Dynamics of Hot QCD Matter 2024 -- Bulk Properties

Amal Sarkar; Amaresh Jaiswal; Ankit Kumar Panda; Anuraag Rathore; Arpan Das; Arvind Khuntia; Ashutosh Dwibedi; Aswathy Menon K.R.; Binoy Krishna Patra; Cho Win Aung

REVIEW 3 major objections 5 minor 1 cited by

Dynamics of Hot QCD Matter 2024 -- Bulk Properties

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Hot QCD Matter 2024 proceedings reports the first nonzero quartic curvature of the QCD pseudo-critical line and a causal third-order viscous hydrodynamics derived from kinetic theory.

desk verdict A useful proceedings snapshot of heavy-ion bulk phenomenology, but its marquee 'first non-zero κ4' claim rests on an uncontrolled high-μB extrapolation and should be read as a model-dependent hint until systematics are shown. read the letter →

arxiv 2412.10779 v1 pith:CQAZ5YRV submitted 2024-12-14 nucl-th hep-exhep-phhep-th

Prabhakar Palni , Amal Sarkar , Santosh K. Das , Anuraag Rathore , Syed Shoaib , Arvind Khuntia , Amaresh Jaiswal , Victor Roy

show 39 more authors

Ankit Kumar Panda Partha Bagchi Hiranmaya Mishra Deeptak Biswas Peter Petreczky Sayantan Sharma Kshitish Kumar Pradhan Ronald Scaria Dushmanta Sahu Raghunath Sahoo Arpan Das Ranjita K Mohapatra Jajati K. Nayak Rupa Chatterjee Munshi G Mustafa Aswathy Menon K.R. Suraj Prasad Neelkamal Mallick Pushpa Panday Binoy Krishna Patra Paramita Deb Raghava Varma Ashutosh Dwibedi Thandar Zaw Win Subhalaxmi Nayak Cho Win Aung Sabyasachi Ghosh Sesha Vempati Sunny Kumar Singh Manu Kurian Vinod Chandra Soham Banerjee Sumit Rohit Kumar Rajkumar Mondal Nilanjan Chaudhuri Pradip Roy Sourav Sarkar Lokesh Kumar

This is my paper · ORCID

classification nucl-thhep-exhep-phhep-th PACS 12.38.-t12.38.Aw

keywords Heavy-ioncollisionsQuark-gluonplasmaBulkpropertiesChiralpseudo-criticallineThird-orderviscoushydrodynamicsHadronresonancegasConserved-chargefluctuationsSpinpolarization

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 proceedings volume assembles nineteen contributions on the bulk properties of quark-gluon plasma. Its two sharpest new claims are that a hadron resonance gas with mean-field repulsion yields a nonzero quartic curvature κ4 of the chiral pseudo-critical line, reported for the first time, and that a Chapman-Enskog derivation from the Boltzmann equation yields a linearly stable and causal third-order viscous hydrodynamics. The volume also presents supporting results on spin polarization, diffusion of conserved charges, electromagnetic-field evolution with baryon stopping, photon mean free paths, and the speed of sound in magnetized nuclear matter. A sympathetic reading is that these model-based results sharpen the finite-density QCD phase diagram and give new hydrodynamic tools for describing the quark-gluon plasma.

What carries the argument

The load-bearing devices are model constructions, not a single identity. For the κ4 claim, the machinery is the QMHRG pressure with mean-field repulsion K = 33 GeV⁻², the renormalized chiral condensate Δ_l^R computed as a mass derivative of the pressure, and the parametrization Tpc(µB)/Tpc(0) = 1 − κ2(µB/Tpc(0))² − κ4(µB/Tpc(0))⁴. For the hydrodynamics claim, the machinery is a Chapman-Enskog-like iterative solution of the Boltzmann equation in relaxation-time approximation, with the substitution ∇⟨μπνλ⟩ → $ρ^{{μνλ}}$ promoting an irreducible rank-3 tensor — symmetric, traceless, and orthogonal to the fluid velocity — to a dynamical variable whose evolution restores linear stability and causality.

What would settle it

A continuum-extrapolated lattice QCD calculation of κ4 with uncertainty below about 10⁻⁵ that is statistically consistent with zero would refute the Section 4 claim, and a full nonlinear numerical evolution of the proposed third-order equations exhibiting runaway modes would refute the Section 10 claim.

