Pith. sign in

REVIEW 2 major objections 4 minor 2 cited by

Moat regimes within a $2+1$ flavor Polyakov-quark-meson model

T0 review · 2 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper argues that adding strange quarks and Polyakov-loop confinement to the 2+1 flavor quark-meson model leaves the moat regimes of the σ and π mesons qualitatively unchanged, so the mismatch with functional renormalization group QCD…

desk verdict Careful PQM moat study whose negative result (strangeness + Polyakov loop don't explain the FRG-QCD mismatch) depends on a renormalization scheme choice the paper itself flags. read the letter →

arxiv 2504.18874 v3 pith:67LKOJD4 submitted 2025-04-26 hep-ph nucl-th

Gaoqing Cao This is my paper · ORCID
classification hep-phnucl-th PACS 11.30.Qc05.30.Fk11.30.Hv12.20.Ds
keywords moatregimePolyakov-quark-mesonmodelQCDphasediagramchiralsymmetryrestorationcriticalendpointwavefunctionrenormalizationmesonspectralfunctionsstrangequark
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 paper sets out to decide whether the moat regime of QCD matter—the region in which meson fields are unstable at zero momentum and prefer spatially modulated correlations—survives in a more realistic effective model. Extending the two-flavor quark-meson analysis to the 2+1 flavor Polyakov-quark-meson model, it includes a strange quark and a Polyakov loop to encode confinement, with parameters fixed to the lattice pseudocritical temperature and to a critical end point at μ_B ≈ 635 MeV. The finding is that the σ and π moat regions keep the same qualitative shape as in the two-flavor model: they sit at large temperature or large baryon chemical potential and re-enter around the zero-temperature chiral critical chemical potential, and they remain detached from the chiral transition line except at low temperature. The author therefore concludes that strangeness and confinement do not resolve the gap between effective-model and functional-renormalization-group predictions for the moat. A consistent secondary result is that meson pole energies increase monotonically with momentum everywhere on the phase diagram, so the static-energy minimum that defines the moat does not imply a soft propagating mode at nonzero momentum.

What carries the argument

The load-bearing object is the static meson energy $E_m(|q|) = G_m^{-1}(0,|q|)^{1/2}$ and its curvature at zero momentum, the wave-function renormalization $Z_m^\perp = \frac{1}{2} \partial^2 E_m^2 / \partial |q|^2$; the moat regime is the set of $(T,\mu_B)$ where $Z_m^\perp < 0$ for σ, π, or K. The sign of $Z_m^\perp$ is decided by a competition between the vacuum and thermal parts of the quark-loop polarization functions. The vacuum part is renormalized by dimensional regularization with the condition that the renormalized polarization vanishes in vacuum; the thermal part contains an infrared $\log m_f$ term that cancels the vacuum logarithm in the chiral limit, which is why the moat boundary can separate from the chiral transition line. Reentrance follows from an auxiliary function $H(\mu_B/T)$ whose sign changes near $\mu_B/T \approx 7$, so the thermal contribution first grows and then falls as temperature rises at fixed high chemical potential. Because the polarization functions depend on energy as well as momentum, the static energy can develop a minimum at nonzero $|q|$ while the pole energy $q_0(|q|)$ stays monotonically increasing.

What would settle it

Recompute the σ and π wave-function renormalizations $Z_{\hat\sigma}^\perp$ and $Z_{\hat\pi}^\perp$ with a hard momentum cutoff Λ in the quark-loop integrals instead of the vacuum-anchored dimensional regularization: the paper states that in that scheme the quark loops contribute positively within $T,\mu_B < \Lambda$, so finding no negative wave-function renormalization would falsify the moat regime. A lattice measurement of the pion static susceptibility at nonzero momentum in the same region would independently settle the sign.

Watch

Extended reading notes

Core claim

The central claim is that the moat regimes for σ and π mesons in the 2+1 flavor PQM model are qualitatively the same as those of the two-flavor quark-meson model, including the reentrance feature around the zero-temperature chiral critical chemical potential and the large-temperature/large-chemical-potential location, with the π moat slightly wider than the σ moat at the low-temperature end. With the model tuned so that the chiral crossover sits at T_c ≈ 156 MeV and the critical end point at (T, μ_B) = (89, 635) MeV, the moat boundary still does not track the chiral transition line; the paper takes this as evidence that the discrepancy with functional renormalization group QCD, where the moat boundary follows the extrapolated crossover, is not cured by strange quarks or Polyakov-loop confinement. The paper attributes the residual difference to the elementary nature of mesons in quark-meson models: because mesons do not emerge as quark-antiquark bound states, the coupling between chiral restoration and meson-field instability is too weak to lock the moat boundary to the transition line. For K mesons the same qualitative features are found, shifted to larger temperature and chemical potential.

