Pith. sign in

REVIEW 4 major objections 5 minor 6 cited by

Locating the QCD critical point with neutron-star observations

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Neutron-star observations, filtered through a holographic model of QCD, place the QCD critical point at a baryon chemical potential of about 626 MeV and a temperature of about 119 MeV.

desk verdict A coherent holographic+NS Bayesian inference that yields a concrete CEP prediction, but the abstract's 'identify' oversells a model-built-in phase transition. read the letter →

arxiv 2506.10065 v1 pith:XUSWO32V submitted 2025-06-11 astro-ph.HE gr-qchep-phhep-thnucl-th

Christian Ecker , Niko Jokela , Matti Järvinen This is my paper
classification astro-ph.HEgr-qchep-phhep-thnucl-th
keywords QCDcriticalpointneutron-starequationofstateholographicgauge/gravitydualityfirst-orderdeconfinementtransitiontidaldeformabilityBayesianinferenceheavy-ioncollisions
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

The paper argues that existing neutron-star observations, combined with a holographic model of QCD, are enough to locate the QCD critical point—the endpoint of the first-order deconfinement transition in the phase diagram. It builds a probabilistic ensemble of equations of state that switch from hadronic matter to quark matter, constrains the ensemble with pulsar masses, X-ray mass-radius measurements, and the GW170817 tidal measurement, and finds a strong first-order transition at zero temperature with onset density $n_{\rm PT}=4.9^{+1.33}_{-1.17}\,n_0$ and strength $\Delta n_{\rm PT}=3.75^{+0.70}_{-0.53}\,n_0$. The resulting critical point sits at $\mu_{\rm crit}=626^{+90}_{-179}$ MeV and $T_{\rm crit}=119^{+14}_{-6}$ MeV. If correct, the prediction gives heavy-ion collision experiments a concrete target to look for critical fluctuations.

What carries the argument

The central object is the hybrid V-QCD equation of state: a holographic model of QCD in the Veneziano limit supplies the quark-matter sector, while nuclear matter is described near saturation by the SFHo nuclear-theory equation of state and by a sampled piecewise-linear sound-speed crust that is iteratively matched to the holographic part at a chemical potential $\mu_*$. Finite-temperature behavior is added through a van der Waals excluded-volume correction, leaving three effective parameters ($W_0$, $b$, $c$) after lattice calibration. The ensemble is weighted by a posterior that combines a chiral effective theory constraint up to about $2\,n_0$, pulsar mass measurements, X-ray mass-radius data, and the GW170817 tidal deformability. The critical endpoint is located by computing the latent heat across the first-order transition line and finding where it vanishes as temperature increases.

What would settle it

A radius measurement for a $1.4\,M_\odot$ neutron star below about 11.7 km, or a precise binary tidal deformability $\tilde{\Lambda}_{1.186}$ below roughly 400, would exclude the stiff equations of state that carry the posterior, and the inferred first-order transition and critical-point coordinates would no longer be supported.

Watch

Extended reading notes

Core claim

The paper's central claim is that the QCD critical endpoint can be inferred, not just estimated, from neutron-star observations once the equation of state is generated by a holographic model (V-QCD in the Veneziano limit) with only three free parameters after lattice calibration. The data select equations of state with a strong first-order deconfinement phase transition at $n_{\rm PT} \approx 4.9\,n_0$, a density jump $\Delta n_{\rm PT} \approx 3.75\,n_0$, and a maximum neutron-star mass $M_{\rm TOV} \approx 2.22\,M_\odot$. Extending the same hybrid equation of state to finite temperature gives a first-order transition line that ends at $(\mu_{\rm crit}, T_{\rm crit}) = (626, 119)$ MeV with the stated 95% credible intervals. The framework stays consistent with the lattice QCD crossover at low density and with the perturbative QCD band at high density, and its predicted $R_{1.4} \approx 12.7$ km and $\tilde{\Lambda}_{1.186} \approx 586$ are testable by future measurements.

Load-bearing premise

All results depend on the assumption that the holographic quark-matter model stays quantitatively faithful to real strong-interaction matter at densities up to several times nuclear saturation, where no independent first-principles check exists.

Editorial extensions

If this is right

  • Heavy-ion collision experiments scanning baryon chemical potentials near 626 MeV should see enhanced critical fluctuations near freeze-out if the critical point is there.
  • The first-order transition at $n_{\rm PT} \approx 4.9\,n_0$ implies that the most massive neutron stars harbor quark-matter cores separated from hadronic matter by a sharp interface.
  • The posterior's predictions—$R_{1.4} \approx 12.7$ km and $\tilde{\Lambda}_{1.186} \approx 586$—give next-generation radius and gravitational-wave measurements a narrow band to confirm or exclude.
  • Because the model matches lattice QCD at low density and neutron-star observations at high density without an imposed perturbative QCD constraint, its consistency with the perturbative QCD band is a derived and checkable consequence.

Reading between the lines

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

  • Beyond the paper: a consistency test the authors do not run is to use the same model, without re-tuning, to predict the freeze-out curve and critical fluctuations seen in heavy-ion data; agreement would independently corroborate the holographic bridge.
  • Beyond the paper: because the inferred transition is strongly first-order, binary neutron-star merger waveforms should carry a signature of quark-matter core formation after merger, which next-generation gravitational-wave detectors could search for.
  • Beyond the paper: the posterior ties the critical-point coordinates to the stiffness of the equation of state, so a future radius measurement lower than 12.7 km by more than a few tenths of a kilometer would shift the CEP toward lower $\mu$ and higher $T$—a correlation that could be tested once both measurement programs mature.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper presents a hybrid holographic equation-of-state framework that combines the V-QCD model with a van der Waals nuclear-matter description, samples a family of beta-equilibrium EOSs, and constrains the ensemble with neutron-star mass, mass-radius, and tidal deformability data. The posterior is used to report a first-order deconfinement phase transition at zero temperature with onset density n_PT/n0 = 4.9^{+1.33}_{-1.17} and strength Delta n_PT/n0 = 3.75^{+0.70}_{-0.53}, and to infer the QCD critical endpoint at (mu_crit, T_crit) = (626^{+90}_{-179}, 119^{+14}_{-6}) MeV.