Watch

Extended reading notes

Core claim

The volume claims that a quark-model hadron resonance gas with a mean-field repulsive interaction among baryons, calibrated to lattice QCD baryon-number fluctuations, reproduces the temperature dependence of susceptibilities up to eighth order and yields a pseudo-critical line whose curvature coefficients are κ2 = 0.0150(2) and κ4 = 3.1(6) × 10⁻⁵ at zero strangeness chemical potential, with the nonzero κ4 reported for the first time. It further claims that relativistic third-order viscous hydrodynamics derived from the Boltzmann equation with relaxation-time approximation is linearly stable and causal only when a new dynamical degree of freedom, an irreducible rank-3 tensor, is promoted from the space-like gradients of the shear-stress tensor; the transport coefficient τρ = τπ = 5η/(ε+P) satisfies the resulting stability and causality constraints. Together with the other contributions, the volume asserts that these advances improve the theoretical description of bulk properties of hot QCD matter and sharpen predictions for heavy-ion collision observables.

Load-bearing premise

The load-bearing premise is that the model parameters — the mean-field repulsion K = 33 GeV⁻² and the van der Waals parameters a and b — calibrated to lattice QCD data at moderate baryon density remain valid when the models are extrapolated up to µB = 750 MeV and down to the lowest beam energies.

Editorial extensions

If this is right

A nonzero κ4 means the pseudo-critical line bends more strongly than a quadratic curve at baryon chemical potentials up to 750 MeV, shifting the location of freeze-out and critical-point searches.
A linearly stable and causal third-order viscous hydrodynamics provides a framework for simulating the quark-gluon plasma at large viscosities where second-order Israel-Stewart theory is known to fail.
The calibrated repulsive QMHRG, with strangeness neutrality imposed through an explicit µS computation, reproduces the lattice NNLO relation µS/µB and supports extending the model beyond µB ≈ 700 MeV with light nuclei and hypernuclei.
The baryon-stopping deceleration ansatz predicts longer-lived electromagnetic fields in low-energy collisions, which could enhance low-pT dilepton and photon production and modify directed flow.
Cross-diffusion coefficients among baryon number, electric charge, and strangeness are non-negligible, so at finite baryon density the diffusion current of one conserved charge is driven by gradients of the others.

Reading between the lines

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

If the nonzero κ4 claim is confirmed, the QCD crossover curve is genuinely quartic in µB, and previous quadratic fits would mis-locate Tpc by tens of MeV near µB ≈ 700 MeV; this arithmetic consequence is ours, not stated in the paper.
The MVDWHRG result that van der Waals parameters decrease exponentially with µB/T suggests that non-critical fluctuation baselines used in the critical-point search should be treated as energy-dependent rather than constant; this can be tested against BES-II data.
Promoting the rank-3 tensor to a dynamical variable in third-order hydrodynamics points to a new transport coefficient, ρ, that could be extracted from kinetic-theory correlation functions; this is an extension the paper does not pursue.
The finding that low-energy photons from the hottest phase have short mean free paths implies that only photons above roughly 200 MeV are clean early-stage probes, and dedicated measurements in that energy window would sharpen the claim.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know before you read it. First, it is a proceedings volume: 19 short contributions, most condensing the authors' own prior papers, with central equations and many figures lifted from companion papers. No code or data. Second, the marquee claim — the first non-zero κ4 for the pseudo-critical line — is more fragile than the abstract suggests. The repulsive mean-field strength K is fixed by comparing zero-density lattice susceptibilities and then applied up to μB = 750 MeV. The quoted uncertainty on κ4 does not include the spread in K, the hadron list, or the half-drop criterion. The authors themselves note that strange and non-strange baryons should have different K and that light nuclei become important around μB ~ 700 MeV. That is an uncontrolled extrapolation, and κ4, being a fourth-order curvature, amplifies any systematic misbehavior. So treat the 'first time' claim as a model-dependent hint, not an established result.

The volume does real work elsewhere. Section 10 derives a causal third-order viscous hydrodynamics from the Boltzmann equation with a single new dynamical degree of freedom, an irreducible rank-3 tensor; the linear stability and causality check is presented, though condensed. Section 6 computes the diffusion matrix for multiple conserved charges and finds non-negligible cross-diffusion coefficients, which matters for low-energy scans. The experimental summary (Section 19) is a competent, well-referenced overview of STAR and ALICE results. As a collective snapshot of the field, it is useful.

