Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Quark mass dependence of a QCD critical point and structure of the Columbia plot

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Lowering light quark masses nudges QCD's critical point to higher temperature and lower chemical potential, evidence for a flat critical surface ending in a tricritical point.

desk verdict New DSE numbers for the CEP's light-quark-mass dependence, but the flat-surface/tricritical interpretation rests on a truncation whose known error is the same size as the trend; the body is honest about this, the abstract is not. read the letter →

arxiv 2507.21680 v2 pith:LEXTGYE4 submitted 2025-07-29 hep-ph hep-lat

Julian Bernhardt , Christian S. Fischer This is my paper
classification hep-phhep-lat PACS 12.38.Mh
keywords QCDcriticalpointColumbiaplotchirallimitDyson-Schwingerequationsquarkmassdependencetricriticalimaginarychemicalpotentialphasetransition
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 asks how the QCD critical point—the conjectured endpoint of a first-order transition line in the QCD phase diagram—moves as the light up/down quark masses are lowered from their physical values toward zero, with the strange quark mass held fixed. Using a truncated Dyson-Schwinger calculation at $N_f=2+1$ flavours with lattice Yang-Mills input, it finds that the critical endpoint's temperature rises only slightly (from about 112 to 115 MeV) while its baryon chemical potential falls from about 630 to 534 MeV as the pion mass drops from 140 to 55 MeV. The curvature coefficient of the pseudocritical line is positive and almost constant ($\kappa_2 \approx 0.0157$–$0.0160$), and the authors read the overall trend as evidence for a nearly flat second-order critical surface in the three-dimensional Columbia plot that extrapolates to a tricritical point near $(T,\mu_B) \approx (117, 473)$ MeV in the chiral limit. At imaginary baryon chemical potential up to $\mu_B/(\pi T) = 7/8$, the transition is a smooth crossover for every finite light-quark mass considered, so the critical surface does not extend into the finite-mass region there. If the picture holds, the physical critical point is insensitive to light-quark mass variations, while the chiral limit contains a separate tricritical singularity.

What carries the argument

The work is carried by a coupled set of Dyson-Schwinger equations for the quark propagators of the up, down and strange quarks at $N_f=2+1$, with the gluon propagator composed of quenched lattice Yang-Mills fits plus an explicitly evaluated quark loop. The dressed quark-gluon vertex is truncated to non-hadronic contributions, omitting meson-exchange diagrams; the paper notes this truncation reproduces the physical critical endpoint of the more complete scheme to within about five percent. The order parameter is the subtracted chiral condensate $\Delta_{\ell s}$ between light and strange quarks, and the chiral susceptibility $\chi_m^{\ell s}=\partial \Delta_{\ell s}/\partial m_\ell$ locates the pseudocritical temperature and its divergence at the critical point. The three-dimensional Columbia plot—the plane of light versus strange quark masses extended by a real/imaginary baryon chemical potential axis—is the organizing object, and the paper maps where its second-order critical surface and crossover hyperplane lie.

What would settle it

Repeat the same pion-mass scan with a quark-gluon vertex that includes meson-exchange diagrams and attempt a direct calculation at $m_\ell=0$; if the critical endpoint temperatures stop rising toward the chiral limit, or if no tricritical point appears near the extrapolated $(T,\mu_B)\approx(117,473)$ MeV, the flat critical surface is an artifact of the truncated vertex.

Watch

Extended reading notes

Core claim

The central claim is that the second-order critical surface containing the QCD critical endpoint is nearly flat in the direction of the light-quark mass. As $m_\pi$ is varied from 140 MeV down to 55 MeV, the critical endpoint moves from $(T,\mu_B)\approx(112,630)$ MeV to $(115,534)$ MeV: the temperature rises slowly, the chemical potential decreases, and the curvature $\kappa_2$ of the pseudocritical line stays almost constant. Extrapolating this trend linearly to $m_\ell=0$ yields a tricritical point near $(117,473)$ MeV, and the authors stress that this extrapolation should be treated cautiously because a direct chiral-limit calculation was not possible and omitted mesonic long-range degrees of freedom may become important there. At imaginary chemical potential up to $\mu_B/(\pi T)=7/8$, the chiral susceptibility is smooth for every finite light-quark mass, so the critical surface does not bend into the finite-mass region. The paper therefore supports the notion that the 3d Columbia plot has a large crossover volume bounded by a flat critical surface ending on a tricritical line in the chiral limit.

