Pith. sign in

REVIEW 3 major objections 4 minor 35 references

Phase and equation of state of finite density QC$_2$D at lower temperature

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read Dense two-color QCD at low temperature breaks the relativistic speed-of-sound bound.

desk verdict A useful T=40 MeV update that sharpens the conformal-bound signal, but the thermodynamic inconsistency the authors admit in the BCS phase keeps the central claim from being solid. read the letter →

arxiv 2412.18825 v1 pith:GCXWXW72 submitted 2024-12-25 hep-lat hep-phnucl-th

Etsuko Itou , Kei Iida , Kotaro Murakami , Daiki Suenaga This is my paper · ORCID
classification hep-lathep-phnucl-th
keywords two-colorQCDlatticeequationofstatespeedsoundconformalboundsuperfluidphasechemicalpotentialtopologicalsusceptibility
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 uses lattice simulations of dense two-color QCD at $T = 40$ MeV and $T = 80$ MeV to establish the phase diagram and equation of state below the pseudo-critical temperature, and specifically to confirm that in the BCS superfluid phase the squared speed of sound exceeds the relativistic conformal bound $c_s^2/c^2 = 1/3$. Breaking that bound matters because it indicates that dense QCD-like matter can be stiffer than a free relativistic gas, a property with direct consequences for neutron-star equations of state. The $T = 40$ MeV run, on a $32^4$ lattice, sharpens earlier $T = 80$ MeV results: the hadronic-matter phase shrinks, the diquark condensate approaches the weak-coupling $\mu^2$ scaling, and smaller statistical errors make the conformal-bound violation clearer. The paper also reports that its BCS-phase pressure data do not satisfy the thermodynamic identity of Eq. (7), a discrepancy it attributes to finite-volume effects and to the pressure definition having 'some room for discussion' (Eq. (4)).

What carries the argument

The central object is the squared speed of sound, $c_s^2(\mu)/c^2 = \Delta p(\mu)/\Delta e(\mu)$ (Eq. (10)), a finite-difference ratio of the pressure defined in Eq. (4) to the energy density obtained from the trace anomaly in Eq. (5). The reference line it is compared against is the conformal bound $c_s^2/c^2 = 1/3$, the value for a non-interacting relativistic gas. The lattice action adds a diquark source term with strength $j$, so the superfluid region can be simulated and observables are extrapolated to $j \to 0$; phase identification uses the diquark condensate $\langle qq \rangle$, the Polyakov loop, and the quark number density. The thermodynamic identity $d(p/\mu^4)/d\mu = (e-3p)/\mu^5$ (Eq. (7)) is the consistency relation that the BCS-phase data fail, which the paper attributes to finite-volume effects and the pressure definition; the conformal-bound claim therefore rests on whether the ratio $\Delta p/\Delta e$ is robust to those same distortions.

What would settle it

Take the $T = 40$ MeV calculation to a larger spatial volume (for example $48^4$ or $64^4$) and include the third term in Eq. (5); if the trace anomaly then changes sign in the BCS phase while $p/\mu^4$ keeps rising, the speed of sound from Eq. (10) could drop below $1/3$, and the claimed conformal-bound breaking would be exposed as a finite-volume artifact. If, instead, $c_s^2/c^2 > 1/3$ persists after the continuum extrapolation, the claim stands.

Watch

Extended reading notes

Core claim

The paper's central claim is that the squared speed of sound in dense two-color QCD, evaluated from the finite-difference ratio $\Delta p/\Delta e$ at fixed temperature, rises through hadronic and BEC phases and then exceeds the conformal bound $c_s^2/c^2 = 1/3$ in the BCS phase. At $T = 40$ MeV the statistical errors are small enough that the violation is confirmed rather than merely indicated, and the same data respect the recently proposed upper bound $c_s^2/c^2 < 0.781$. Around the BEC region, pressure and energy density follow chiral perturbation theory, with fitted pion decay constants $F = 51.1(5)$ MeV (from $p$) and $F = 56.7(7)$ MeV (from $e$), close to an earlier value of $F = 60.8(1.6)$ MeV. The paper further argues that confinement persists into the BCS phase, since the topological susceptibility stays almost $\mu$-independent while the pressure rises, and that the diquark condensate in the BCS phase approaches the zero-temperature weak-coupling $\langle qq \rangle \propto \mu^2$ behavior. The authors note that their BCS data violate the thermodynamic relation $d(p/\mu^4)/d\mu = (e-3p)/\mu^5$, attributing this to finite-volume effects and to the pressure definition.