Soft spots, in proportion: several sections fit parameters to lattice or experimental data and then describe the model output as a prediction. Section 5's exponential fit to the van der Waals parameters is a parameterization extending beyond the fitted region. Section 11 compares baryon fluctuations to net-proton data, which is a proxy. These are worth flagging but not disqualifying for a proceedings.

Who is the reader? Someone wanting a quick map of current heavy-ion bulk phenomenology — spin hydrodynamics, EM fields, fluctuations, transport — will get a fair tour. The two strongest claims should be checked against the full papers (Refs. 27 and the companion to Section 10). I would recommend sending this to peer review rather than desk-rejecting: the claims are important enough to warrant referee scrutiny, and a serious referee can request the κ4 systematics be shown. If it were a standalone research paper, I would want those systematics before acceptance; for a proceedings volume, it deserves the referee time.

Referee Report

3 major / 5 minor

Summary. This proceedings volume collects 19 short contributions from the Hot QCD Matter 2024 conference, spanning event-shape classifiers in pp collisions, spin hydrodynamics and polarization, baryon stopping and electromagnetic fields, the chiral pseudo-critical line in a hadron resonance gas model, proton-number cumulants in a modified van der Waals HRG, multi-charge diffusion, photon mean free paths and initial-state photon probes, small-system flow in p–O and p–C collisions, third-order viscous hydrodynamics, finite-size PNJL fluctuations, Wiedemann–Franz law violation in QGP and graphene, non-resistive magnetohydrodynamics, longitudinal spin polarization, Gribov-resummed meson screening masses, AMPT studies of net-strangeness moments, the speed of sound in magnetized nuclear matter, NNLO HTL perturbation theory, and selected experimental highlights from STAR and ALICE. The most concrete new claims are the first reported nonzero value of κ4 for the chiral pseudo-critical line (Section 4) and the derivation of a linearly stable and causal third-order viscous hydrodynamics from kinetic theory (Section 10).

Significance. If the headline claims hold, the volume makes useful contributions: a nonzero κ4 sharpens the extrapolation of the QCD phase diagram to finite baryon density, and a causal third-order hydrodynamic framework would extend the theory toolkit for heavy-ion phenomenology. Several other contributions, notably the explicit diffusion-matrix calculation in Section 6, the NNLO HTLpt thermodynamics in Section 18, and the experimental summary in Section 19, are informative and suitable for a proceedings. The volume is a collection of extended abstracts, not a monograph, and it ships no code or machine-checked derivations; most quantitative results are quoted from companion papers. The load-bearing strength of the volume therefore rests on whether the few genuinely new claims are adequately supported, and in the two headline cases (Sections 4 and 10) the support is currently incomplete.

major comments (3)

[Section 4, Eq. (12), Figs. 7–9] The claim of a first-time nonzero κ4 = 3.1(6)×10^-5 rests on an uncontrolled extrapolation. The mean-field strength K = 33 GeV^-2 is fixed in Section 4.2 by comparing QMHRG susceptibilities with lattice baryon-number fluctuations at zero chemical potential, and the same K is then used up to µB = 750 MeV to compute the pseudo-critical line and fit κ4. The section itself notes in Section 4.4 that strange and non-strange baryons should have different K values and in Section 4.5 that light nuclei and hypernuclei become important near µB ≈ 700 MeV. The quoted uncertainty on κ4 does not include systematic errors from K, the hadron-list composition, or the half-drop criterion. Because κ4 is the fourth-order curvature, small misbehavior of the high-µB model is amplified in this coefficient. I recommend either providing a systematic error band from K and hadron-list variations or explicitly softening the 'first time' claim.
[Section 5, Eq. (13), Fig. 10] The MVDWHRG cumulant ratios presented as 'predictions' for STAR data are obtained by an exponential extrapolation of the van der Waals parameters a and b, which are fitted at only four values of µB/T up to 2.5 (Table 1). The exponential ansatz in Eq. (13) is introduced without physical justification, and its parameters p1–p4 carry uncertainties that are not propagated into the cumulant ratios. The summary statement that this provides 'stringent limits to the non-critical fluctuations' is therefore not supported by the analysis as presented. Please quantify the extrapolation uncertainty, restrict the claim to the region where the parameterization is controlled, or reframe the result as a model-dependent illustration.
[Section 10, Eqs. (37)–(38)] The central claim that the derived third-order theory is linearly stable and causal is not demonstrated in the manuscript. The text states that a Chapman-Enskog-like iterative solution is used and that 'our results for the transport coefficient... is found to be consistent with these constraints,' but neither the iterative derivation nor the linear stability and causality analysis is shown. Equations (37) and (38) are presented as final evolution equations without derivation or a reference to a companion paper containing the details. For this claim to be verifiable, the authors should either include the linearized perturbation equations and the resulting constraints on transport coefficients, or cite the paper where the complete derivation appears.