Load-bearing premise

The load-bearing premise, stated in Sec. II.C, is a specific way of removing the infinities from the quark-loop diagrams: subtract them so the vacuum polarization is zero in vacuum rather than cutting off high momenta; if a momentum cutoff is the correct regulator, the quark loops always stiffen the meson fields and no moat regime appears.

Editorial extensions

If this is right

  • The moat regimes of σ and π mesons remain confined to the large-temperature/large-chemical-potential region, so a measurement or calculation in that corner of the phase diagram is the only place to look for spatially modulated mesonic correlations.
  • Reentrance around the zero-temperature chiral critical chemical potential means a system can leave the moat regime and then re-enter it as temperature rises at fixed high μ_B; the model predicts the upper boundary where temperature again suppresses the moat.
  • The moat boundary is not the chiral transition line in this model, so the critical end point at (89, 635) MeV is not located at the entrance of the moat regime; the connection seen in functional renormalization group calculations is not reproduced here.
  • Pole energies of σ, π, and K mesons are monotonically increasing functions of momentum even deep inside the moat regime, so static screening masses should not be used as a proxy for dynamical meson dispersion relations in medium.
  • The π moat is slightly wider than the σ moat at the low-temperature end because quark-mass-squared terms enhance the σ wave-function renormalization; in the exact chiral limit the two boundaries coincide.

Reading between the lines

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

  • If the vacuum-subtraction scheme is the right regulator, moat regimes may be a generic feature of any quark-meson description, and the sharp contrast with functional renormalization group QCD points to dynamical meson composition—rather than flavor content or confinement—as the decisive ingredient.
  • The predicted upper branch of the reentrance region, where temperature decreases with μ_B at fixed large chemical potential, could be looked for in functional renormalization group calculations pushed to higher temperature; finding it would unify the two pictures.
  • Because the pion wave-function renormalization changes sign twice for μ_B well above the zero-temperature chiral critical chemical potential, heavy-ion collision scans that sweep temperature at nearly fixed baryon density could in principle see two separate windows of enhanced nonzero-momentum correlations.
  • The same wave-function-renormalization machinery applied to vector or axial-vector mesons would show whether spatial modulation is special to chiral partners or common to all mesonic excitations.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The manuscript extends previous two-flavor quark-meson studies of moat regimes to a 2+1 flavor Polyakov-quark-meson model. After fixing model parameters to reproduce the lattice pseudocritical temperature and the FRG-QCD critical end point, the author computes the mesonic wave function renormalizations Z⊥ to second order in momentum and uses their sign to identify moat regimes for σ, π, and K mesons. The main reported finding is that the moat regimes for σ and π retain the same qualitative features found in the two-flavor QM model—occupying the large-temperature/large-chemical-potential region with reentrance around the zero-temperature chiral critical chemical potential—so that including strangeness and the Polyakov loop does not bring the moat boundaries onto the chiral transition line as claimed by FRG-QCD.

Significance. The paper is carefully executed: the analytic expansions in Appendices A and B are consistent, and the numerical results follow from the stated gap equations and small-momentum expansions. The central negative result—that the moat boundaries do not coincide with the chiral transition line—is a genuine output rather than a fitted quantity, and the comparison with FRG-QCD is not forced because the CEP is used only for calibration. However, the significance is substantially qualified by the paper's own admission in Sec. II.C that a momentum cutoff would make the quark-loop contribution to Z⊥ positive and would eliminate moat regimes altogether. The claimed discrepancy with FRG-QCD is therefore conditional on a specific renormalization convention for the vacuum quark loops, not a parameter-free prediction of the Lagrangian.