Significance. If the V-QCD model is quantitatively reliable in the dense regime, the framework is valuable: it connects lattice-QCD thermodynamics, nuclear theory, neutron-star observations, and heavy-ion collision phenomenology in one thermodynamically consistent description, and it produces falsifiable predictions for the phase-transition location and the critical endpoint. The paper also provides a concrete EOS that can be used in merger simulations and other astrophysical modeling. However, the significance is conditional on the V-QCD high-density behavior, which is not independently verified in this regime, and on the model class always containing a first-order transition and a critical point.

major comments (4)
  1. [Abstract and Sec. IIB] The claim that the data 'identify a strong first-order deconfinement transition' is an overstatement. In Sec. IIB, the matching procedure explicitly searches for a pressure-equality point between the holographic nuclear and quark-matter EOSs, and every EOS in the sampled family therefore contains a first-order phase transition by construction. The posterior in Eq. (5) updates parameters within this PT-containing family but cannot distinguish 'PT present' from 'no PT'. The same applies to the critical endpoint, which is an inherent feature of the V-QCD phase structure. To support the word 'identify', the paper would need a model comparison against a no-PT prior, e.g., a smooth crossover or a family without an enforced pressure-equality crossing, with a reported Bayes factor or posterior model probability. At minimum, the abstract and conclusions should be rephrased to say that the PT and CEP are predictions of the V-QCD-based model conditioned on the data, not empirical discoveries.
  2. [Sec. IIC] The determination of the critical endpoint relies on a step that is not fully specified: the latent heat is fit with a polynomial in the regime T <~ 110 MeV, and the CEP is located where the latent heat vanishes. No details are given for the degree of the polynomial, the exact fit range, the number of points used, or the sensitivity of T_crit and mu_crit to these choices. Since the CEP location is a central quantitative result, this extraction must be made reproducible and its systematic uncertainty quantified. I request the explicit fitting procedure, including an uncertainty estimate from varying the fit range and polynomial order.
  3. [Sec. IIB] The iterative matching procedure is asserted to converge with 'typically a single iteration is sufficient', but no convergence criterion, residual measure, or distribution of iteration counts is reported. The matching at mu_star is load-bearing for the entire EOS family, because it determines the connection between the piecewise c_s^2 crust EOS and the V-QCD nuclear-matter EOS. The paper should state the convergence tolerance, report how many iterations are needed in practice, and show that residual discontinuities in p, n, or c_s are negligible. Without this, the posterior for the phase-transition parameters and the CEP is not fully reproducible.
  4. [Sec. III, Eq. (5)] The statistical setup needs more precision. The prior is described as uniform, but it is not stated whether this is uniform in W0, delta b, c, v0, n*, and the c_s^2 segment values, or in some transformed variables. Also, the normalization 'such that the optimal model having the highest likelihood has unit weight' suggests that displayed weights are relative likelihoods rather than a normalized posterior; while this does not change percentile estimates if the weight normalization is constant, the text should clarify how the 95% credible intervals are computed from these weights and how the uniform prior is defined over the sampled parameter ranges.
minor comments (5)
  1. [Sec. IIC] In Eq. (4), the minimization over Y_q is stated but the precise domain and the role of the f_SFHo subtraction are not explained; a brief clarification would help the reader reproduce the thermal extension.
  2. [Sec. IIB] The sentence 'we first linearly rescale c_s^{-2} in the crust region' is ambiguous: it is not clear whether c_s^{-2} is rescaled as a function of mu or whether the chemical-potential axis is rescaled. Please spell out the operation.
  3. [Fig. 5] The inset labels the region around the reported CEP as the 'expected critical region' but the posterior distribution itself is difficult to discern at the printed scale; a zoomed panel with the full posterior cloud and the 95% contour would make the central result easier to evaluate.
  4. [Sec. I, footnote [58]] The footnote states that the pQCD criterion would constrain W0 at densities above ~17 n0 but then says comparisons in that regime are not meaningful. This is internally somewhat inconsistent with the earlier claim that the prior 'naturally falls within the pQCD uncertainty band'; please clarify the density range over which the pQCD consistency claim is intended to hold.
  5. [Sec. IV] The 'optimal model' is used repeatedly (e.g., red curves in Figs. 1-5), but its precise definition is not given; please state explicitly that it is the sample with the highest likelihood in the posterior ensemble.

Circularity Check

2 steps flagged · score 6.0 of 10

The claim to 'identify' a first-order deconfinement transition and locate the CEP is built into the EOS construction: every sampled EOS contains a PT by the pressure-matching step, so the posterior cannot provide evidence for the PT's existence.

  1. self definitional [Abstract; Sec. IIB 'Matching the components']
    "Abstract: 'we identify a strong first-order deconfinement transition at zero temperature, with a transition strength of ΔnPT/n0 = 3.75...' Sec. IIB: 'the first-order PT between holographic nuclear and QM is found by searching for the point where the pressures as a function of the chemical potential match.'"