minor comments (5)

[Section 15] There are unresolved placeholder references 'figure (??)' in Sections 15.2 and 15.3; these must be replaced with the actual figure numbers before publication.
[Acknowledgments] The conference dates are given as 'July 1-32, 2024'; this should read 'July 1–3, 2024'.
[Section 11, Figs. 20–22] The figure captions label the horizontal axis as 'collision centrality' (e.g., 'plotted with respect to collision centrality'), but the axis is collision energy √s; also 'croosover' in Section 11.4 should be 'crossover'.
[Section 13, Table 2] In Table 2, both the RTA and ERTA columns are labeled ℓ = 0, which makes the comparison between RTA and ERTA results unclear; the ERTA column should presumably correspond to a nonzero ℓ value.
[Throughout] There are numerous typographical errors, including 'Gev/c' (Section 1), 'retarted time' and 'cross-subsection' (Section 3), 'upto' (Section 4), 'van der W aals' (Section 5), 'hardons' and 'off-equillibrium' (Section 6), 'energy rage' and 'od (1+1)D' (Section 7), 'F ranz' and 'disspative' (Section 12), 'choosen' and 'vlues' (Section 17), and '0.2< pT <1.6' lacking units (Section 16). A thorough proofread is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No constructional circularity: the volume's claimed results are model outputs checked against external lattice/STAR data, not re-labelings of fitted inputs.

full rationale

I walked the claimed derivation chains in the sections singled out as load-bearing. Section 4 fixes the mean-field repulsion K=33 GeV^-2 by comparing QMHRG baryon susceptibilities chi_B^n (n=2,4,6,8) with lattice QCD, and then extracts kappa_4 from the half-drop criterion applied to the renormalized chiral condensate; the fitted susceptibilities are derivatives of the pressure with respect to mu_B/T, while kappa_4 is the fourth-order curvature of the pseudo-critical line defined by the condensate's half-drop, and no equation of the section identifies one with the other. Section 5 fits the van der Waals parameters a and b to lattice pressure/energy density at four mu_B/T values and then evaluates proton cumulant ratios at a freeze-out curve obtained from particle yields; the STAR cumulant data are not inputs to any of the fits, so the comparison is an external test rather than a forced result. Section 10 derives the third-order viscous evolution equations from the RTA Boltzmann equation by Chapman-Enskog iteration and imports the rank-three tensor promotion from the authors' earlier Ref. [79] as an explicit prior assumption; this is a stated ansatz, not a hidden identification of the derivation's output with its input, and the linear causality statement is checked by perturbation analysis rather than assumed. The volume does cite the authors' own prior works for figures, parameters, and derivations (e.g., Fig. 7 from Ref. 27 in Section 4; settings from Ref. 56 in Section 9; details from Ref. 154 in Section 5), but these are journal-published, externally falsifiable results and none is invoked as a forbidden uniqueness theorem that forces the conclusion. I therefore find no specific equation or fitted parameter that reduces by construction to the claimed prediction.