Load-bearing premise

The argument assumes that finite-volume distortions and the omitted third term in the trace anomaly leave the ratio $\Delta p/\Delta e$ essentially unchanged in the BCS phase, even though the same data violate the exact thermodynamic relation $d(p/\mu^4)/d\mu = (e-3p)/\mu^5$ that the paper itself quotes as Eq. (7).

Editorial extensions

If this is right

  • If the claim survives, dense two-color QCD is a first-principles example of matter stiffer than a free relativistic gas, showing that the conformal bound is not a universal ceiling for dense QCD-like theories.
  • Independent lattice results in three-color QCD with isospin chemical potential are reported to show the same violation, so the effect may be generic to dense superfluid QCD matter rather than specific to two colors.
  • A squared sound speed above $1/3$ supports stiff equations of state for dense matter, consistent with phenomenological constraints from neutron-star observations and with higher maximum neutron-star masses.
  • The BEC-phase fits to chiral perturbation theory yield a lattice estimate of the pion decay constant $F \approx 51$–$57$ MeV, compatible with the earlier value $60.8$ MeV, and thereby anchor the equation of state at low density.
  • The near-$\mu$-independence of the topological susceptibility in the superfluid phases indicates that confining gluonic dynamics persists even at high density, so the system cannot be described as a free quark gas even where $\langle qq \rangle$ and the pressure are large.

Reading between the lines

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

  • Editorial inference: if the conformal-bound violation survives the continuum and thermodynamic limits, the same $\Delta p/\Delta e$ method applied to three-color isospin QCD should produce a plateau above $1/3$ at comparable densities; a common plateau would point to pairing or superfluidity as the stiffening mechanism.
  • Editorial inference: the paper's own failure of Eq. (7) in the BCS phase offers a direct adjudication path — recompute $c_s^2$ with an improved pressure definition and with the third term of Eq. (5) included; if the trace anomaly then keeps its sign while $p/\mu^4$ rises, the violation could be a finite-volume artifact.
  • Editorial inference: the $\mu^2$ scaling of $\langle qq \rangle$ at $T = 40$ MeV implies a nearly $\mu$-independent diquark gap $\Delta(\mu)$; a direct measurement of $\Delta(\mu)$ would test whether the stiffening tracks the pairing gap across the BCS phase.
  • Editorial inference: the shrinking hadronic-matter phase as $T$ decreases from 80 to 40 MeV suggests that the nonzero quark number density there comes from thermal excitation of the lightest diquark; a spectral-function study of the diquark channel near $\mu \simeq m_{PS}/2$ could test this directly.
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

3 major / 4 minor

Summary. This manuscript reports lattice simulations of two-color QCD with two flavors of Wilson fermions at beta=0.80, kappa=0.159 on 32^4 (T=40 MeV), 16^4 (T=80 MeV), and 32^3 x 8 (T=160 MeV) lattices. It presents a phase diagram separating hadronic, BEC, BCS, and QGP phases using the Polyakov loop, the diquark condensate, and the quark number density; it then constructs the equation of state through Eqs. (4) and (5) and the speed of sound through Eq. (10). The central claim is that in the BCS phase, especially at T=40 MeV, the squared speed of sound exceeds the conformal bound c_s^2/c^2=1/3, and that this is accompanied by a negative trace anomaly. The paper also reports the topological susceptibility, ChPT fits for the BEC phase, and comparisons with related lattice, model, and neutron-star studies.