Load-bearing premise

The calculation omits meson-exchange diagrams in the quark-gluon vertex, and the authors state that these omitted long-range mesonic degrees of freedom become more important in the chiral limit; if they change the light-quark-mass dependence of the critical endpoint, the flat surface and the tricritical extrapolation could be artifacts of the truncation.

Editorial extensions

If this is right

  • At physical quark masses the critical endpoint sits near $(T,\mu_B)\approx(112,630)$ MeV, and lowering the pion mass to 55 MeV moves it to $(115,534)$ MeV, so the second-order surface in the $(T,\mu_B,m_\ell)$ space is nearly flat.
  • A linear extrapolation of the endpoint locations to $m_\ell=0$ gives a tricritical point near $(117,473)$ MeV, implying that the chiral limit of QCD has a genuine critical singularity at finite baryon chemical potential.
  • At imaginary baryon chemical potential up to $\mu_B/(\pi T)=7/8$, the chiral transition remains a smooth crossover for every finite light-quark mass studied, so no second-order critical surface reaches the finite-mass part of the Columbia plot.
  • The pseudocritical line's curvature $\kappa_2$ stays between about 0.0157 and 0.0160 as the pion mass changes, so the shape of the crossover line in $\mu_B^2$ is nearly independent of the light-quark mass.

Reading between the lines

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

  • Extending beyond the paper: if the flat surface survives inclusion of meson-exchange diagrams—which the paper reports shift the physical critical endpoint by only about five percent—then the endpoint's position is insensitive to moderate light-quark mass variations, and lattice simulations at heavier-than-physical pions could constrain the physical endpoint.
  • The near-constancy of $\kappa_2$ across pion masses suggests the curvature of the pseudocritical line is fixed by physics unrelated to chiral criticality; a scaling analysis around $\mu_B=0$ with mesonic backcoupling included could test whether the chiral-limit curvature instead decreases, as the paper notes a comparison with scaling fits hints.
  • Because the paper could not compute the chiral limit directly, the tricritical point could lie away from the linear extrapolation; a direct $m_\ell=0$ calculation with meson-exchange diagrams included would settle whether the flat-surface picture extends all the way to the chiral limit.
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 manuscript studies how the location of the QCD critical endpoint depends on the degenerate up/down quark mass at fixed strange quark mass, using a combination of lattice Yang--Mills input and truncated Dyson--Schwinger equations. The central numerical result is a set of four critical-endpoint positions for pion masses 140, 110, 80, and 55 MeV: as the pion mass decreases, the endpoint temperature rises slightly (112 to 115 MeV) and the baryon chemical potential decreases (630 to 534 MeV). From these points the authors infer a flat second-order critical surface in the three-dimensional Columbia plot and, via a linear extrapolation, a tricritical point at (T, mu_B) = (117, 473) MeV in the chiral limit. They also compute the curvature coefficient kappa_2 of the pseudocritical line at each pion mass and verify that the transition remains a crossover for imaginary chemical potential up to near the Roberge--Weiss line. The authors explicitly acknowledge the main limitations: the vertex truncation omits long-range mesonic fluctuations, the direct chiral-limit calculation failed, and the linear extrapolation to the tricritical point is not reliable.