Assumptions & free parameters 8 free parameters · 9 assumptions · 1 invented entities

The central claims rest on a small number of calibrated parameters and on model assumptions that the proceedings text often delegates to companion papers. The free parameters listed are the ones explicitly fitted to data or chosen by hand; the invented entity is the rank-3 tensor introduced in Section 10.

free parameters (8)

K (mean-field repulsion strength) = 33 GeV^-2
Section 4.2: fixed by comparing QMHRG baryon number susceptibilities χ_B^n (n=2,4,6,8) to lattice QCD; used for the pseudo-critical line and κ2, κ4 extraction.
VDW parameter a fit constants p1 and p2 = p1=1.66±0.05 GeV fm^3, p2=-0.88±0.04
Section 5.2: exponential fit to lQCD pressure/energy density at several µB/T; the resulting µB/T-dependent a enters the cumulant predictions compared to STAR.
VDW parameter b fit constants p3 and p4 = p3=541.93±15.98 GeV^-3, p4=-0.61±0.03
Section 5.2: same fit; b(params) controls excluded volume repulsion in the MVDWHRG.
Deceleration ansatz parameters A, τh, ∆τ = A=β_NN/2 per Eq. (6); τh and ∆τ varied (e.g., ∆τ=1,3 fm)
Section 3.2: the novel baryon-stopping ansatz β(τ)=A(1-tanh((τ-τh)/∆τ)) is tuned to reproduce ~1 unit rapidity loss at high energies and ~1.2 units plus 80% velocity change at √s_NN=4 GeV.
Spin relaxation time τs = 4.9 fm/c (Λ data), 7.5 fm/c (Λbar data)
Section 14.3: fitted to reproduce longitudinal polarization sign and magnitude; the fit is a stated assumption ('additional assumptions... required').
PNJL model parameters (T0, a0, a1, a2, b3, b4, κ) = T0=175 MeV, a0=6.75, a1=-9.0, a2=0.25, b3=0.805, b4=7.555, κ=0.1
Section 11.2: Polyakov loop potential parameters typically fitted to lattice QCD pressure; used for conserved charge fluctuations and the CEP location.
Momentum dependence exponent ℓ (ERTA) = ℓ=0.5 in Fig. 25; ℓ=1 for λφ^4 comparison
Section 13.2: relaxation time τ_R=τ0( u·p/T)^ℓ with τ0=κ̄/T; ℓ is a model input controlling the transport coefficients.
Walecka model couplings gσ, gω, b, c = not quoted in text
Section 17.2: fitted to nuclear matter saturation properties; used for magnetized nuclear matter speed of sound and CEP shift.

assumptions (9)

domain assumption Boltzmann equation with relaxation-time approximation accurately describes the near-equilibrium dynamics of QGP and hadronic matter.
Used in Sections 6, 10, 13, 14 as the starting point for transport coefficient derivations.
domain assumption The hadron resonance gas model with a repulsive mean-field interaction captures the relevant degrees of freedom of QCD in the hadronic phase.
Section 4 uses QMHRG with K=33 GeV^-2 to describe chiral transition up to µB=750 MeV; Section 6 uses HRG for diffusion coefficients.
domain assumption Lattice QCD results for baryon susceptibilities and the EoS are reliable and can be used to calibrate model parameters.
Sections 4, 5, 11, 18 calibrate against lattice data.
ad hoc to paper The Chapman-Enskog-like iterative solution of the Boltzmann equation can be truncated at third order and the promotion of ∇<μπνλ> to an independent field ρμνλ restores causality.
Section 10 introduces ρμνλ (Eq. 36) to cure acausality; the validity of this promotion is not proven beyond linear analysis.
ad hoc to paper A single global mean-field repulsion strength K applies to all (anti-)baryons, including strange and non-strange.
Section 4.6 admits 'we have considered the same values of K for repulsive interactions among strange and non-strange baryons, whereas these strengths have to be different in a more realistic model.'
ad hoc to paper The exponential parameterization of VDW parameters a and b as functions of µB/T remains valid outside the fitted region.
Section 5.2 uses a=p1 exp(p2 µB/T), b=p3 exp(p4 µB/T) and then applies the model to all BES energies; this is an extrapolation beyond the fitted µB/T values.
ad hoc to paper The deceleration ansatz β(τ)=A(1-tanh((τ-τh)/∆τ)) is a realistic description of baryon stopping.
Section 3.2: no first-principles derivation; introduced as a 'novel deceleration ansatz' with parameters tuned to known stopping characteristics.
domain assumption Background electromagnetic fields evolving according to retarded Liénard-Wiechert formulas can be treated independently of the medium's back-reaction (non-resistive approach).
Sections 3 and 13 compute EM fields or MHD with assumptions of vacuum or non-resistive evolution; conductivity only discussed qualitatively.
standard math Thermodynamic identities relating pressure derivatives to cumulants are valid.
Used throughout (Eq. 14 in Section 5, Eq. 11 in Section 4).

invented entities (1)

ρμνλ (irreducible rank-3 tensor)
purpose: Promoted from ∇<μπνλ> to an independent dynamical variable to restore causality in third-order viscous hydrodynamics.
Section 10, Eq. (36) and the evolution equation (38). The new degree of freedom is a theoretical construct; no independent experimental or observational handle is provided.