    The matching procedure is applied to every sampled parameter set, so no EOS in the ensemble can lack a first-order PT. The posterior (5) only weights parameters within this always-PT family; it never compares against a no-PT model. The reported nPT and ΔnPT are deterministic functions of the construction, and the abstract's 'identify' converts a model assumption into a data-driven discovery. The likelihood cannot discriminate 'PT present' from 'no PT', so the central PT claim reduces by construction to the input model.

  2. self definitional [Sec. IIC 'Finite temperature extension'; Sec. IV 'Results']
    "Sec. IIC: 'To locate the CEP systematically, one may evaluate the latent heat Δϵ across the PT as a function of temperature and determine where it vanishes.' Sec. IV: 'The resulting posterior yields 95% credible intervals for the CEP location: (μcrit,Tcrit) = (626+90−179, 119+14−6) MeV.'"

    The CEP is defined as the endpoint of the PT line in the same construction, and the PT line exists by the pressure-matching assumption for every EOS in the ensemble. The NS data constrain low-density EOS parameters, but the CEP location is a model extrapolation from the always-PT family; no data considered here can falsify the existence of a CEP within this framework. The reported credible interval is therefore a reparametrization of the model's built-in phase structure rather than an independent empirical localization.

full rationale

The paper's EOS predictions for neutron-star properties (R1.4, MTOV, tidal deformability) are self-contained and benchmarked against independent model-agnostic results, so those are not circular. The circularity is concentrated in the headline claims about the phase transition and critical point. The matching step in Sec. IIB defines every hybrid EOS to contain a first-order deconfinement transition by construction, and the finite-temperature extension in Sec. IIC locates a CEP as the endpoint of that guaranteed PT line. The Bayesian posterior (5) updates the sampled parameters using astrophysical data, but it never tests whether a PT or CEP exists, because the prior model family excludes the no-PT hypothesis. Consequently, the abstract's statements that the data 'identify a strong first-order deconfinement transition' and yield credible intervals for the CEP location overstate what the inference can show: those quantities are properties of the assumed V-QCD-based model class, not empirical discoveries. This warrants a score of 6: the central existence claims reduce by construction, while the actual numerical locations are still model outputs conditioned on data rather than direct fits to CEP observations.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particles; it postulates a first-order phase transition and a critical point as predictions of the model. The free parameters are the uncertainty in the hybrid construction; the axioms are the model assumptions.

free parameters (6)
  • W0 = sampled in [0,6]
    Controls the quark matter EOS in V-QCD; sampled uniformly in the prior and weighted by NS data through the posterior (Sec IIA).
  • n* = sampled in [1.2,2] n0
    Target baryon density for the matching of the crust and V-QCD NM; prior range is provisional (Sec IIB).
  • c_s coefficients = N piecewise values
    Speed-of-sound interpolation coefficients sampled between HS and V-QCD values, introduced in Eq. (1) (Sec IIA).
  • v0 = 0.56, 0.8, 1.0 fm^3
    Excluded volume in the vdW thermal correction; sampled discretely (Sec IIC).
  • δb = determined by matching
    Relative deviation of the V-QCD parameter b, solved by requiring continuity of p/n at μ* (Sec IIB).
  • c = determined by matching
    Normalization of pressure in V-QCD, solved by requiring continuity of n at μ* (Sec IIB).
assumptions (4)
  • domain assumption V-QCD is a valid holographic model for QCD thermodynamics at high density
    The entire framework rests on this. The paper calibrates the model to lattice QCD at low density and assumes it extends to high density (Sec IIA).
  • domain assumption The hybrid construction with piecewise-linear sound speed and iterative matching is thermodynamically consistent
    Assumed in Sec IIB; convergence is not proven (only 'typically a single iteration is sufficient').
  • domain assumption The vdW and SFHo models correctly describe thermal corrections to the nuclear matter EOS
    Used in Sec IIC to extend the cold EOS to finite temperature.
  • domain assumption Uniform prior over model parameters
    Assumed in Sec III for the Bayesian analysis.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Locating the QCD critical point with neutron-star observations." pith.science (2026). https://pith.science/paper/XUSWO32V

@misc{pith2026250610065,
  author       = {Pith},
  title        = {Pith review of: Locating the QCD critical point with neutron-star observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XUSWO32V}},
  note         = {Machine review of arXiv:2506.10065}
}
abstract

We present a probabilistic model for the QCD critical endpoint (CEP) and the equation of state (EOS) at $\beta$-equilibrium, constrained by neutron-star observations. Using a hybrid framework that combines the holographic V-QCD model with an effective van der Waals description of nuclear matter, we generate a large ensemble of EOSs incorporating nuclear theory uncertainties. Constraining this ensemble with neutron-star mass-radius data and tidal deformability measurements from gravitational waves, we identify a strong first-order deconfinement transition at zero temperature, with a transition strength of $\Delta n_{\rm{PT}}/n_0 = 3.75^{+0.70}_{-0.53}$ and onset density $n_{\rm{PT}}/n_0 = 4.9^{+1.33}_{-1.17}$. The resulting posterior yields $95\%$ credible intervals for the CEP location: $\mu_{\rm{crit}} = 626^{+90}_{-179}\,\rm{MeV}$, $T_{\rm{crit}} = 119^{+14}_{-6}\,\rm{MeV}$.

Figures

Figures reproduced from arXiv: 2506.10065 by the authors.

Figure 1
Figure 1. FIG. 1. Top: Posterior probability and prior (gray) distribu [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Top: Posterior distribution of the correlation be [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. FIG. 5. Top: Phase diagram for locally charge neutral [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

Discussion (0). Sign in to comment.