Significance. If established, the observation c_s^2>1/3 in dense two-color QCD would be a nontrivial first-principles result with direct relevance to the stiffness of dense QCD-like matter and to neutron-star phenomenology. The new T=40 MeV data set with smaller statistical errors is a useful addition, and the consistency of the BEC-phase pressure and energy density with the ChPT forms (Eqs. (8)-(9)) is a genuine cross-check. The authors are also transparent in reporting the thermodynamic-identity check (Eq. (7)) that reveals a systematic problem in the BCS phase. However, because the central claim is built on exactly the pressure and trace-anomaly data that fail that check, the claim is not yet established beyond systematic ambiguity.

major comments (3)
  1. [§3, Eq. (7) and Fig. 5] The paper's own data violate the thermodynamic identity in the BCS phase, which is precisely the region where the conformal bound is claimed to be exceeded. At zero temperature Eq. (7) requires d(p/mu^4)/dmu = (e-3p)/mu^5; at the fixed nonzero temperatures used here the exact relation is d(p/mu^4)/dmu = (e-3p-Ts)/mu^5 with entropy density s>=0. A positive left-hand side therefore requires e-3p >= Ts > 0, yet the right panel of Fig. 3 shows a negative trace anomaly in the BCS phase while the left panel shows p/mu^4 increasing monotonically. Since c_s^2 in Eq. (10) is the slope of p versus e, any systematic suppression of Delta e from the neglected third term in Eq. (5), from finite-volume effects, or from the 'room for discussion' in Eq. (4) will directly inflate Delta p/Delta e. The attribution to finite-volume effects is not supported by any volume-scaling analysis or by a comparison of the two lattice volumes. Thus the statement in Section 3 that the conformal bound is 'clearly exceeded' is not quantitatively established by the present analysis.
  2. [§3, Eq. (5)] The third term in the trace anomaly, proportional to a d j / d a times (dS/dj), is neglected without a numerical estimate. In the BCS phase the diquark condensate is nonzero, so the j-dependence of the action is not expected to vanish identically. If this term contributes with the opposite sign and sufficient magnitude, it could remove or reduce the negative trace anomaly that underlies the claimed violation of the conformal bound. The authors should either provide a numerical evaluation of the dS/dj term from their existing j-dependence data or give a quantitative argument for why it is negligible in the BCS region.
  3. [§3, Eq. (10) and Fig. 5] The speed-of-sound result is presented at a single lattice spacing and a single spatial volume for each temperature, with no continuum extrapolation and no finite-volume scaling. Given that finite-volume effects are explicitly invoked in the same section to explain the violation of Eq. (7), it is essential to show that those effects do not also move c_s^2 below 1/3. Without such a check, the 'confirmation' of the conformal-bound violation at T=40 MeV rests on unquantified systematic uncertainties in exactly the region where the thermodynamic inconsistency is largest.
minor comments (4)
  1. [Abstract and §2] The superscripts are lost in several places: '324 lattice', '164 lattice', and '323 x 8' should be written as 32^4, 16^4, and 32^3 x 8 for clarity.
  2. [Fig. 3 and caption] The right panel plots the first and second terms of Eq. (5) separately, but the caption says '- (e-3p)_f / mu^4'. Please clarify whether the plotted fermionic contribution already includes the sign flip, and define the symbols in the caption.
  3. [§3, text after Eq. (9)] The sentence 'the best fit values were obtained as F = 51.1(5) MeV and F = 56.7(7) MeV from the fits of p/mu_c^4 and e/mu_c^4' would benefit from stating the fit range in mu and the number of data points used, since the two F values differ by about 10%.
  4. [References] Reference [9] contains a colloquial title ('What's up with that?!?'): this is acceptable in a proceedings, but the authors may wish to use the formal title in the bibliography.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: c_s^2 > 1/3 is a direct lattice measurement; the acknowledged thermodynamic inconsistency and neglected trace-anomaly term are systematics concerns, not circular steps.