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Cite this review

Pith. "Pith review of Dynamics of Hot QCD Matter 2024 -- Bulk Properties." pith.science (2026). https://pith.science/paper/CQAZ5YRV

@misc{pith2026241210779,
  author       = {Pith},
  title        = {Pith review of: Dynamics of Hot QCD Matter 2024 -- Bulk Properties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CQAZ5YRV}},
  note         = {Machine review of arXiv:2412.10779}
}

read the original abstract

The second Hot QCD Matter 2024 conference at IIT Mandi focused on various ongoing topics in high-energy heavy-ion collisions, encompassing theoretical and experimental perspectives. This proceedings volume includes 19 contributions that collectively explore diverse aspects of the bulk properties of hot QCD matter. The topics encompass the dynamics of electromagnetic fields, transport properties, hadronic matter, spin hydrodynamics, and the role of conserved charges in high-energy environments. These studies significantly enhance our understanding of the complex dynamics of hot QCD matter, the quark-gluon plasma (QGP) formed in high-energy nuclear collisions. Advances in theoretical frameworks, including hydrodynamics, spin dynamics, and fluctuation studies, aim to improve theoretical calculations and refine our knowledge of the thermodynamic properties of strongly interacting matter. Experimental efforts, such as those conducted by the ALICE and STAR collaborations, play a vital role in validating these theoretical predictions and deepening our insight into the QCD phase diagram, collectivity in small systems, and the early-stage behavior of strongly interacting matter. Combining theoretical models with experimental observations offers a comprehensive understanding of the extreme conditions encountered in relativistic heavy-ion and proton-proton collisions.

Figures

Figures reproduced from arXiv: 2412.10779 by the authors.

**Figure 2.** The average transverse momentum ⟨pT ⟩ as a function of RT in the transverse region for different spherocity classes: (left) for S0 = 0 − 20%, and (right) for S0 = 80 − 100%. three regions: (i) toward, (ii) away, and (iii) transverse, based on the azimuthal angle difference with the leading particle’s path. Particles in the toward region are within azimuthal angle |△ϕ| < 60◦ , while those in the away region are influ… view at source ↗

**Figure 3.** Spherocity plots for different RT values in the transverse region: (top-left) 0 < RT < 1, (top-right) 1 < RT < 2, (bottom-left) 2 < RT < 3, and (bottom-right) 3 < RT < 4. and is defined as S0 = π 2 4 min nˆ P i |⃗pT ,i × nˆ| P i ⃗pT ,i 2 (1) Now (RT ) is defined as the ratio of multiplicity of the inclusive charged-particles to its event-averaged multiplicity (⟨Ninc⟩) in the transverse region, serving as a tool to… view at source ↗

Figures from the paper (41 more)

**Figure 4.** Figure 4: The longitudinal polarization shown as a function of the azimuthal angle [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Parametrized velocity (solid lines) and the corresponding acceleration [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: (Color online) Comparison of |Bx|, |By| (top two panels), and |Ex|, |Ez| (bottom two panels) with (blue dashed lines) and without deceleration (red solid lines) at √ sNN = 4 GeV with b = 3 fm at robs = (0, 0, 0). • For central collisions (b = 3 fm), we observe that the…

**Figure 7.** Figure 7: The sixth (left) and eighth (right) order baryon number fluctuation results [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]

**Figure 8.** Figure 8: Left: The µB dependence of the renormalized chiral condensate for different temperature values T = 25-150 MeV. Right: Pseudo-critical lines from ideal and repulsive QMHRG model, both for the µS = 0 and net S = 0 case (see the text for details). from the static quark an…