Forward citations

Cited by 6 Pith papers

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

  1. Holographic Soliton Crystals for Dense Nuclear Matter and Neutron Stars

    hep-ph 2026-07 conditional novelty 7.0 of 10

    A crystal of holographic baryons in the Witten-Sakai-Sugimoto model yields a nuclear-matter equation of state compatible with neutron-star observations.

  2. Quark flavors in hot and dense holographic QCD: setup and comparison to data

    hep-ph 2025-07 conditional novelty 7.0 of 10

    A 2+1 flavor holographic QCD model fitted to lattice thermodynamics predicts a smoother nuclear-to-quark matter transition with lower latent heat than earlier V-QCD models.

  3. The equation of state and surface tension of QCD in the first order phase transition region

    hep-ph 2025-07 conditional novelty 5.0 of 10

    A parametrized order-parameter model yields the equation of state, spinodal boundaries, and surface tension for the first-order QCD phase transition.

  4. Testing the effective action approach to bubble nucleation in holography

    hep-th 2025-07 conditional novelty 5.0 of 10

    A two-derivative holographic effective action reproduces critical bubble solutions from the full gravity theory to within a few percent across thin-wall and thick-wall regimes.

  5. The effect of charm quark on the QCD chiral phase diagram

    hep-ph 2026-03 conditional novelty 4.0 of 10

    Adding a dynamical charm quark moves the predicted QCD critical endpoint from (102.9 MeV, 618.8 MeV) to (104.3 MeV, 600.1 MeV).

  6. Exploring the QCD phase diagram through correlations and fluctuations

    nucl-th 2025-12 accept novelty 3.0 of 10

    A synthesis of the QCD critical point search: theoretical estimates cluster at T_C≈100–120 MeV, μ_B≈550–650 MeV, and BES-II cumulant data match non-critical baselines above 10 GeV while 7.7–9 GeV deviations remain une...

Reference graph

Works this paper leans on

89 extracted references · 4 canonical work pages · cited by 6 Pith papers

  1. [1]

    Vuorinen, Particle-theory Input for Neutron- star Physics, Acta Phys

    A. Vuorinen, Particle-theory Input for Neutron- star Physics, Acta Phys. Polon. B 55, 4 (2024), arXiv:2405.01141 [hep-ph]

    arXiv 2024

  2. [2]

    L. Du, A. Sorensen, and M. Stephanov, The QCD phase diagram and Beam Energy Scan physics: A theory overview, Int. J. Mod. Phys. E 33, 2430008 (2024), arXiv:2402.10183 [nucl-th]

    arXiv 2024

  3. [3]

    J¨ arvinen and E

    M. J¨ arvinen and E. Kiritsis, Holographic Models for QCD in the Veneziano Limit, JHEP 03, 002, arXiv:1112.1261 [hep-ph]

    arXiv

  4. [4]

    Demircik, C

    T. Demircik, C. Ecker, and M. J¨ arvinen, Dense and Hot QCD at Strong Coupling, Phys. Rev. X 12, 041012 (2022), arXiv:2112.12157 [hep-ph]

    arXiv 2022

  5. [5]

    J¨ arvinen, Holographic modeling of nuclear matter and neutron stars, Eur

    M. J¨ arvinen, Holographic modeling of nuclear matter and neutron stars, Eur. Phys. J. C 82, 282 (2022), arXiv:2110.08281 [hep-ph]

    arXiv 2022

  6. [6]

    Hoyos, N

    C. Hoyos, N. Jokela, and A. Vuorinen, Holographic ap- proach to compact stars and their binary mergers, Prog. Part. Nucl. Phys. 126, 103972 (2022), arXiv:2112.08422 [hep-th]

    arXiv 2022

  7. [7]

    H. T. Cromartie et al. (NANOGrav), Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar, Nature Astron. 4, 72 (2019), arXiv:1904.06759 [astro-ph.HE]

    arXiv 2019

  8. [8]

    Fonseca et al., Refined Mass and Geometric Measure- ments of the High-mass PSR J0740+6620, Astrophys

    E. Fonseca et al., Refined Mass and Geometric Measure- ments of the High-mass PSR J0740+6620, Astrophys. J. Lett. 915, L12 (2021), arXiv:2104.00880 [astro-ph.HE]

    arXiv 2021

Show all 89 references
  1. [9]

    T. E. Riley et al., A N ICERView of PSR J0030+0451: Millisecond Pulsar Parameter Estimation, Astrophys. J. Lett. 887, L21 (2019), arXiv:1912.05702 [astro-ph.HE]. 7

    2019 arXiv

  2. [10]

    M. C. Miller et al. , PSR J0030+0451 Mass and Radius from N ICERData and Implications for the Properties of Neutron Star Matter, Astrophys. J. Lett. 887, L24 (2019), arXiv:1912.05705 [astro-ph.HE]

    2019 arXiv

  3. [11]

    T. E. Riley et al. , A NICER View of the Massive Pul- sar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy, Astrophys. J. Lett. 918, L27 (2021), arXiv:2105.06980 [astro-ph.HE]

    2021 arXiv

  4. [12]

    B. P. Abbott et al. (LIGO Scientific, Virgo), GW170817: Measurements of neutron star radii and equation of state, Phys. Rev. Lett. 121, 161101 (2018), arXiv:1805.11581 [gr-qc]

    2018 arXiv

  5. [13]

    J. M. Lattimer, Neutron Stars and the Nuclear Matter Equation of State, Ann. Rev. Nucl. Part. Sci. 71, 433 (2021)

    2021

  6. [14]