full rationale

The central claim that c_s^2 exceeds the conformal bound in the BCS phase is obtained by applying Eq. (10) to the lattice pressure from Eq. (4) and the energy density built from Eq. (5). These quantities are not defined in terms of the target result: Eq. (4) integrates the measured lattice number density relative to the Stefan-Boltzmann number density, and Eq. (5) uses nonperturbative beta-function coefficients from Ref. [20]. That reference is a separate scale-setting lattice determination by members of the same group; it is parameter-free, does not assume the conformal-bound violation, and therefore counts as independent support rather than a circular input. The ChPT comparison in the BEC phase fits F from the same p and e data, but the ChPT sound-speed curve shown in Fig. 5 depends only on mu_c, not on the fitted F, and the fit is presented as a consistency check, not as the origin of the BCS-phase violation. The paper explicitly identifies two limitations in the BCS region: it states 'Our data are inconsistent with this equation' (the thermodynamic identity Eq. 7) and 'we neglected the third term in Eq. (5) in our analysis.' These are acknowledged systematic uncertainties in the extraction of c_s^2, not cases where a prediction reduces by construction to a fitted parameter or to a self-citation chain. No step of the derivation equates an output to an input by definition. Even if the thermodynamic inconsistency weakens the claim, that is a correctness risk, not circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central conformal-bound claim rests on lattice data whose conversion to physical quantities uses same-group beta functions and relies on ChPT only for the BEC-phase fits. The most significant added assumption is the neglect of the third term in the trace anomaly and the finite-volume reliability in the BCS phase.

free parameters (3)
  • pion decay constant F (ChPT fit) = F = 51.1(5) MeV from p fit; 56.7(7) MeV from e fit
    Fitted using ChPT forms (Eqs. 8, 9) to pressure and internal energy data in the BEC phase; compared with earlier value 60.8(1.6) MeV. Not needed for the conformal-bound claim.
  • critical chemical potential mu_c/m_PS = 0.47
    Obtained from fitting the diquark condensate scaling near the superfluid transition at T=40 MeV; used to test the ChPT prediction <qq> = A(mu - mu_c)^{1/2}.
  • nonperturbative beta function coefficients at the simulation point = a d(beta)/da = -0.352, a d(kappa)/da = 0.0282
    Inputs from prior same-group calculation (Ref. [20]); used in the trace anomaly Eq. (5). Not fitted in this paper, but essential to computing e - 3p.
assumptions (4)
  • domain assumption Iwasaki gauge action plus naive Wilson fermions at (beta, kappa) = (0.80, 0.159) faithfully represents two-color QCD thermodynamics at T = 40-80 MeV.
    Section 2; the paper presents no continuum extrapolation or physical-quark-mass tuning in this proceedings.
  • domain assumption Chiral perturbation theory formulas for pressure and energy density (Eqs. 8, 9) remain valid in the BEC phase over the mu range fitted.
    Section 3; used to extract F and to produce the ChPT sound-velocity curve in Fig. 5.
  • domain assumption The nonperturbative beta function coefficients from Ref. [20] are correct at this lattice coupling.
    Section 3, Eq. (6); computed by the same group and used to convert lattice derivatives into the trace anomaly.
  • ad hoc to paper The diquark source Jacobian, the third term in Eq. (5), is negligible for the trace anomaly.
    Section 3; the paper states 'we neglected the third term in Eq. (5) in our analysis' without a numerical estimate of its size.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Phase and equation of state of finite density QC$_2$D at lower temperature." pith.science (2026). https://pith.science/paper/GCXWXW72

@misc{pith2026241218825,
  author       = {Pith},
  title        = {Pith review of: Phase and equation of state of finite density QC$_2$D at lower temperature},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GCXWXW72}},
  note         = {Machine review of arXiv:2412.18825}
}
abstract

We investigate the phase structure and the equation of state (EoS) for dense two-color QCD at low temperatures, $T = 40$ MeV ($32^4$ lattice) and $T = 80$ MeV ($16^4$ lattice). A rich phase structure below the pseudo-critical temperature $T_c$ as a function of quark chemical potential $\mu$ has been revealed. By performing $T = 40$ MeV simulations, essentially similar results to the previous ones at $T = 80$ MeV are obtained, but several finer understandings are achieved. Breaking of the conformal bound is also confirmed thanks to smaller statistical errors. This talk is mainly based on Refs.~\cite{Iida:2022hyy, Iida:2024irv}. It also includes related studies and subsequent developments that were not mentioned in the original papers.