Significance. If the mass-dependence trend were robust, the paper would provide a useful qualitative constraint on the structure of the Columbia plot, supporting a large crossover region and a tricritical point at finite chemical potential. The check at imaginary chemical potential is a falsifiable statement that could be compared with future lattice data, and the consistency of kappa_2 with existing lattice extractions at the physical point is a positive feature. The strengths of the paper are its clear framing, the explicit comparison with prior functional and lattice results in Table 1, and the honest discussion of the truncation dependence and of the failure of the direct chiral-limit computation. However, the central claim of a flat critical surface rests on a mass-dependence signal whose size is comparable to the known truncation uncertainty quoted by the authors themselves, so the significance of the claim is currently conditional rather than established.

major comments (4)
  1. [Section 2.1 and Section 3, Fig. 5] The central mass-dependence trend is computed with the version-(i) vertex truncation that omits the (pseudo)scalar-meson exchange diagrams, and the authors state in Section 2.1 that including those diagrams shifts the physical CEP by about (5, 36) MeV. The observed trend across the four pion masses is a 3 MeV rise in T_CEP and a 96 MeV drop in mu_CEP. The temperature change is therefore smaller than the known truncation shift, and the chemical-potential change is only about 2.7 times that shift. Because the omitted mesonic degrees of freedom become more important as the chiral limit is approached, the slopes in Fig. 5 could be substantially altered by the truncation. The manuscript should provide a systematic estimate of the truncation error along the mass trajectory, for example by repeating at least one additional pion mass with the type-(iia) truncation or by using the known physical-point shift to bound the slope uncertainty. Without such an estimate, the flatness of the second-order surface is not established.
  2. [Section 3, Table 2 and Fig. 5] The table of CEP locations and the figure have no error bars or extraction uncertainties. It is therefore unclear whether the differences between the four pion masses are numerically significant relative to the sensitivity of the DSE solution algorithm, the finite-grid resolution, and the criterion used to locate the critical point. The manuscript should state how the CEP was identified, what numerical tolerance was achieved, and whether the 3 MeV temperature variation is larger than the numerical noise.
  3. [Section 3, linear extrapolation to the chiral limit] The tricritical point at (117, 473) MeV is obtained by a linear extrapolation of the four CEP locations, but the authors themselves state that 'there is no convincing reason to assume that a linear extrapolation should be reliable close to the chiral limit.' The chiral limit is a singular point where tricritical scaling should generate non-analytic mass dependence, so the linear fit is not justified. Since the direct calculation in the chiral limit failed, the paper provides no independent check of the extrapolation. The abstract's closing statement that the results 'support the notion of a tricritical point' should be tempered; the current evidence only shows consistency with such a point under an unverified linearity assumption.
  4. [Section 3, Eq. (8) and kappa_2 comparison] The values of kappa_2 are extracted by assuming the simple form T(mu) = T(0)(1 - kappa_2 (mu/T(0))^2) with all higher-order coefficients set to zero, over a large chemical-potential range. These are not Taylor coefficients around mu = 0, and the statement that kappa_2 is 'more or less constant' with varying light-quark mass may be an artifact of the assumed functional form. The manuscript should either restrict the extraction to the small-mu regime or explicitly label these as effective fit parameters rather than curvature coefficients, and the comparison with the scaling analysis of Ref. [24] should be framed accordingly.
minor comments (5)
  1. [Section 2.1] There is a typo 'MeVMeV' in the sentence giving the CEP locations with and without meson fluctuations; it should read 'MeV' only once.
  2. [Table 1 caption] The caption begins with 'T able 1' instead of 'Table 1'.
  3. [Section 3, Fig. 5] The left panel of Fig. 5 would benefit from error bars and from a legend that distinguishes the four pion-mass data points more clearly; currently the reader must infer the pion mass from the adjacent text.
  4. [Section 3, Eq. (8)] The phrase 'analytically extract' is misleading because the coefficient is obtained by a numerical fit; 'extract by fitting' would be more accurate.
  5. [Section 2.1, Eq. (2)] The notation Z_l^m / Z_s^m is slightly hard to parse; adding parentheses or a sentence defining the mass renormalization constants would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the CEP locations and mass-dependence trend are computed outputs, and kappa2 is an explicitly fitted parameter, not a prediction.

