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arxiv: 2606.09310 · v1 · pith:55YMKBPEnew · submitted 2026-06-08 · ✦ hep-ph

Fluctuations and correlations of conserved charges in the Polyakov chiral SU(3) quark mean field model

Dhananjay Singh , Arvind Kumar This is my paper

Pith reviewed 2026-06-27 16:15 UTC · model grok-4.3

classification ✦ hep-ph
keywords Polyakov chiral SU(3) quark mean field modelconserved charge susceptibilitiesgeneralized susceptibilitiesbaryon chemical potentialchiral crossoverPolyakov loopvacuum termfluctuation ratios
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The pith

Including the vacuum term in the PCQMF model makes the baryon kurtosis ratio cross zero at μ_B/T_pc ≈ 2.15 while the no-sea version stays positive.

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

The paper computes generalized susceptibilities of conserved charges up to eighth order in the Polyakov chiral SU(3) quark mean field model, both with the fermion vacuum term (vac=1) and in a refitted no-sea variant (vac=0). At zero chemical potential it reports the chiral and deconfinement temperatures plus all diagonal and off-diagonal correlators through fourth order. At finite baryon density along the pseudocritical line it tracks the evolution of baryon, charge and strangeness susceptibilities and shows that only the vac=1 variant produces a zero crossing in the kurtosis ratio R_42^B. A reader would care because these ratios are directly linked to measurable event-by-event fluctuations in heavy-ion collisions and could distinguish how vacuum contributions shape the QCD phase diagram at moderate density.

Core claim

In the vac=1 variant the kurtosis ratio R_42^B crosses zero at μ_B/T_pc ≈ 2.15 while the no-sea variant remains positive; the higher-order ratios R_51^B and R_62^B start negative and become more negative with increasing μ_B. The calculation includes diagonal susceptibilities through eighth order, all twelve independent fourth-order off-diagonal correlators, and selected odd-order baryon susceptibilities, with the vacuum term producing larger BQ amplitudes and multiple zero crossings in χ_6^B.

What carries the argument

The Polyakov chiral SU(3) quark mean field model with the fermion vacuum term (vac=1 variant), whose thermodynamic potential is differentiated repeatedly to obtain the generalized susceptibilities of baryon number, electric charge and strangeness.

If this is right

  • Twin maxima develop in χ_4^B and χ_6^Q and twin minima in χ_8^B and χ_8^Q when the chiral-deconfinement splitting is resolved by higher derivatives.
  • The BQ off-diagonal correlators maintain larger amplitudes in the vac=1 variant across the chiral crossover.
  • The BS, QS and mixed BQS fourth-order correlators peak near the strange-melting temperature, where the no-sea variant dominates.
  • Multiple zero crossings appear in χ_6^B only when the vacuum term is retained.

Where Pith is reading between the lines

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

  • The zero crossing in R_42^B supplies a concrete, density-dependent signature that lattice groups could target to test the necessity of vacuum contributions in effective models.
  • Because the sign change occurs at μ_B/T values already accessible in the RHIC beam-energy scan, the result directly informs which model variant better matches fluctuation data.
  • Repeating the calculation at small nonzero μ_Q and μ_S would map how the reported patterns extend into the three-dimensional chemical-potential space relevant to real collisions.

Load-bearing premise

The model parameters fitted to vacuum meson masses or lattice results remain valid when extrapolated to finite baryon density and when higher-order derivatives of the thermodynamic potential are taken.

What would settle it

A lattice QCD or experimental determination of the baryon kurtosis ratio R_42^B at μ_B/T_pc ≈ 2.15 that remains positive rather than crossing zero would falsify the reported distinction between the vac=1 and vac=0 variants.

Figures

Figures reproduced from arXiv: 2606.09310 by Arvind Kumar, Dhananjay Singh.

Figure 1
Figure 1. Figure 1: FIG. 1. Order parameters vs temperature at [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Bulk thermodynamics at [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Pseudocritical temperature [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Diagonal second-order susceptibilities (a) Baryon [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Second-order off-diagonal correlators (a) Baryon-c [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Higher-order diagonal baryon susceptibilities and [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Higher-order diagonal charge and strangeness susce [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Complete fourth-order off-diagonal BQS tensor vs tem [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Susceptibility ratios (a) [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Second- and fourth-order diagonal susceptibiliti [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Second-order off-diagonal correlators (a) Baryon- [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Complete fourth-order off-diagonal BQS tensor vs te [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Diagonal baryon susceptibilities at [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Cumulant ratios along the pseudocritical line [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Diagonal baryon susceptibilities and their fourth [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
read the original abstract

We compute generalized susceptibilities of conserved charges in the Polyakov chiral SU(3) quark mean field (PCQMF) model with the fermion vacuum term. At $\mu_B = 0$ MeV, the calculation covers the diagonal $\chi_n^{B,Q,S}$ through eighth order and all twelve independent fourth-order off-diagonal correlators. Extending to finite $\mu_B$ at $\mu_Q = \mu_S = 0$, we compute $\chi_n^B$ through eighth order, $\chi_n^{Q,S}$ through fourth order, the second-order off-diagonals, all twelve fourth-order off-diagonal correlators, and the odd-order baryon susceptibilities $\chi_1^B$, $\chi_3^B$, $\chi_5^B$. The calculation includes the vacuum term (vac=1) and is repeated for an independently refitted no-sea variant (vac=0). At $\mu_B = 0$ MeV, the chiral pseudocritical temperature is $T_{\mathrm{pc}} = 170.5$ MeV (vac=1) and $166.4$ MeV (vac=0), while the Polyakov-loop deconfinement temperature is $T_{\mathrm{dec}} = 144.4$ MeV (vac=1) and $146.6$ MeV (vac=0). In vac=1, the derivative $-d\Delta_{l,s}/dT$ of the subtracted chiral condensate develops an inflection near $T_{\mathrm{dec}}$. Higher derivative orders resolve the chiral-deconfinement splitting as twin maxima in $\chi_4^B$ and $\chi_6^Q$, twin minima in $\chi_8^B$ and $\chi_8^Q$, and multiple zero crossings in $\chi_6^B$. Among the fourth-order off-diagonal correlators, vac=1 amplitudes exceed vac=0 in the BQ channel across the chiral crossover. The BS, QS, and mixed BQS components peak near the strange-melting temperature, where vac=0 dominates. Along $T_{\mathrm{pc}}(\mu_B)$, the kurtosis ratio $R_{42}^B \equiv \chi_4^B/\chi_2^B$ of vac=1 crosses zero at $\mu_B/T_{\mathrm{pc}} \approx 2.15$, while vac=0 stays positive across the full range. The higher-order ratios $R_{51}^B \equiv \chi_5^B/\chi_1^B$ and $R_{62}^B \equiv \chi_6^B/\chi_2^B$ start negative in vac=1 and grow more negative as $\mu_B$ increases.