Figures

Figures reproduced from arXiv: 2412.18825 by the authors.

Figure 1
Figure 1. Schematic QC2D phase diagram. In our previous work [10], we clarified the phase structure at 𝑇 = 160 MeV and 80 MeV, while in our recent work, we addressed what it is like at 𝑇 = 40 MeV. non-zero beyond 𝜇 ≈ 𝑚PS/2. The chiral perturbation theory (ChPT) gives the critical chemical potential as 𝜇𝑐 = 𝑚PS/2 and the scaling behavior around 𝜇𝑐 as ⟨𝑞𝑞⟩ = 𝐴(𝜇 − 𝜇𝑐) 1/2 . (1) Our data are almost consistent with these predicti… view at source ↗
Figure 2
Figure 2. The 𝜇-dependence of the topological susceptibility (red data) at 𝑇 = 160 MeV, 80 MeV, and 40 MeV. At 𝑇 = 160 MeV and 80 MeV, we also show the magnitude of the Polyakov loop (blue data) to see the confining behavior. After determining the phase diagram, we investigated the 𝜇-dependence of the topological susceptibility in Refs. [2, 10], 𝜒𝑄 = ⟨𝑄 2 ⟩ − ⟨𝑄⟩ 2 . (2) Here, 𝑄 denotes the topological charge, which we measur… view at source ↗
Figure 3
Figure 3. Pressure (left panel) and trace anomaly (right panel) as a function of 𝜇. The right panel depicts the first (circle-red symbol) and second (cross-blue symbol) terms in Eq. (5) at 𝑇 = 40 MeV separately. the other hand, we plotted the first (gluonic) term and minus the second (fermionic) term of the trace anomaly (5) at 𝑇 = 40 MeV as ⟨𝑒 − 3𝑝⟩𝑔 (circle-red symbols) and −⟨𝑒 − 3𝑝⟩𝑓 (cross-green symbols), respectively, in… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The pressure and internal energy around the BEC phase. The cyan and orange curves represent the fitting functions for 𝑝/𝜇 4 𝑐 and 𝑒/𝜇 4 𝑐 , respectively, whose forms are given by the ChPT theory as shown in Eqs. (8) and (9). If we focus on the BEC phase, on the other h…
Figure 5
Figure 5. Figure 5: The squared sound velocity at 𝑇 = 40 MeV and 𝑇 = 80 MeV. The cyan curve is the prediction of ChPT given by 𝑐 2 s /𝑐 2 = (1 − 𝜇 4 𝑐 /𝜇 4 )/(1 + 3𝜇 4 𝑐 /𝜇 4 ). The horizontal line (orange) depicts the conformal bound, 𝑐 2 s /𝑐 2 = 1/3. at fixed temperature. The predictio…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

35 extracted references · 6 canonical work pages

  1. [1]

    Iida and E

    K. Iida and E. Itou,Velocity of sound beyond the high-density relativistic limit from lattice simulation of dense two-color QCD,PTEP 2022 (2022) 111B01 [2207.01253]. 8 Phase and equation of state of finite density QC2D at lower temperature Etsuko Itou

    arXiv 2022

  2. [2]

    K. Iida, E. Itou, K. Murakami and D. Suenaga,Lattice study on finite density QC2D towards zero temperature, JHEP 10(2024) 022 [2405.20566]

    arXiv 2024

  3. [3]

    Nagata,Finite-density lattice QCD and sign problem: Current status and open problems, Prog

    K. Nagata,Finite-density lattice QCD and sign problem: Current status and open problems, Prog. Part. Nucl. Phys.127(2022) 103991 [2108.12423]

    arXiv 2022

  4. [4]

    Cherman, T.D

    A. Cherman, T.D. Cohen and A. Nellore,A Bound on the speed of sound from holography, Phys. Rev. D80(2009) 066003 [0905.0903]

    arXiv 2009

  5. [5]