full rationale

The central claims rest on four DSE-computed critical endpoint locations (Fig. 5), which are outputs of the calculation, not inputs fitted to reproduce a target CEP. The framework is inherited from prior work by the same group, but the present calculation independently reproduces the physical CEP and matches external benchmarks: Table 1 compares crossover temperatures with FRG and lattice results, and the physical-point kappa2 is compared with lattice extractions. The kappa2 values are obtained by fitting Eq. (8) to the authors' own pseudocritical lines, but the paper explicitly labels this as an extraction ('we are able to analytically extract the corresponding curvature coefficient') and cautions that the numbers do not originate from an expansion around muB=0. A fit of one's own data is not a prediction, and no fitted quantity is renamed as an independent result. The acknowledged omission of mesonic long-range degrees of freedom is a truncation-systematics concern, not a circularity: the computed trend could change under a better truncation, but the derivation does not reduce to its own inputs. No self-citation is load-bearing in the sense of supplying the claimed result itself, and no uniqueness theorem or ansatz is smuggled in via citation. The linear extrapolation to a tricritical point is explicitly flagged as unreliable and is not presented as a derived prediction. Therefore the paper is self-contained against external benchmarks and no circular step can be exhibited.

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

The framework rests on standard DSE mathematics plus two domain assumptions inherited from prior work: the quenched-lattice gluon input of Eq. (7) and the vertex truncation without meson diagrams. Two ad hoc modeling choices are used to interpret the results: the quadratic form of Eq. (8) for kappa2 and the linear extrapolation to the tricritical point. No new entities are introduced. The free parameter list is empty because the mass-dependent CEP results are computed outputs, not fitted inputs.

assumptions (4)
  • domain assumption Quenched lattice Yang-Mills gluon propagator plus explicit quark loop approximates the full gluon propagator of 2+1 flavor QCD at finite temperature and chemical potential.
    Used in Eq. (7); the pure Yang-Mills part is taken from quenched lattice fits [51,52,53] while the quark loop is computed within the DSE framework.
  • domain assumption The truncated quark-gluon vertex without meson-exchange diagrams (truncation version (i)) captures the light-quark mass dependence of the critical endpoint.
    Explicitly chosen in Section 2.1 because version (iia) is too expensive; the authors note that mesonic long-range degrees may become important near the chiral limit.
  • ad hoc to paper The pseudocritical line can be parametrized by T(mu) = T(0)(1 - kappa2 (mu/T(0))^2) with higher-order coefficients set to zero.
    Eq. (8) is used to extract kappa2; the authors admit that assuming this simple form over a large range of chemical potential is probably not justified.
  • ad hoc to paper The linear extrapolation of CEP locations in m_pi to the chiral limit locates the tricritical point.
    Section 3 gives (T, mu) = (117, 473) MeV from a linear fit; the paper explicitly warns that there is no convincing reason for linearity near the chiral limit.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quark mass dependence of a QCD critical point and structure of the Columbia plot." pith.science (2026). https://pith.science/paper/LEXTGYE4

@misc{pith2026250721680,
  author       = {Pith},
  title        = {Pith review of: Quark mass dependence of a QCD critical point and structure of the Columbia plot},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LEXTGYE4}},
  note         = {Machine review of arXiv:2507.21680}
}
abstract

We study the quark-mass dependence of the QCD critical point at varying bare up/down quark masses with fixed strange quark mass. We explore the corresponding second-order critical surface in the three-dimensional Columbia plot and study the extension of the associated crossover hyperplane at real and imaginary baryon chemical potential. To this end, we employ a by now well-tested combination of lattice Yang--Mills theory and a (truncated) version of Dyson--Schwinger equations at $N_f=2+1$ quark flavours. We find evidence for a positive curvature of the second order surface at (large) real chemical potential and a crossover region for imaginary chemical potential. Our results support the notion of a tricritical point at finite chemical potential in the chiral limit.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. On the nature of the QCD chiral phase transition with imaginary chemical potential

    hep-lat 2025-12 conditional novelty 5.0 of 10

    First-order chiral regions observed on coarse staggered lattices disappear in tricritical points as the lattice spacing decreases at imaginary chemical potential, implying a second-order continuum transition.