    A. M. Halasz, A. D. Jackson, R. E. Shrock, M. A. Stephanov, and J. J. M. Verbaarschot, On the phase diagram of QCD, Phys. Rev. D 58, 096007 (1998), arXiv:hep-ph/9804290

    1998 arXiv

  7. [15]

    Jokela, M

    N. Jokela, M. J¨ arvinen, and J. Remes, Holographic QCD in the Veneziano limit and neutron stars, JHEP 03, 041, arXiv:1809.07770 [hep-ph]

    arXiv

  8. [16]

    Jokela, M

    N. Jokela, M. J¨ arvinen, and J. Remes, Holographic QCD in the NICER era, Phys. Rev. D 105, 086005 (2022), arXiv:2111.12101 [hep-ph]

    2022 arXiv

  9. [17]

    Jokela, M

    N. Jokela, M. J¨ arvinen, G. Nijs, and J. Remes, Unified weak and strong coupling framework for nuclear mat- ter and neutron stars, Phys. Rev. D 103, 086004 (2021), arXiv:2006.01141 [hep-ph]

    2021 arXiv

  10. [18]

    Lovato et al

    A. Lovato et al. , Long Range Plan: Dense matter the- ory for heavy-ion collisions and neutron stars, (2022), arXiv:2211.02224 [nucl-th]

    2022 arXiv

  11. [19]

    P. J. Gunkel and C. S. Fischer, Locating the critical end- point of QCD: Mesonic backcoupling effects, Phys. Rev. D 104, 054022 (2021), arXiv:2106.08356 [hep-ph]

    2021 arXiv

  12. [20]

    W.-j. Fu, J. M. Pawlowski, and F. Rennecke, QCD phase structure at finite temperature and density, Phys. Rev. D 101, 054032 (2020), arXiv:1909.02991 [hep-ph]

    2020 arXiv

  13. [21]

    Gao and J

    F. Gao and J. M. Pawlowski, Chiral phase structure and critical end point in QCD, Phys. Lett. B 820, 136584 (2021), arXiv:2010.13705 [hep-ph]

    2021 arXiv

  14. [22]

    Buballa, NJL model analysis of quark matter at large density, Phys

    M. Buballa, NJL model analysis of quark matter at large density, Phys. Rept. 407, 205 (2005), arXiv:hep- ph/0402234

    2005

  15. [23]

    Roessner, C

    S. Roessner, C. Ratti, and W. Weise, Polyakov loop, di- quarks and the two-flavour phase diagram, Phys. Rev. D 75, 034007 (2007), arXiv:hep-ph/0609281

    2007 arXiv

  16. [24]

    Costa, M

    P. Costa, M. C. Ruivo, and C. A. de Sousa, Ther- modynamics and critical behavior in the Nambu-Jona- Lasinio model of QCD, Phys. Rev. D 77, 096001 (2008), arXiv:0801.3417 [hep-ph]

    2008 arXiv

  17. [25]

    Steinheimer, M

    J. Steinheimer, M. Omana Kuttan, T. Reichert, Y. Nara, and M. Bleicher, Predicting the QCD critical point and EoS from combining HIC and neutron star observations, (2025), arXiv:2501.12849 [hep-ph]

    2025 arXiv

  18. [26]

    Fujimoto, K

    Y. Fujimoto, K. Fukushima, and K. Murase, Mapping neutron star data to the equation of state using the deep neural network, Phys. Rev. D 101, 054016 (2020), arXiv:1903.03400 [nucl-th]

    2020 arXiv

  19. [27]

    Carvalho, M

    V. Carvalho, M. Ferreira, T. Malik, and C. Providˆ encia, Decoding neutron star observations: Revealing compo- sition through Bayesian neural networks, Phys. Rev. D 108, 043031 (2023), arXiv:2306.06929 [nucl-th]

    2023 arXiv

  20. [28]

    Di Clemente, M

    F. Di Clemente, M. Scialpi, and M. Bejger, Explainable autoencoder for neutron star dense matter parameter estimation, Mach. Learn. Sci. Tech. 6, 025044 (2025), arXiv:2501.15222 [physics.comp-ph]

    2025 arXiv

  21. [29]

    R. Li, S. Han, Z. Lin, L. Wang, K. Zhou, and S. Shi, Toward constraining QCD phase transitions in neu- tron star interiors: Bayesian inference with a Tolman- Oppenheimer-Volkof linear response analysis, Phys. Rev. D 111, 074026 (2025), arXiv:2501.15810 [nucl-th]

    2025 arXiv

  22. [30]

    Bigazzi, R

    F. Bigazzi, R. Casero, A. L. Cotrone, E. Kiritsis, and A. Paredes, Non-critical holography and four- dimensional CFT’s with fundamentals, JHEP 10, 012, arXiv:hep-th/0505140

    arXiv

  23. [31]

    Casero, E

    R. Casero, E. Kiritsis, and A. Paredes, Chiral symme- try breaking as open string tachyon condensation, Nucl. Phys. B 787, 98 (2007), arXiv:hep-th/0702155

    2007 arXiv

  24. [32]

    G¨ ursoy and E

    U. G¨ ursoy and E. Kiritsis, Exploring improved holo- graphic theories for QCD: Part I, JHEP 02, 032, arXiv:0707.1324 [hep-th]

    arXiv

  25. [33]

    G¨ ursoy, E

    U. G¨ ursoy, E. Kiritsis, and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 02, 019, arXiv:0707.1349 [hep-th]

    arXiv

  26. [34]