    Holography and the speed of sound at high temperatures

    P.M. Hohler and M.A. Stephanov,Holography and the speed of sound at high temperatures, Phys. Rev. D80(2009) 066002 [0905.0900]

    work page Pith review arXiv 2009

  6. [6]

    Brandt, F

    B.B. Brandt, F. Cuteri and G. Endrodi,Equation of state and speed of sound of isospin-asymmetric QCD on the lattice, JHEP 07(2023) 055 [2212.14016]

    arXiv 2023

  7. [7]

    Abbott, W

    R. Abbott, W. Detmold, F. Romero-López, Z. Davoudi, M. Illa, A. Parreño et al.,Lattice quantum chromodynamics at large isospin density: 6144 pions in a box, 2307.15014

    arXiv

  8. [8]

    Abbott, W

    R. Abbott, W. Detmold, M. Illa, A. Parreño, R.J. Perry, F. Romero-López et al.,QCD constraints on isospin-dense matter and the nuclear equation of state, 2406.09273

    arXiv

Show all 35 references
  1. [9]

    Hands, S

    S. Hands, S. Kim, D. Lawlor, A. Lee-Mitchell and J.-I. Skullerud,Dense QC2D. What’s up with that?!?, 12, 2024 [2412.15872]

    2024 arXiv

  2. [10]

    K. Iida, E. Itou and T.-G. Lee,Two-colour QCD phases and the topology at low temperature and high density, JHEP 01(2020) 181 [1910.07872]

    2020 arXiv

  3. [11]

    Ishiguro, K

    K. Ishiguro, K. Iida and E. Itou,Flux tube profiles in two-color QCD at low temperature and high density, PoS LATTICE2021(2022) 063 [2111.13067]

    2022 arXiv

  4. [12]

    Murakami, D

    K. Murakami, D. Suenaga, K. Iida and E. Itou,Measurement of hadron masses in 2-color finite density QCD,PoS LATTICE2022(2023) 154 [2211.13472]

    2023 arXiv

  5. [13]

    Murakami, E

    K. Murakami, E. Itou and K. Iida,Chemical potential (in)dependence of hadron scatterings in the hadronic phase of QCD-like theories and its applications, 2309.08143

    arXiv

  6. [14]

    Schäfer,Patterns of symmetry breaking in QCD at high baryon density,Nucl

    T. Schäfer,Patterns of symmetry breaking in QCD at high baryon density,Nucl. Phys. B575 (2000) 269 [hep-ph/9909574]

    2000 arXiv

  7. [15]

    M.HanadaandN.Yamamoto, UniversalityofPhasesinQCDandQCD-likeTheories ,JHEP 02 (2012) 138 [1103.5480]

    2012 arXiv

  8. [16]

    Kanazawa, T

    T. Kanazawa, T. Wettig and N. Yamamoto,Banks-Casher-type relation for the BCS gap at high density, Eur. Phys. J. A49(2013) 88 [1211.5332]

    2013 arXiv

  9. [17]

    Hands, S

    S. Hands, S. Kim and J.-I. Skullerud,Deconfinement in dense 2-color QCD,Eur. Phys. J. C 48 (2006) 193 [hep-lat/0604004]. 9 Phase and equation of state of finite density QC2D at lower temperature Etsuko Itou

    2006 arXiv

  10. [18]

    Braguta, E.M

    V.V. Braguta, E.M. Ilgenfritz, A.Y. Kotov, A.V. Molochkov and A.A. Nikolaev,Study of the phase diagram of dense two-color QCD within lattice simulation,Phys. Rev. D94 (2016) 114510 [1605.04090]

    2016 arXiv

  11. [19]

    T. Boz, P. Giudice, S. Hands and J.-I. Skullerud,Dense two-color QCD towards continuum and chiral limits,Phys. Rev. D101 (2020) 074506 [1912.10975]

    2020 arXiv

  12. [20]

    K. Iida, E. Itou and T.-G. Lee,Relative scale setting for two-color QCD with𝑁𝑓=2 Wilson fermions, PTEP 2021(2021) 013B05 [2008.06322]