Reference graph

Works this paper leans on

56 extracted references · 4 canonical work pages · cited by 1 Pith paper

  1. [18]

    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, (2021) 054022,arXiv:2106.08356 [hep-ph]

    arXiv 2021

  2. [24]

    Curvature of the chiral phase transition line from the magnetic equation of state of (2+1)-flavor QCD

    H. T. Ding, O. Kaczmarek, F. Karsch, P. Petreczky, M. Sarkar, C. Schmidt, and S. Sharma, “Curvature of the chiral phase transition line from the magnetic equation of state of (2+1)-flavor QCD”,Phys. Rev. D 109 no. 11, (2024) 114516, arXiv:2403.09390 [hep-lat]

    arXiv 2024

  3. [1]

    The Order of the quantum chromodynamics transition predicted by the standard model of particle physics

    Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, “The Order of the quantum chromodynamics transition predicted by the standard model of particle physics”, Nature 443 (2006) 675–678, arXiv:hep-lat/0611014 [hep-lat]

    arXiv 2006

  4. [2]

    Is there still anytc mystery in lattice qcd? results with physical masses in the continuum limit iii

    W uppertal-BudapestCollaboration, S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, “Is there still anytc mystery in lattice qcd? results with physical masses in the continuum limit iii”, JHEP 09 (2010) 073, arXiv:1005.3508 [hep-lat]

    arXiv 2010

  5. [3]

    The chiral and deconfinement aspects of the qcd transition

    A. Bazavov et al., “The chiral and deconfinement aspects of the qcd transition”,Phys. Rev. D 85 (2012) 054503, arXiv:1111.1710 [hep-lat]

    arXiv 2012

  6. [4]

    Chiral crossover in qcd at zero and non-zero chemical potentials

    HotQCD Collaboration, A. Bazavovet al., “Chiral crossover in qcd at zero and non-zero chemical potentials”, Phys. Lett. B 795 (2019) 15–21, arXiv:1812.08235 [hep-lat]

    arXiv 2019

  7. [5]

    Qcd crossover at finite chemical potential from lattice simulations

    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 lattice simulations”, Phys. Rev. Lett. 125 no. 5, (2020) 052001, arXiv:2002.02821 [hep-lat]

    arXiv 2020

  8. [6]

    The qcd equation of state with dynamical quarks

    S. Borsanyi, G. Endrodi, Z. Fodor, A. Jakovac, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, “The qcd equation of state with dynamical quarks”,JHEP 11 (2010) 077, arXiv:1007.2580 [hep-lat]

    arXiv 2010

Show all 56 references
  1. [7]

    Full result for the qcd equation of state with 2+1 flavors

    S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, “Full result for the qcd equation of state with 2+1 flavors”,Phys. Lett. B 730 (2014) 99–104, arXiv:1309.5258 [hep-lat]

    2014 arXiv

  2. [8]

    Equation of state in ( 2+1 )-flavor qcd

    HotQCD Collaboration, A. Bazavovet al., “Equation of state in ( 2+1 )-flavor qcd”,Phys. Rev. D 90 (2014) 094503, arXiv:1407.6387 [hep-lat]

    2014 arXiv

  3. [9]

    Thermodynamics of strong-interaction matter from lattice qcd

    H.-T. Ding, F. Karsch, and S. Mukherjee, “Thermodynamics of strong-interaction matter from lattice qcd”, Int. J. Mod. Phys. E 24 no. 10, (2015) 1530007, arXiv:1504.05274 [hep-lat]

    2015 arXiv

  4. [10]

    The qcd equation of state to o(µ6 b) from lattice qcd

    A. Bazavov et al., “The qcd equation of state to o(µ6 b) from lattice qcd”,Phys. Rev. D 95 no. 5, (2017) 054504, arXiv:1701.04325 [hep-lat]

    2017 arXiv

  5. [11]

    Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at nonvanishing net baryon-number density

    HotQCD Collaboration, D. Bollweg, D. A. Clarke, J. Goswami, O. Kaczmarek, F. Karsch, S. Mukherjee, P. Petreczky, C. Schmidt, and S. Sharma, “Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at nonvanishing net baryon-number density”,Phys. ...