**Figure 9.** Figure 9: Left: The µB/T dependence of the µS/µB (see the text for details). Right: Relative abundances of baryons and nuclei, hyper-nuclei states along the pseudocritical lines. with the following ansatz,26 Tpc(µB) Tpc(0) = 1 − κ2 µB Tpc(0)2 − κ4 µB Tpc(0)4 we obtain the…

**Figure 10.** Figure 10: (Colour Online) The net proton cumulant ratios as functions of centre [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]

**Figure 11.** Figure 11: Left: variation of κBB/T2 with T and µB for the IHRG and EVHRG models. Here we also assumed that µQ = 0 = µS. Right: variation of κBB/T2 with T and µB for the IHRG model. But here we consider nS = 0 and µQ = 0. We compare our results with the results obtained in Ref.1…

**Figure 12.** Figure 12: Left: variation of the cross diffusion coefficient ( [PITH_FULL_IMAGE:figures/full_fig_p026_12.png]

**Figure 13.** Figure 13: The λ values are plotted as a function of temperature T at different photon energies. The mean free path has been found to be extremely large around the [PITH_FULL_IMAGE:figures/full_fig_p029_13.png]

**Figure 13.** Figure 13: Mean free path of photons versus temperature coming with different ener [PITH_FULL_IMAGE:figures/full_fig_p030_13.png]

**Figure 14.** Figure 14: Mean free path of photons of different energies from expanding plasma [PITH_FULL_IMAGE:figures/full_fig_p031_14.png]

**Figure 15.** Figure 15: (Color online) Distribution of entropy density at the formation time [PITH_FULL_IMAGE:figures/full_fig_p032_15.png]

**Figure 16.** Figure 16: (Color online) The ratio of thermal photon [PITH_FULL_IMAGE:figures/full_fig_p033_16.png]

**Figure 17.** Figure 17: Nucleon density distribution on the transverse plane for 0–5% O+O colli [PITH_FULL_IMAGE:figures/full_fig_p034_17.png]

**Figure 18.** Figure 18: Centrality dependence of ⟨ϵ2⟩ and ⟨ϵ3⟩ for p–O (left) and p–C (right) collisions at √ sNN = 9.9 TeV using AMPT for SOG and α–cluster nuclear density profiles. Ratio ⟨ϵ3⟩/⟨ϵ2⟩ as a function of centrality is plotted in the lower panel.56 We observe that the ⟨ϵ2⟩ rises s…

**Figure 19.** Figure 19: v2{2} and v3{2} as a function of centrality for SOG and α-cluster density profiles in p–O and p–C collisions at √ sNN = 9.9 TeV.56 well carried forward to the final state beyond central collisions, possibly due to a very small number of participants. For both p–O and …

**Figure 20.** Figure 20: (Color online) Sσ (left panel) and kσ2 (right panel) of baryon fluctuation have been plotted with respect to collision centrality. Interestingly, the plot of the Sσ with collision energy ( [PITH_FULL_IMAGE:figures/full_fig_p045_20.png]

**Figure 21.** Figure 21: (Color online) Sσ (top panel) and kσ2 (bottom panel) of charge fluctuation have been plotted with respect to collision centrality. C4/C2S ) with respect to different collision energies for the PNJL model. In recent experimental data no significant deviation of the str…

**Figure 22.** Figure 22: (Color online) Sσ (top panel) and kσ2 (bottom panel) of strangeness fluctuation have been plotted with respect to collision centrality. 0 20 40 60 80 100 120 140 160 180 200 0 50 100 150 200 250 300 350 R=2 fm R=4 fm Infinite Volume (CEP)R=4 fm=(316,45.7) (CEP)Infini…

**Figure 23.** Figure 23: (Color online)Phase diagram of the PNJL model for infinite and finite [PITH_FULL_IMAGE:figures/full_fig_p047_23.png]

**Figure 24.** Figure 24: The Condensed Matter Physics (CMP) and High Energy Physics (HEP) [PITH_FULL_IMAGE:figures/full_fig_p051_24.png]

