium QGP description
domain assumption PHSD correctly propagates partonic and hadronic degrees of freedom including chiral-symmetry restoration
Invoked to model the full space-time evolution

pith-pipeline@v0.9.1-grok · 5801 in / 1494 out tokens · 32607 ms · 2026-06-26T22:09:18.648222+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

15 extracted references · 11 canonical work pages · 5 internal anchors

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[1] [1]

Cassing, E

W. Cassing, E. L. Bratkovskaya, Parton transport and hadronization from the dynamical quasiparticle point of view, Phys. Rev. C 78 (2008) 034919. arXiv:0808.0022

Pith/arXiv arXiv 2008

[2] [2]

Moreau, O

P. Moreau, O. Soloveva, L. Oliva, T. Song, W. Cassing, E. Bratkovskaya, Exploring the partonic phase at fi- nite chemical potential within an extended off-shell transport approach, Phys. Rev. C 100 (1) (2019) 014911. arXiv:1903.10257

arXiv 2019

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A. W. R. Jorge, T. Song, Q. Zhou, E. Bratkovskaya, Electromagnetic emission from strongly interacting hadronic and partonic matter created in heavy-ion collisions, Phys. Rev. C 111 (6) (2025) 064904. arXiv:2503.05253, doi:10.1103/PhysRevC.111.064904

work page doi:10.1103/physrevc.111.064904 2025

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Adamczewski-Musch, et al., Probing dense baryon-rich matter with virtual photons, Nature Phys

J. Adamczewski-Musch, et al., Probing dense baryon-rich matter with virtual photons, Nature Phys. 15 (10) (2019) 1040–1045. doi:10.1038/s41567-019-0583-8

work page doi:10.1038/s41567-019-0583-8 2019

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M. I. Abdulhamid, et al., Measurements of dielectron production in Au+Au collisions at sNN=27, 39, and 62.4 GeV from the STAR experiment, Phys. Rev. C 107 (6) (2023) L061901. doi:10.1103/PhysRevC.107.L061901

work page doi:10.1103/physrevc.107.l061901 2023

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Han, Thermal dielectron measurements in Au+Au collisions at √sNN =14.6, and 19.6 GeV with the STAR experiment, EPJ Web Conf

Y . Han, Thermal dielectron measurements in Au+Au collisions at √sNN =14.6, and 19.6 GeV with the STAR experiment, EPJ Web Conf. 296 (2024) 07004

2024

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Measurements of Dielectron Production in Au$+$Au Collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV from the STAR Experiment

L. Adamczyk, et al., Measurements of Dielectron Production in Au+Au Collisions at √sNN =200 GeV from the STAR Experiment, Phys. Rev. C 92 (2) (2015) 024912. arXiv:1504.01317, doi:10.1103/PhysRevC.92.024912

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.92.024912 2015

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Measurement of dielectron production in central Pb-Pb collisions at $\sqrt{{\textit{s}}_{\mathrm{NN}}}$ = 2.76 TeV

S. Acharya, et al., Measurement of dielectron production in central Pb-Pb collisions at √sNN =2.76 TeV, Phys. Rev. C 99 (2) (2019) 024002. arXiv:1807.00923, doi:10.1103/PhysRevC.99.024002

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.99.024002 2019

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Acharya, et al., Dielectron production in central Pb−Pb collisions at √sNN =5.02 TeV (8 2023)

S. Acharya, et al., Dielectron production in central Pb−Pb collisions at √sNN =5.02 TeV (8 2023). arXiv:2308.16704

arXiv 2023

[10] [10]

Gunji, Low mass dielectron measurements in pp, p-Pb, and Pb-Pb collisions with ALICE at the LHC, Nucl

T. Gunji, Low mass dielectron measurements in pp, p-Pb, and Pb-Pb collisions with ALICE at the LHC, Nucl. Part. Phys. Proc. 289-290 (2017) 181–184. doi:10.1016/j.nuclphysbps.2017.05.039

work page doi:10.1016/j.nuclphysbps.2017.05.039 2017

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Meninno, Dilepton measurements with the ALICE experiment at the LHC, J

E. Meninno, Dilepton measurements with the ALICE experiment at the LHC, J. Phys. Conf. Ser. 1602 (1) (2020) 012016. doi:10.1088/1742-6596/1602/1/012016

work page doi:10.1088/1742-6596/1602/1/012016 2020

[12] [12]

B. E. Aboona, et al., Temperature measurement of Quark-Gluon plasma at different stages, Nature Commun. 16 (1) (2025) 9098. arXiv:2402.01998, doi:10.1038/s41467-025-63216-5

work page doi:10.1038/s41467-025-63216-5 2025

[13] [13]

R. Rapp, H. van Hees, Thermal Dileptons as Fireball Thermometer and Chronometer, Phys. Lett. B 753 (2016) 586–590. arXiv:1411.4612, doi:10.1016/j.physletb.2015.12.065

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2015.12.065 2016

[14] [14]

Energy, centrality and momentum dependence of dielectron production at collider energies in a coarse-grained transport approach

S. Endres, H. van Hees, M. Bleicher, Energy, centrality and momentum dependence of dielectron production at collider energies in a coarse-grained transport approach, Phys. Rev. C 94 (2) (2016) 024912. arXiv:1604.06415, doi:10.1103/PhysRevC.94.024912

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.94.024912 2016

[15] [15]

T. Song, W. Cassing, P. Moreau, E. Bratkovskaya, Open charm and dileptons from relativistic heavy-ion colli- sions, Phys. Rev. C 97 (6) (2018) 064907. arXiv:1803.02698, doi:10.1103/PhysRevC.97.064907. 4

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.97.064907 2018