    2023 arXiv

  6. [12]

    Lattice QCD constraints on the critical point from an improved precision equation of state

    S. Borsanyi, Z. Fodor, J. N. Guenther, P. Parotto, A. Pasztor, C. Ratti, V. Vovchenko, and C. H. Wong, “Lattice QCD constraints on the critical point from an improved precision equation of state”,arXiv:2502.10267 [hep-lat]

    arXiv

  7. [13]

    Phase structure of three and four flavor QCD

    C. S. Fischer, J. Luecker, and C. A. Welzbacher, “Phase structure of three and four flavor QCD”,Phys. Rev. D 90 (2014) 034022, arXiv:1405.4762 [hep-ph]

    2014 arXiv

  8. [14]

    Baryon number fluctuations in the QCD phase diagram from Dyson-Schwinger equations

    P. Isserstedt, M. Buballa, C. S. Fischer, and P. J. Gunkel, “Baryon number fluctuations in the QCD phase diagram from Dyson-Schwinger equations”,Phys. Rev. D 100 no. 7, (2019) 074011, arXiv:1906.11644 [hep-ph]

    2019 arXiv

  9. [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, (2020) 054032,arXiv:1909.02991 [hep-ph]

    2020 arXiv

  10. [16]

    QCD phase structure from functional methods

    F. Gao and J. M. Pawlowski, “QCD phase structure from functional methods”, Phys. Rev. D 102 (2020) 034027, arXiv:2002.07500 [hep-ph] . 7

    2020 arXiv

  11. [17]

    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 (2021) 136584, arXiv:2010.13705 [hep-ph]

    2021 arXiv

  12. [19]

    QCD equation of state and thermodynamic observables from computationally minimal Dyson-Schwinger equations

    Y. Lu, F. Gao, Y.-X. Liu, and J. M. Pawlowski, “QCD equation of state and thermodynamic observables from computationally minimal Dyson-Schwinger equations”, Phys. Rev. D 110 no. 1, (2024) 014036,arXiv:2310.18383 [hep-ph]

    2024 arXiv

  13. [20]

    Bayesian location of the QCD critical point from a holographic perspective

    M. Hippert, J. Grefa, T. A. Manning, J. Noronha, J. Noronha-Hostler, I. Portillo Vazquez, C. Ratti, R. Rougemont, and M. Trujillo, “Bayesian location of the QCD critical point from a holographic perspective”,Phys. Rev. D 110 no. 9, (2024) 094006,arXiv:2309.00579 [nucl-th]

    2024 arXiv

  14. [21]

    QCD critical point, Lee-Yang edge singularities, and Padé resummations

    G. Basar, “QCD critical point, Lee-Yang edge singularities, and Padé resummations”,Phys. Rev. C 110 no. 1, (2024) 015203, arXiv:2312.06952 [hep-th]

    2024 arXiv

  15. [22]

    Searching for the QCD critical endpoint using multi-point Padé approximations

    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 Padé approximations”, arXiv:2405.10196 [hep-lat]

    arXiv

  16. [23]

    Locating the QCD critical point from first principles through contours of constant entropy density

    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”, arXiv:2410.16206 [hep-ph]

  17. [25]

    Remarks on the Chiral Phase Transition in Chromodynamics

    R. D. Pisarski and F. Wilczek, “Remarks on the Chiral Phase Transition in Chromodynamics”,Phys. Rev. D 29 (1984) 338–341

    1984

  18. [26]

    Chiral Phase Transition Temperature in ( 2+1 )-Flavor QCD

    HotQCD Collaboration, H. T. Dinget al., “Chiral Phase Transition Temperature in ( 2+1 )-Flavor QCD”,Phys. Rev. Lett. 123 no. 6, (2019) 062002,arXiv:1903.04801 [hep-lat]

    2019 arXiv

  19. [27]

    On the order of the QCD chiral phase transition for different numbers of quark flavours