    2021 arXiv

  13. [21]

    Astrakhantsev, V.V

    N. Astrakhantsev, V.V. Braguta, E.M. Ilgenfritz, A.Y. Kotov and A.A. Nikolaev,Lattice study of thermodynamic properties of dense QC2D,Phys. Rev. D102(2020) 074507 [2007.07640]

    2020 arXiv

  14. [22]

    Masuda, T

    K. Masuda, T. Hatsuda and T. Takatsuka,Hadron–quark crossover and massive hybrid stars, PTEP 2013 (2013) 073D01 [1212.6803]

    2013 arXiv

  15. [23]

    G. Baym, T. Hatsuda, T. Kojo, P.D. Powell, Y. Song and T. Takatsuka,From hadrons to quarks in neutron stars: a review,Rept. Prog. Phys.81 (2018) 056902 [1707.04966]

    2018 arXiv

  16. [24]

    McLerran and S

    L. McLerran and S. Reddy,Quarkyonic Matter and Neutron Stars,Phys. Rev. Lett.122 (2019) 122701 [1811.12503]

    2019 arXiv

  17. [25]

    Fujimoto and K

    Y. Fujimoto and K. Fukushima,Equation of state of cold and dense QCD matter in resummed perturbation theory,Phys. Rev. D105 (2022) 014025 [2011.10891]

    2022 arXiv

  18. [26]

    Kojo,Stiffening of matter in quark-hadron continuity, Phys

    T. Kojo,Stiffening of matter in quark-hadron continuity, Phys. Rev. D104 (2021) 074005 [2106.06687]

    2021 arXiv

  19. [27]

    Kojo and D

    T. Kojo and D. Suenaga,Peaks of sound velocity in two color dense QCD: Quark saturation effects and semishort range correlations, Phys. Rev. D105 (2022) 076001 [2110.02100]

    2022 arXiv

  20. [28]

    Braun, A

    J. Braun, A. Geißel and B. Schallmo,Speed of sound in dense strong-interaction matter, 2206.06328

    arXiv

  21. [29]

    Hippert, J

    M. Hippert, J. Noronha and P. Romatschke,Upper Bound on the Speed of Sound in Nuclear Matter from Transport, 2402.14085

    arXiv

  22. [30]

    Kojo, P.D

    T. Kojo, P.D. Powell, Y. Song and G. Baym,Phenomenological QCD equation of state for massive neutron stars, Phys. Rev. D91(2015) 045003 [1412.1108]

    2015 arXiv

  23. [31]

    Leonhardt, M

    M. Leonhardt, M. Pospiech, B. Schallmo, J. Braun, C. Drischler, K. Hebeler et al., Symmetric nuclear matter from the strong interaction,Phys. Rev. Lett.125(2020) 142502 [1907.05814]

    2020 arXiv

  24. [32]

    Fujimoto,Interplay between the weak-coupling results and the lattice data in dense QCD, 2408.12514

    Y. Fujimoto,Interplay between the weak-coupling results and the lattice data in dense QCD, 2408.12514. 10 Phase and equation of state of finite density QC2D at lower temperature Etsuko Itou

    arXiv

  25. [33]

    Fukushima and S

    K. Fukushima and S. Minato,Speed of sound and trace anomaly in a unified treatment of the two-color diquark superfluid, the pion-condensed high-isospin matter, and the 2SC quark matter, 2411.03781

    arXiv

  26. [34]

    Altiparmak, C

    S. Altiparmak, C. Ecker and L. Rezzolla,On the Sound Speed in Neutron Stars,Astrophys. J. Lett. 939(2022) L34 [2203.14974]

    2022 arXiv

  27. [35]

    Annala, T

    E. Annala, T. Gorda, J. Hirvonen, O. Komoltsev, A. Kurkela, J. Nättilä et al.,Strongly interacting matter exhibits deconfined behavior in massive neutron stars,Nature Commun. 14 (2023) 8451 [2303.11356]. 11

    2023 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.