    G¨ ursoy, E

    U. G¨ ursoy, E. Kiritsis, L. Mazzanti, and F. Nitti, Im- proved Holographic Yang-Mills at Finite Temperature: Comparison with Data, Nucl. Phys. B 820, 148 (2009), arXiv:0903.2859 [hep-th]

    2009 arXiv

  27. [35]

    Panero, Thermodynamics of the QCD plasma and the large-N limit, Phys

    M. Panero, Thermodynamics of the QCD plasma and the large-N limit, Phys. Rev. Lett. 103, 232001 (2009), arXiv:0907.3719 [hep-lat]

    2009 arXiv

  28. [36]

    However, their impact is subleading compared to other error sources, and their correlated systematic nature makes consistent probabilistic treatment challeng- ing

    Ideally, one would also sample over lattice QCD uncer- tainties. However, their impact is subleading compared to other error sources, and their correlated systematic nature makes consistent probabilistic treatment challeng- ing

  29. [37]

    Ishii, M

    T. Ishii, M. J¨ arvinen, and G. Nijs, Cool baryon and quark matter in holographic QCD, JHEP 07, 003, arXiv:1903.06169 [hep-ph]

    1903 arXiv

  30. [38]

    Ecker, M

    C. Ecker, M. J¨ arvinen, G. Nijs, and W. van der Schee, Gravitational waves from holographic neutron star merg- ers, Phys. Rev. D 101, 103006 (2020), arXiv:1908.03213 [astro-ph.HE]

    2020 arXiv

  31. [39]

    Hempel and J

    M. Hempel and J. Schaffner-Bielich, Statistical Model for a Complete Supernova Equation of State, Nucl. Phys. A 837, 210 (2010), arXiv:0911.4073 [nucl-th]

    2010 arXiv

  32. [40]

    Typel, M

    S. Typel, M. Oertel, and T. Kl¨ ahn, CompOSE Comp- Star online supernova equations of state harmonis- ing the concert of nuclear physics and astrophysics compose.obspm.fr, Phys. Part. Nucl. 46, 633 (2015), arXiv:1307.5715 [astro-ph.SR]

    2015 arXiv

  33. [41]

    Typel et al

    S. Typel et al. (CompOSE Core Team), CompOSE Reference Manual, Eur. Phys. J. A 58, 221 (2022), arXiv:2203.03209 [astro-ph.HE]

    2022 arXiv

  34. [42]

    Moller, J

    P. Moller, J. R. Nix, and K. L. Kratz, NU- CLEAR PROPERTIES FOR ASTROPHYSICAL AND RADIOACTIVE-ION-BEAM APPLICATIONS, Atom. Data Nucl. Data Tabl. 66, 131 (1997), arXiv:nucl- th/9601043

    1997

  35. [43]

    A. W. Steiner, M. Hempel, and T. Fischer, Core-collapse supernova equations of state based on neutron star ob- servations, Astrophys. J.774, 17 (2013), arXiv:1207.2184 [astro-ph.SR]

    2013 arXiv

  36. [44]

    The two models agree well across their overlapping density range

    We model the low-density regime using the SFHo EOS instead of the commonly used Baym–Pethick– Sutherland (BPS) EOS [87] because SFHo includes a 8 finite-temperature extension, which we adopt in the full hybrid framework. The two models agree well across their overlapping density range

  37. [45]

    Annala, T

    E. Annala, T. Gorda, A. Kurkela, J. N¨ attil¨ a, and A. Vuorinen, Evidence for quark-matter cores in mas- sive neutron stars, Nature Phys. 16, 907 (2020), arXiv:1903.09121 [astro-ph.HE]

    2020 arXiv

  38. [46]

    P. M. Chesler, N. Jokela, A. Loeb, and A. Vuori- nen, Finite-temperature Equations of State for Neu- tron Star Mergers, Phys. Rev. D 100, 066027 (2019), arXiv:1906.08440 [astro-ph.HE]

    2019 arXiv

  39. [47]

    Due to the mean-field character of the potential term in the vdW interactions, it enters additively and is under- stood to be included in the difference between fex and fcold

  40. [48]

    Drischler, S

    C. Drischler, S. Han, J. M. Lattimer, M. Prakash, S. Reddy, and T. Zhao, Limiting masses and radii of neutron stars and their implications, Phys. Rev. C 103, 045808 (2021), arXiv:2009.06441 [nucl-th]

    2021 arXiv

  41. [49]

    Gorda, O

    T. Gorda, O. Komoltsev, and A. Kurkela, Ab-initio QCD Calculations Impact the Inference of the Neutron-star- matter Equation of State, Astrophys. J. 950, 107 (2023), arXiv:2204.11877 [nucl-th]

    2023 arXiv

  42. [50]

    Demorest, T

    P. Demorest, T. Pennucci, S. Ransom, M. Roberts, and J. Hessels, Shapiro Delay Measurement of A Two Solar Mass Neutron Star, Nature 467, 1081 (2010), arXiv:1010.5788 [astro-ph.HE]

    2010 arXiv

  43. [51]

    M. C. Miller et al., The Radius of PSR J0740+6620 from NICER and XMM-Newton Data, Astrophys. J. Lett. 918, L28 (2021), arXiv:2105.06979 [astro-ph.HE]

    2021 arXiv

  44. [52]

    Antoniadis et al

    J. Antoniadis et al. , A Massive Pulsar in a Com- pact Relativistic Binary, Science 340, 6131 (2013), arXiv:1304.6875 [astro-ph.HE]

    2013 arXiv

  45. [53]