    F. Cuteri, O. Philipsen, and A. Sciarra, “On the order of the QCD chiral phase transition for different numbers of quark flavours”, JHEP 11 (2021) 141, arXiv:2107.12739 [hep-lat]

    2021 arXiv

  20. [28]

    Chiral susceptibility in ( 2+1 )-flavor QCD

    J. Braun, W.-j. Fu, J. M. Pawlowski, F. Rennecke, D. Rosenblüh, and S. Yin, “Chiral susceptibility in ( 2+1 )-flavor QCD”, Phys. Rev. D 102 no. 5, (2020) 056010, arXiv:2003.13112 [hep-ph]

    2020 arXiv

  21. [29]

    Phase structure of 2+1-flavour QCD and the magnetic equation of state

    F. Gao and J. M. Pawlowski, “Phase structure of 2+1-flavour QCD and the magnetic equation of state”, Phys. Rev. D 105 no. 9, (12, 2021) 094020, arXiv:2112.01395 [hep-ph]

    2021 arXiv

  22. [30]

    QCD phase transitions in the light quark chiral limit

    J. Bernhardt and C. S. Fischer, “QCD phase transitions in the light quark chiral limit”,Phys. Rev. D 108 no. 11, (2023) 114018, arXiv:2309.06737 [hep-ph]

    2023 arXiv

  23. [31]

    On the existence of a phase transition for qcd with three light quarks

    F. R. Brown, F. P. Butler, H. Chen, N. H. Christ, Z.-h. Dong, W. Schaffer, L. I. Unger, and A. Vaccarino, “On the existence of a phase transition for qcd with three light quarks”, Phys. Rev. Lett. 65 (1990) 2491–2494

    1990

  24. [32]

    On the strength of theUA(1) anomaly at the chiral phase transition inNf = 2 QCD

    B. B. Brandt, A. Francis, H. B. Meyer, O. Philipsen, D. Robaina, and H. Wittig, “On the strength of theUA(1) anomaly at the chiral phase transition inNf = 2 QCD”, JHEP 12 (2016) 158, arXiv:1608.06882 [hep-lat]

    2016 arXiv

  25. [33]

    Evidence of effective axial U(1) symmetry restoration at high temperature QCD

    A. Tomiya, G. Cossu, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko, and J. Noaki, “Evidence of effective axial U(1) symmetry restoration at high temperature QCD”,Phys. Rev. D 96 no. 3, (2017) 034509,arXiv:1612.01908 [hep-lat]

    2017 arXiv

  26. [34]

    Role of the axial U(1) anomaly in the chiral susceptibility of QCD at high temperature

    JLQCD Collaboration, S. Aoki, Y. Aoki, H. Fukaya, S. Hashimoto, C. Rohrhofer, and K. Suzuki, “Role of the axial U(1) anomaly in the chiral susceptibility of QCD at high temperature”, PTEP 2022 no. 2, (2022) 023B05, arXiv:2103.05954 [hep-lat]

    2022 arXiv

  27. [35]

    The chiral transition andU (1)A symmetry restoration from lattice QCD using Domain Wall Fermions

    HotQCD Collaboration, A. Bazavovet al., “The chiral transition andU (1)A symmetry restoration from lattice QCD using Domain Wall Fermions”,Phys. Rev. D 86 (2012) 094503, arXiv:1205.3535 [hep-lat]

    2012 arXiv

  28. [36]

    QCD chiral transition, U(1)A symmetry and the dirac spectrum using domain wall fermions

    M. I. Buchoffet al., “QCD chiral transition, U(1)A symmetry and the dirac spectrum using domain wall fermions”, Phys. Rev. D 89 no. 5, (2014) 054514, arXiv:1309.4149 [hep-lat]

    2014 arXiv

  29. [37]

    QCD Phase Transition with Chiral Quarks and Physical Quark Masses

    T. Bhattacharyaet al., “QCD Phase Transition with Chiral Quarks and Physical Quark Masses”,Phys. Rev. Lett. 113 no. 8, (2014) 082001,arXiv:1402.5175 [hep-lat]