major comments (2)
  1. [Sec. II.C (paragraph following Eq. (20))] The central negative result depends on the renormalization scheme. The text states that with a momentum cutoff "the quark loops always contribute positively to the wave function renormalizations within the effective range T, μ_B < Λ, thus no moat regimes can be justified at all." Since the entire moat-regime analysis and the comparison with FRG-QCD rest on the sign of Z⊥ in Eqs. (B23)–(B27), the claim that strange and Polyakov-loop effects do not bridge the gap is not a prediction of the Lagrangian alone. The author should test the robustness of the moat boundaries under a second regulator (for example, a momentum cutoff with a counterterm chosen to satisfy the same on-shell renormalization condition) or give a physical argument for why dimensional regularization with Π^v(q^2)=0 at vacuum masses is the appropriate choice for composite mesons with cutoff scales near Λ_QCD.
  2. [Appendix B (final paragraph)] The cancellation between the thermal ln m_f and the vacuum ln m_f terms leaves a finite remainder whose sign is scheme-dependent. Because Z⊥ is the criterion for a moat, the statement that "the moat boundaries are not necessarily locked to the chiral transition line" is weaker than the paper's later conclusion. The finite subtraction terms in Eqs. (B23)–(B27) are not dictated by symmetry; they are conventions. The abstract and Sec. IV should either present the result as conditional on the chosen subtraction or provide evidence that the qualitative features survive a change of renormalization scheme.
minor comments (4)
  1. [Title and headers] The heading "SUMMAR Y" is missing its final letter, and the end of Sec. I contains "in in Sec. IV."
  2. [Fig. 1 caption] The caption contains "cyan diamands" (should be "cyan diamonds") and "stars to split" (should be "starts to split").
  3. [Appendix A, Eq. (A2)] The vacuum masses m_f0 are used in Eqs. (A2)–(A5) and in the main text but are only defined parenthetically inside Appendix A; they should be defined in Sec. II.B or II.C.
  4. [Sec. III.B, Fig. 5 discussion] The sentence "there are always local peaks in the curves for all μ_B except μ_B(CEP)" is slightly confusing because the following discussion attributes peaks for μ_B < μ_B(CEP) to the chiral crossover; please clarify whether "peaks" refers to local maxima of Z⊥ or to features of its temperature derivative.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fitted CEP is declared as an input, and the moat boundaries are independent outputs of the model calculation.

full rationale

The derivation is self-contained in the sense that matters for circularity. The only externally imposed quantities are the pseudocritical temperature and the FRG-QCD CEP used to fix g_m, stated openly in Sec. II: "Fitting to Tc = 156 MeV and mu_B(CEP) = 635 MeV, the quark-meson coupling constant can be fixed to g_m = 5.756." The paper does not present the resulting CEP location as an independent prediction; it only says the model is "consistent" with it after disclosing that the parameters were chosen to reproduce it. The moat boundaries, reentrance, and pole-energy monotonicity are computed from the gap equations and the polarization functions in Appendices A and B, with no parameter tuned to the moat data, and the non-coincidence with the FRG-QCD moat boundaries is an independent negative result. The paper's own caveat in Sec. II.C, that with a momentum cutoff "the quark loops always contribute positively to the wave function renormalizations... thus no moat regimes can be justified at all," is a renormalization-scheme dependence rather than a circular reduction: the scheme choice is an explicit input assumption, and the claimed result follows from that assumption without being identical to the fit inputs. The self-citations [21,22] appear only as background on quarkyonic matter in the introduction and are not load-bearing. No step was found in which a fitted parameter is renamed as a prediction or in which an equation reduces to its own input by construction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central results rest on a calibrated effective model: the sigma-pi-K sector parameters are fixed by vacuum meson masses, and the quark-meson coupling is tuned so the model reproduces the lattice pseudocritical temperature and the FRG-QCD critical end point. The moat boundaries are then a prediction of this calibrated model, not fitted. The main axioms are the mean-field treatment, real Polyakov loop, the vacuum renormalization scheme, and the elementary-field assumption. No new particles or forces are introduced.