    Saffer et al

    A. Saffer et al. , A Lower Mass Estimate for PSR J0348+0432 Based on CHIME/Pulsar Precision Timing, Astrophys. J. Lett. 983, L20 (2025), arXiv:2412.02850 [astro-ph.HE]

    2025 arXiv

  46. [54]

    E. S. Fraga, A. Kurkela, and A. Vuorinen, Interacting Quark Matter Equation of State for Compact Stars, As- trophys. J. Lett. 781, L25 (2014), arXiv:1311.5154 [nucl- th]

    2014 arXiv

  47. [55]

    Gorda, A

    T. Gorda, A. Kurkela, R. Paatelainen, S. S¨ appi, and A. Vuorinen, Soft Interactions in Cold Quark Matter, Phys. Rev. Lett. 127, 162003 (2021), arXiv:2103.05658 [hep-ph]

    2021 arXiv

  48. [56]

    Gorda, R

    T. Gorda, R. Paatelainen, S. S¨ appi, and K. Sepp¨ anen, Equation of State of Cold Quark Matter to O(α3 s ln αs), Phys. Rev. Lett. 131, 181902 (2023), arXiv:2307.08734 [hep-ph]

    2023 arXiv

  49. [57]

    Gorda, O

    T. Gorda, O. Komoltsev, A. Kurkela, and A. Mazeli- auskas, Bayesian uncertainty quantification of perturba- tive QCD input to the neutron-star equation of state, JHEP 06, 002, arXiv:2303.02175 [hep-ph]

    arXiv

  50. [58]

    At densities above ∼ 17n0, this criterion would begin to constrain the parameter W0 from below

    While the precise pQCD criterion of [88] is generally not satisfied at high densities, our model remains consistent with it at lower densities. At densities above ∼ 17n0, this criterion would begin to constrain the parameter W0 from below. However, at such high densities, the ...

  51. [59]

    Ecker and L

    C. Ecker and L. Rezzolla, Impact of large-mass con- straints on the properties of neutron stars, Mon. Not. Roy. Astron. Soc. 519, 2615 (2022), arXiv:2209.08101 [astro-ph.HE]

    2022 arXiv

  52. [60]

    Altiparmak, C

    S. Altiparmak, C. Ecker, and L. Rezzolla, On the sound speed in neutron stars, The Astrophysical Journal Letters 939, L34 (2022)

    2022

  53. [61]

    Fujimoto, K

    Y. Fujimoto, K. Fukushima, S. Kamata, and K. Murase, Uncertainty quantification in the machine-learning infer- ence from neutron star probability distribution to the equation of state, Phys. Rev. D 110, 034035 (2024), arXiv:2401.12688 [nucl-th]

    2024 arXiv

  54. [62]

    Fujimoto, K

    Y. Fujimoto, K. Fukushima, L. D. McLerran, and M. Praszalowicz, Trace Anomaly as Signature of Confor- mality in Neutron Stars, Phys. Rev. Lett. 129, 252702 (2022), arXiv:2207.06753 [nucl-th]

    2022 arXiv

  55. [63]

    Marczenko, L

    M. Marczenko, L. McLerran, K. Redlich, and C. Sasaki, Reaching percolation and conformal limits in neutron stars, Phys. Rev. C107, 025802 (2023), arXiv:2207.13059 [nucl-th]

    2023 arXiv

  56. [64]

    Annala, T

    E. Annala, T. Gorda, J. Hirvonen, O. Komoltsev, A. Kurkela, J. N¨ attil¨ a, and A. Vuorinen, Strongly in- teracting matter exhibits deconfined behavior in mas- sive neutron stars, Nature Commun. 14, 8451 (2023), arXiv:2303.11356 [astro-ph.HE]

    2023 arXiv

  57. [65]

    Musolino, C

    C. Musolino, C. Ecker, and L. Rezzolla, On the Max- imum Mass and Oblateness of Rotating Neutron Stars with Generic Equations of State, Astrophys. J. 962, 61 (2024), arXiv:2307.03225 [gr-qc]

    2024 arXiv

  58. [66]

    I. Tews, T. Kr¨ uger, K. Hebeler, and A. Schwenk, Neu- tron matter at next-to-next-to-next-to-leading order in chiral effective field theory, Phys. Rev. Lett. 110, 032504 (2013), arXiv:1206.0025 [nucl-th]

    2013 arXiv

  59. [67]

    Hebeler, J

    K. Hebeler, J. M. Lattimer, C. J. Pethick, and A. Schwenk, Equation of state and neutron star prop- erties constrained by nuclear physics and observation, Astrophys. J. 773, 11 (2013), arXiv:1303.4662 [astro- ph.SR]

    2013 arXiv

  60. [68]

    B. P. Abbott et al. (LIGO Scientific, Virgo, Fermi- GBM, INTEGRAL), Gravitational Waves and Gamma- rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A, Astrophys. J. Lett. 848, L13 (2017), arXiv:1710.05834 [astro-ph.HE]

    2017 arXiv

  61. [69]

    S. J. Magnall, C. Ecker, L. Rezzolla, P. D. Lasky, and S. R. Goode, Physics-Informed Priors Improve Gravitational-Wave Constraints on Neutron-Star Matter, (2025), arXiv:2504.21526 [astro-ph.HE]

    2025 arXiv

  62. [70]

    Borsanyi, Z

    S. Borsanyi, Z. Fodor, J. N. Guenther, R. Kara, S. D. Katz, P. Parotto, A. Pasztor, C. Ratti, and K. K. Szabo, QCD Crossover at Finite Chemical Potential from Lat- tice Simulations, Phys. Rev. Lett. 125, 052001 (2020), arXiv:2002.02821 [hep-lat]