**Figure 25.** Figure 25: The dashed lines are the ERTA results for [PITH_FULL_IMAGE:figures/full_fig_p054_25.png]

**Figure 26.** Figure 26: (Color online) Longitudinal polarization as a function of azimuthal angle ϕp for 30–60% Au-Au collisions at √ sNN = 200 GeV. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -0.0006 -0.0004 -0.0002 0.0000 0.0002 0.0004 0.0006 ϕp(rad) P(ϕp) τs = 0.0 fm/c τs = 4.9 fm/c τs = 7.5 fm/c 0-15%…

**Figure 29.** Figure 29: The graphs which contribute to meson correlation function: (left) free [PITH_FULL_IMAGE:figures/full_fig_p058_29.png]

**Figure 30.** Figure 30: Left Panel: Temperature variation of scaled Gribov mass parameter obtained using lattice (thermodynamics) data.110 Right Panel: The temperature dependence of the scaled screening mass. The dashed line represents the free theory result from (m = 2πT). We compare the …

**Figure 31.** Figure 31: Moments for net-kaon distribution from C1 to C4 for nine centralities and different energies [PITH_FULL_IMAGE:figures/full_fig_p063_31.png]

**Figure 32.** Figure 32: Moments for net-strangeness distribution from [PITH_FULL_IMAGE:figures/full_fig_p064_32.png]

**Figure 33.** Figure 33: Volume independent ratio of higher moments first two figures show [PITH_FULL_IMAGE:figures/full_fig_p064_33.png]

**Figure 34.** Figure 34: α dependence of κσ2 for different energies of magnetic field shifts the location of the spinodal lines and the critical endpoint (CEP) in the T − µB plane. Due to the directional nature of the background magnetic field, thermodynamic quantities, like the squared speed…

**Figure 35.** Figure 35: (b). At low temperatures, these figures show multiple roots for the nucleon mass within a specific range of µB. As temperature increases, these multiple solutions disappear at a particular T and µB, known as the critical endpoint (CEP), beyond which the phase transit…

**Figure 36.** Figure 36: Parallel component of squared speed of sound as a function of chemical [PITH_FULL_IMAGE:figures/full_fig_p068_36.png]

**Figure 37.** Figure 37: Diagrams containing fermionic lines relevant for NLO thermodynamics [PITH_FULL_IMAGE:figures/full_fig_p069_37.png]

**Figure 38.** Figure 38: Three loop HTL Feynman diagrams that will contribute to the thermody [PITH_FULL_IMAGE:figures/full_fig_p070_38.png]

**Figure 39.** Figure 39: The shorthand notations used in Fig. 38. [PITH_FULL_IMAGE:figures/full_fig_p071_39.png]

**Figure 40.** Figure 40: The NNLO HTLpt resummed result at finite T and chemical potential(s) is [PITH_FULL_IMAGE:figures/full_fig_p073_40.png]

**Figure 41.** Figure 41: Conjectured QCD phase diagram.218 It consists of various phase structures such as critical point and first-order phase boundary. Experimentally extracted freeze-out points are shown by the red solid circles.219 Also shown are the different regions covered by various e…

**Figure 42.** Figure 42: Left: Physical background (hadronic cocktail) subtracted thermal dielectron [PITH_FULL_IMAGE:figures/full_fig_p075_42.png]

**Figure 43.** Figure 43: Left: Residuals in cumulant ratio C4/C2 from experimental data with respect to models not including the critical point plotted as a function of collision energy.221 Right: Particle yield ratios of K0 S /Λ, Λ/p, and Ξ−/Λ as a function of collision energy along with the…

**Figure 44.** Figure 44: NCQ scaled v2 versus NCQ scaled transverse energy for various mesons and baryons in Au+Au collisions at √ sNN = 3.0 − 4.5 GeV.223 central Au+Au collisions at √ sNN = 3.0 − 4.5 GeV. At top RHIC energy, this measurement shows that all baryons and mesons follow a single …

**Figure 45.** Figure 45: Left: Ratios of various particles’ yields to pions as a function of charged [PITH_FULL_IMAGE:figures/full_fig_p077_45.png]

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Investigation of the Spectator Effect on Light Nuclei Production in Nucleus-Nucleus Collisions at High Baryon Density Region
hep-ph 2025-11 conditional novelty 5.0 of 10

Spectator nucleons enhance low-pT light-nucleus production in peripheral, forward-rapidity 3 GeV Au+Au collisions, so pT-integrated yields obtained by Blast-Wave extrapolation are underestimated.

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