free parameters (5)
  • gm (quark-meson coupling) = 5.756
    Fixed by fitting the model to reproduce lattice pseudocritical temperature Tc = 156 MeV and the FRG-QCD critical end point at mu_B(CEP) = 635 MeV (Sec. III). This is a calibration to external results, not a prediction.
  • m_f(500) (sigma/f0(500) mass) = 475 MeV (central), 400/550 MeV for error estimate
    Used to fix m_phi and h1 via vacuum meson observables (Sec. III, Table I). Chosen as the average of the PDG range; contributes systematic uncertainty.
  • h2 = 46.5
    Fixed by vacuum meson masses (f_pi, m_pi, m_K, m_eta, m_eta'), Sec. III, from Ref. [31].
  • kappa (anomaly coefficient) = 4810 MeV
    Fixed by vacuum meson masses, Sec. III, from Ref. [31].
  • c0, c8 (explicit symmetry breaking terms) = (286 MeV)^3 and -(311 MeV)^3
    Fixed by vacuum meson masses, Sec. III, from Ref. [31].
assumptions (5)
  • domain assumption Mean-field approximation with homogeneous condensates for sigma_l, sigma_s, and Polyakov loop L
    Used to derive the thermodynamic potential and gap equations in Sec. II.B. Ignores mesonic fluctuations, which FRG studies identify as the driver of the moat regime.
  • domain assumption Polyakov loop taken real (L = L*)
    Explicitly assumed in Sec. II.B for finite mu_B. The paper notes L != L* at finite mu_B and that this introduces a sign problem, so results at large mu_B are only qualitative.
  • domain assumption Renormalization of vacuum polarization by dimensional regularization with condition that it vanishes in vacuum
    Applied in Appendix A and discussed in Sec. II.C. The paper states that a cutoff regularization would eliminate moat regimes entirely, so the existence and boundaries of moat regimes depend on this scheme choice.
  • domain assumption Elementary meson fields, not emergent quark-antiquark bound states
    The QM-like model treats sigma, pi, K as fundamental fields in the Lagrangian (Sec. II.A). The paper itself suggests this may be why meson instabilities do not lock to the chiral transition (Sec. IV).
  • standard math Isotropy and expansion of polarization functions to order q^2 for wave function renormalization
    Z_perp is defined via the q^2 coefficient of the static propagator inverse in Appendix B; the expansion assumes small q and no non-analyticities at q=0.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Moat regimes within a $2+1$ flavor Polyakov-quark-meson model." pith.science (2026). https://pith.science/paper/67LKOJD4

@misc{pith2026250418874,
  author       = {Pith},
  title        = {Pith review of: Moat regimes within a $2+1$ flavor Polyakov-quark-meson model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/67LKOJD4}},
  note         = {Machine review of arXiv:2504.18874}
}
abstract

To better understand recent predictions on the moat regime of quantum chromodynamics (QCD) matter, this paper extends the previous work within the two-flavor quark-meson (QM) model to the more realistic $2+1$ flavor Polyakov-quark-meson (PQM) model. Mainly, two effects are further taken into account: strange quark and confinement coded through Polyakov loop. Model parameters are chosen to consistently reproduce the pseudocritical temperature from lattice QCD, $T_{\rm C}\sim 156~ {\rm MeV}$, and the baryon chemical potential at the critical end point (CEP) from FRG-QCD, $\mu_{\rm B(CEP)}\sim 635~ {\rm MeV}$. It is found that the basic features of moat regimes for $\sigma$ and $\pi$ mesons remain similar to those from QM model: Moat regimes cover the region where temperature or baryon chemical potential is large; reentrances occur around the critical baryon chemical potential of chiral transition at zero temperature. Thus, the FRG-QCD results can still not be well understood, especially why the CEP should locate at the entrances of moat regimes for $\sigma$ and $\pi$ mesons. Nevertheless, some basic features can be understood qualitatively, and it is consistent that the pole energies are increasing functions of momenta in the whole $T-\mu_{\rm B}$ plane. The moat regime and pole energy of $K$ mesons are also studied with the features similar.

Figures

Figures reproduced from arXiv: 2504.18874 by the authors.

Figure 1
Figure 1. FIG. 1. The [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The moat regimes presented by [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The order parameters, light quark mass [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The auxiliary function [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The wave function renormalization of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The pole energy [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Unified QMF equation of state for neutron star matter: Static and dynamic properties

    nucl-th 2025-05 conditional novelty 6.0 of 10

    The quark mean-field model predicts larger crust clusters and a slower direct-Urca cooling phase than the relativistic mean-field model, while both reproduce the observed crustal cooling of the transient KS 1731-260.

  2. Isentropic thermodynamics across the hadron-quark mixed phase in a two-phase model with a PNJL quark description

    hep-ph 2026-03 conditional novelty 5.0 of 10

    In a two-phase RMF+PNJL model, isentropic trajectories through the hadron-quark mixed phase heat at low entropy per baryon and cool near the critical end point, with entropy-dependent speed-of-sound structures.