    2020 arXiv

  63. [71]

    Bazavov et al

    A. Bazavov et al. (HotQCD), Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795, 15 (2019), arXiv:1812.08235 [hep-lat]

    2019 arXiv

  64. [72]

    Lysenko, M

    A. Lysenko, M. I. Gorenstein, R. Poberezhniuk, and V. Vovchenko, Chemical freeze-out curve in heavy-ion collisions and the QCD critical point, Phys. Rev. C 111, 054903 (2025), arXiv:2408.06473 [nucl-th]

    2025 arXiv

  65. [73]

    Basar, QCD critical point, Lee-Yang edge singulari- ties, and Pad´ e resummations, Phys

    G. Basar, QCD critical point, Lee-Yang edge singulari- ties, and Pad´ e resummations, Phys. Rev. C110, 015203 (2024), arXiv:2312.06952 [hep-th]

    2024 arXiv

  66. [74]

    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 approxi- mations, (2024), arXiv:2405.10196 [hep-lat]. 9

    2024 arXiv

  67. [75]

    H. Shah, M. Hippert, J. Noronha, C. Ratti, and V. Vovchenko, Locating the QCD critical point from first principles through contours of constant entropy density, (2024), arXiv:2410.16206 [hep-ph]

    2024

  68. [76]

    Jokela, M

    N. Jokela, M. J¨ arvinen, and A. Piispa, Refining holo- graphic models of the quark-gluon plasma, Phys. Rev. D 110, 126013 (2024), arXiv:2405.02394 [hep-th]

    2024 arXiv

  69. [77]

    Kovensky and A

    N. Kovensky and A. Schmitt, Isospin asymmetry in holo- graphic baryonic matter, SciPost Phys. 11, 029 (2021), arXiv:2105.03218 [hep-ph]

    2021 arXiv

  70. [78]

    Bartolini and S

    L. Bartolini and S. B. Gudnason, Symmetry energy in holographic QCD, SciPost Phys. 16, 156 (2024), arXiv:2209.14309 [hep-ph]

    2024 arXiv

  71. [79]

    Bartolini, S

    L. Bartolini, S. B. Gudnason, and M. J¨ arvinen, Isospin asymmetry and neutron stars in holographic QCD in the Veneziano limit, Phys. Rev. D 111, 106021 (2025), arXiv:2504.01758 [hep-ph]

    2025

  72. [80]

    Ecker, K

    C. Ecker, K. Topolski, M. J¨ arvinen, and A. Stehr, Prompt black hole formation in binary neutron star mergers, Phys. Rev. D 111, 023001 (2025), arXiv:2402.11013 [astro-ph.HE]

    2025 arXiv

  73. [81]

    Tootle, C

    S. Tootle, C. Ecker, K. Topolski, T. Demircik, M. J¨ arvinen, and L. Rezzolla, Quark formation and phe- nomenology in binary neutron-star mergers using V- QCD, SciPost Phys. 13, 109 (2022), arXiv:2205.05691 [astro-ph.HE]

    2022 arXiv

  74. [82]

    Hoyos, N

    C. Hoyos, N. Jokela, M. J¨ arvinen, J. G. Subils, J. Tar- rio, and A. Vuorinen, Transport in strongly coupled quark matter, Phys. Rev. Lett. 125, 241601 (2020), arXiv:2005.14205 [hep-th]

    2020 arXiv

  75. [83]

    Hoyos, N

    C. Hoyos, N. Jokela, M. J¨ arvinen, J. G. Subils, J. Tarrio, and A. Vuorinen, Holographic approach to transport in dense QCD matter, Phys. Rev. D 105, 066014 (2022), arXiv:2109.12122 [hep-th]

    2022 arXiv

  76. [84]

    Cruz Rojas, T

    J. Cruz Rojas, T. Gorda, C. Hoyos, N. Jokela, M. J¨ arvinen, A. Kurkela, R. Paatelainen, S. S¨ appi, and A. Vuorinen, Estimate for the Bulk Viscosity of Strongly Coupled Quark Matter Using Perturbative QCD and Holography, Phys. Rev. Lett. 133, 071901 (2024), arXiv:2402.00621 [hep-ph]

    2024 arXiv

  77. [85]

    Cruz Rojas, T

    J. Cruz Rojas, T. Demircik, and M. J¨ arvinen, Modu- lated instabilities and the AdS2 point in dense holo- graphic matter, Phys. Rev. D 111, 046017 (2025), arXiv:2405.02399 [hep-th]

    2025 arXiv

  78. [86]

    Demircik, N

    T. Demircik, N. Jokela, M. Jarvinen, and A. Piispa, Is holographic quark-gluon plasma homogeneous?, (2024), arXiv:2405.02392 [hep-ph]

    2024 arXiv

  79. [87]

    G. Baym, C. Pethick, and P. Sutherland, The Ground State of Matter at High Densities: Equation of State and Stellar Models, Astrophys. J. 170, 299 (1971)

    1971

  80. [88]

    Komoltsev and A

    O. Komoltsev and A. Kurkela, How Perturbative QCD Constrains the Equation of State at Neutron- Star Densities, Phys. Rev. Lett. 128, 202701 (2022), arXiv:2111.05350 [nucl-th]

    2022 arXiv

  81. [89]

    Kurkela, P

    A. Kurkela, P. Romatschke, and A. Vuorinen, Cold Quark Matter, Phys. Rev. D 81, 105021 (2010), arXiv:0912.1856 [hep-ph]

    2010 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.