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 computes generalized susceptibilities of conserved charges (B, Q, S) and their correlations in the Polyakov chiral SU(3) quark mean field model, both with the fermion vacuum term (vac=1) and an independently refitted no-sea variant (vac=0). At μ_B=0 it reports diagonal χ_n^{B,Q,S} through order 8 and all 12 independent fourth-order off-diagonal correlators; along the T_pc(μ_B) line at μ_Q=μ_S=0 it reports χ_n^B through order 8, χ_n^{Q,S} through order 4, second-order off-diagonals, all fourth-order off-diagonals, and the odd-order baryon susceptibilities, together with the ratios R_42^B, R_51^B and R_62^B. Key reported features include T_pc=170.5 MeV (vac=1) versus 166.4 MeV (vac=0), a zero crossing of R_42^B at μ_B/T_pc≈2.15 only in vac=1, and R_51^B, R_62^B starting negative and becoming more negative with increasing μ_B in vac=1.

Significance. If robust, the work supplies concrete higher-order fluctuation predictions from an effective model that can be confronted with lattice QCD and heavy-ion data, with the explicit vac=1 versus vac=0 comparison and the full set of fourth-order off-diagonal correlators constituting a useful addition to the literature on conserved-charge fluctuations.

major comments (1)
  1. [finite-μ_B results (abstract and corresponding numerical sections)] The zero crossing of R_42^B at μ_B/T_pc≈2.15 (vac=1) and the negative, increasingly negative behavior of R_51^B and R_62^B are obtained from up to eighth-order derivatives of the thermodynamic potential whose parameters (constituent quark masses, scalar/pseudoscalar couplings, Polyakov-loop parameters) were fixed exclusively at μ_B=0. No variation of these free parameters or propagation of their uncertainties is reported for the finite-density line, so the location of the crossing and the sign pattern are not shown to be stable; this directly affects the central claim of qualitatively different behavior between the two variants.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for recognizing the potential utility of the higher-order susceptibilities and the vac=1 versus vac=0 comparison. We address the single major comment below.

read point-by-point responses

  1. Referee: [finite-μ_B results (abstract and corresponding numerical sections)] The zero crossing of R_42^B at μ_B/T_pc≈2.15 (vac=1) and the negative, increasingly negative behavior of R_51^B and R_62^B are obtained from up to eighth-order derivatives of the thermodynamic potential whose parameters (constituent quark masses, scalar/pseudoscalar couplings, Polyakov-loop parameters) were fixed exclusively at μ_B=0. No variation of these free parameters or propagation of their uncertainties is reported for the finite-density line, so the location of the crossing and the sign pattern are not shown to be stable; this directly affects the central claim of qualitatively different behavior between the two variants.

    Authors: The PCQMF parameters are fixed by fitting to vacuum hadron properties and lattice QCD thermodynamics at μ_B=0, which is the conventional procedure for effective QCD models. The finite-μ_B results are therefore genuine predictions of each variant. The vac=1 and vac=0 cases are independently refitted at μ_B=0, so the reported qualitative difference in the sign pattern and zero-crossing of the ratios directly reflects the presence or absence of the vacuum term within the same modeling framework. While an explicit variation of parameters or uncertainty propagation along the finite-density line would be a useful extension, it lies outside the scope of the present work; the central claim concerns the model-level distinction between the two variants rather than a claim of parameter-independent robustness. revision: no

Circularity Check

0 steps flagged

No significant circularity; standard parameter fit followed by extrapolation

full rationale

The paper constructs the PCQMF thermodynamic potential, fits its parameters (constituent masses, couplings, Polyakov parameters) to vacuum meson masses or μ_B=0 lattice quantities, then evaluates up to eighth-order derivatives to obtain susceptibilities and ratios R_42^B, R_51^B, R_62^B along T_pc(μ_B). This is ordinary model extrapolation; the finite-μ_B sign changes and zero crossing are outputs of the functional form and are not equivalent by construction to the μ_B=0 fit data. The vac=0 variant is independently refitted, and no load-bearing self-citation or self-definitional step is present. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central results rest on the mean-field treatment of an effective Lagrangian whose parameters are fixed by external data; no independent derivation or machine-checked proof is supplied.

free parameters (1)
  • PCQMF coupling constants and Polyakov potential parameters
    These parameters are adjusted to reproduce vacuum meson masses, decay constants or lattice thermodynamics and then used to generate all susceptibilities.
axioms (1)
  • domain assumption The mean-field approximation captures the thermodynamics of the model at the temperatures and densities considered.
    All susceptibilities are obtained from derivatives of the mean-field thermodynamic potential.

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Reference graph

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