Reference graph

Works this paper leans on

35 extracted references · 29 canonical work pages · cited by 2 Pith papers

  1. [1]

    σ and π mesons are chiral partners, so their moat boundaries are close to each other in the chiral symme- try restoration phase

    work page

  2. [2]

    Since chiral symmetry is not exact in QCD, the terms proportional to quark mass square would enhance the wave function renormalization of σ meson at larger tem- perature or baryon chemical potential, hence its moat boundary lies well within that of pions

    work page

  3. [3]

    The pole energy is also explored: Consistent with FRG-QCD calculations, it monotonically increases with momentum regardless in the case of vacuum, high density or deep moat regime

    The lower branches are caused by chiral symme- try restoration, the upper branches correspond to the lower branches of the reentrance region, and an extra top branches of the reentrance region are expected to exist. The pole energy is also explored: Consistent with FRG-QCD calculations, it monotonically increases with momentum regardless in the case of va...

    work page

  4. [4]

    C. F. von Weizsacker, The theory of nuclear masses, Z. Physik, 96: 431 (1935)

    work page 1935

  5. [5]

    Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions,

    B. A. Li, L. W. Chen and C. M. Ko, “Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions,” Phys. Rept. 464, 113-281 (2008)

    work page 2008

  6. [6]

    Discontinuities in the Nuclear Mass Surface,

    A. E. S. Green and D. F. Edwards, “Discontinuities in the Nuclear Mass Surface,” Phys. Rev. 91, 46-53 (1953)

    work page 1953

  7. [7]

    Coulomb Radius Constant from Nuclear Masses,

    A. E. S. Green, “Coulomb Radius Constant from Nuclear Masses,” Phys. Rev. 95, 1006-1009 (1954)

    work page 1954

  8. [8]

    Vacuum Stability and Vac- uum Excitation in a Spin 0 Field Theory,

    T. D. Lee and G. C. Wick, “Vacuum Stability and Vac- uum Excitation in a Spin 0 Field Theory,” Phys. Rev. D 9, 2291-2316 (1974)

    work page 1974

Show all 35 references
  1. [9]

    The QCD phase diagram from analytic continuation,

    R. Bellwied, S. Borsanyi, Z. Fodor, J. G¨ unther, S. D. Katz, C. Ratti and K. K. Szabo, “The QCD phase diagram from analytic continuation,” Phys. Lett. B 751, 559-564 (2015)

    2015

  2. [10]

    Chiral crossover in QCD at zero and non-zero chemical potentials,

    A. Bazavov et al. [HotQCD], “Chiral crossover in QCD at zero and non-zero chemical potentials,” Phys. Lett. B 795, 15-21 (2019)

    2019

  3. [11]

    Decoding the phase structure of QCD via particle production at high energy,

    A. Andronic, P. Braun-Munzinger, K. Redlich and J. Stachel, “Decoding the phase structure of QCD via particle production at high energy,” Nature 561, no.7723, 321-330 (2018)

    2018

  4. [12]

    Bulk Properties of the Medium Produced in Relativistic Heavy-Ion Collisions from the Beam Energy Scan Program,

    L. Adamczyk et al. [STAR], “Bulk Properties of the Medium Produced in Relativistic Heavy-Ion Collisions from the Beam Energy Scan Program,” Phys. Rev. C 96, no.4, 044904 (2017)

    2017

  5. [13]

    Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview,

    X. Luo and N. Xu, “Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview,” Nucl. Sci. Tech. 28, no.8, 112 (2017)

    2017

  6. [14]

    Properties of 15 QCD Matter at High Baryon Density,

    X. Luo, Q. Wang, N. Xu and P. Zhuang, “Properties of 15 QCD Matter at High Baryon Density,” Springer, 2022, ISBN 978-981-19-4440-6, 978-981-19-4443-7, 978-981-19- 4441-3

    2022

  7. [15]

    QCD phase structure at finite temperature and density,

    W. j. Fu, J. M. Pawlowski and F. Rennecke, “QCD phase structure at finite temperature and density,” Phys. Rev. D 101, no.5, 054032 (2020)

    2020

  8. [16]

    Chiral phase structure and critical end point in QCD,

    F. Gao and J. M. Pawlowski, “Chiral phase structure and critical end point in QCD,” Phys. Lett. B 820, 136584 (2021)

    2021

  9. [17]

    Locating the critical endpoint of QCD: Mesonic backcoupling effects,

    P. J. Gunkel and C. S. Fischer, “Locating the critical endpoint of QCD: Mesonic backcoupling effects,” Phys. Rev. D 104, no.5, 054022 (2021)

    2021

  10. [18]

    Probing QCD critical point and induced gravitational wave by black hole physics,

    R. G. Cai, S. He, L. Li and Y. X. Wang, “Probing QCD critical point and induced gravitational wave by black hole physics,” Phys. Rev. D 106, no.12, L121902 (2022)

    2022

  11. [19]

    Locating the critical poi nt for the hadron to quark-gluon plasma phase transition from finite-size scaling of proton cumulants in heavy-ion collisions,

    A. Sorensen and P. Sorensen, “Locating the critical poi nt for the hadron to quark-gluon plasma phase transition from finite-size scaling of proton cumulants in heavy-ion collisions,” [arXiv:2405.10278 [nucl-th]]

    arXiv

  12. [20]

    Searching for the QCD critical endpoint using multi-point Pad´ e ap- proximations,

    D. A. Clarke, P. Dimopoulos, F. Di Renzo, J. Goswami, C. Schmidt, S. Singh and K. Zambello, “Searching for the QCD critical endpoint using multi-point Pad´ e ap- proximations,” [arXiv:2405.10196 [hep-lat]]

    arXiv

  13. [21]

    Phases of cold, dense quarks at large N(c),

    L. McLerran and R. D. Pisarski, “Phases of cold, dense quarks at large N(c),” Nucl. Phys. A 796, 83-100 (2007)

    2007

  14. [22]

    The Quarkyonic Star,

    K. Fukushima and T. Kojo, “The Quarkyonic Star,” As- trophys. J. 817, no.2, 180 (2016)

    2016

  15. [23]

    Quarkyonic Matter and Neutron Stars,

    L. McLerran and S. Reddy, “Quarkyonic Matter and Neutron Stars,” Phys. Rev. Lett. 122, no. 12, 122701 (2019)

    2019

  16. [24]

    A field theoretical model for quarky- onic matter,

    G. Cao and J. Liao, “A field theoretical model for quarky- onic matter,” JHEP 10, 168 (2020)

    2020

  17. [25]

    Quarkyonic matter state of neutron stars,

    G. Cao, “Quarkyonic matter state of neutron stars,” Phys. Rev. D 105, no.11, 114020 (2022)

    2022

  18. [26]

    Signatures of Moat Regimes in Heavy-Ion Collisions,

    R. D. Pisarski and F. Rennecke, “Signatures of Moat Regimes in Heavy-Ion Collisions,” Phys. Rev. Lett. 127, no.15, 152302 (2021)

    2021

  19. [27]

    Moat Regimes in QCD and their Signatures in Heavy-Ion Collisions,

    F. Rennecke and R. D. Pisarski, “Moat Regimes in QCD and their Signatures in Heavy-Ion Collisions,” PoS CPOD2021, 016 (2022)

    2022

  20. [28]

    Particle interferometry in a moat regime,

    F. Rennecke, R. D. Pisarski and D. H. Rischke, “Particle interferometry in a moat regime,” Phys. Rev. D 107, no.11, 116011 (2023)

    2023

  21. [29]

    The QCD moat regime and its real- time properties,

    W. j. Fu, J. M. Pawlowski, R. D. Pisarski, F. Rennecke, R. Wen and S. Yin, “The QCD moat regime and its real- time properties,” [arXiv:2412.15949 [hep-ph]]

    arXiv

  22. [30]

    Phase struc- ture of quark matter and in-medium properties of mesons from Callan-Symanzik flows,

    S. T¨ opfel, J. M. Pawlowski and J. Braun, “Phase struc- ture of quark matter and in-medium properties of mesons from Callan-Symanzik flows,” [arXiv:2412.16059 [hep- ph]]

    arXiv

  23. [31]

    Thermo- dynamics of (2+1)-flavor QCD: Confronting Models with Lattice Studies,

    B. J. Schaefer, M. Wagner and J. Wambach, “Thermo- dynamics of (2+1)-flavor QCD: Confronting Models with Lattice Studies,” Phys. Rev. D 81, 074013 (2010)

    2010

  24. [32]

    Phases of QCD: Lattice thermodynamics and a field theoretical model,

    C. Ratti, M. A. Thaler and W. Weise, “Phases of QCD: Lattice thermodynamics and a field theoretical model,” Phys. Rev. D 73, 014019 (2006)

    2006

  25. [33]

    T. K. Herbst, J. M. Pawlowski and B. J. Schaefer, Phys. Lett. B 696, 58-67 (2011)

    2011

  26. [34]

    The Three-flavor chiral phase structure in hot and dense QCD matter,

    B. J. Schaefer and M. Wagner, “The Three-flavor chiral phase structure in hot and dense QCD matter,” Phys. Rev. D 79, 014018 (2009)

    2009

  27. [35]

    A Model study of the sign problem in the mean-field approximation,

    K. Fukushima and Y. Hidaka, “A Model study of the sign problem in the mean-field approximation,” Phys. Rev. D 75, 036002 (2007)

    2007

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.