    2014 arXiv

  30. [38]

    Microscopic origin ofUA(1) symmetry violation in the high temperature phase of QCD

    V. Dick, F. Karsch, E. Laermann, S. Mukherjee, and S. Sharma, “Microscopic origin ofUA(1) symmetry violation in the high temperature phase of QCD”,Phys. Rev. D91 no. 9, (2015) 094504,arXiv:1502.06190 [hep-lat]

    2015 arXiv

  31. [39]

    Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD

    H. T. Ding, S. T. Li, S. Mukherjee, A. Tomiya, X. D. Wang, and Y. Zhang, “Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD”,Phys. Rev. Lett. 126 no. 8, (2021) 082001,arXiv:2010.14836 [hep-lat]

    2021 arXiv

  32. [40]

    Eigenvalue spectra of QCD and the fate of UA(1) breaking towards the chiral limit

    O. Kaczmarek, L. Mazur, and S. Sharma, “Eigenvalue spectra of QCD and the fate of UA(1) breaking towards the chiral limit”,Phys. Rev. D 104 no. 9, (2021) 094518, arXiv:2102.06136 [hep-lat]

    2021 arXiv

  33. [41]

    Mass sensitivity of the three-flavor chiral phase transition

    S. Resch, F. Rennecke, and B.-J. Schaefer, “Mass sensitivity of the three-flavor chiral phase transition”, arXiv:1712.07961 [hep-ph]

    arXiv

  34. [42]

    Conjectures about the Chiral Phase Transition in QCD from Anomalous Multi-Instanton Interactions

    R. D. Pisarski and F. Rennecke, “Conjectures about the Chiral Phase Transition in QCD from Anomalous Multi-Instanton Interactions”, Phys. Rev. Lett. 132 no. 25, (2024) 251903, arXiv:2401.06130 [hep-ph]

    2024 arXiv

  35. [43]

    Anomalous U(1)A couplings and the Columbia plot

    F. Giacosa, G. Kovács, P. Kovács, R. D. Pisarski, and F. Rennecke, “Anomalous U(1)A couplings and the Columbia plot”, Phys. Rev. D 111 no. 1, (2025) 016014, arXiv:2410.08185 [hep-ph]

    2025 arXiv

  36. [44]

    Continuum limit and universality of the Columbia plot

    P. de Forcrand and M. D’Elia, “Continuum limit and universality of the Columbia plot”,PoS LA TTICE2016 (2017) 081, arXiv:1702.00330 [hep-lat]

    2017 arXiv

  37. [45]

    Chiral phase transition in three-flavor QCD from lattice QCD

    L. Dini, P. Hegde, F. Karsch, A. Lahiri, C. Schmidt, and S. Sharma, “Chiral phase transition in three-flavor QCD from lattice QCD”,Phys. Rev. D 105 no. 3, (2022) 034510, arXiv:2111.12599 [hep-lat]

    2022 arXiv

  38. [46]

    Second-order chiral phase transition in three-flavor quantum chromodynamics?

    G. Fejos, “Second-order chiral phase transition in three-flavor quantum chromodynamics?”,Phys. Rev. D 105 no. 7, (2022) L071506,arXiv:2201.07909 [hep-ph]

    2022 arXiv

  39. [47]

    The chiral phase transition at non-zero imaginary baryon chemical potential for different numbers of quark flavours

    A. D’Ambrosio, O. Philipsen, and R. Kaiser, “The chiral phase transition at non-zero imaginary baryon chemical potential for different numbers of quark flavours”,PoS LA TTICE2022(2023) 172, arXiv:2212.03655 [hep-lat]

    2023 arXiv

  40. [48]

    Toward the chiral phase transition in the Roberge-Weiss plane

    F. Cuteri, J. Goswami, F. Karsch, A. Lahiri, M. Neumann, O. Philipsen, C. Schmidt, and A. Sciarra, “Toward the chiral phase transition in the Roberge-Weiss plane”,Phys. Rev. D 106 no. 1, (2022) 014510,arXiv:2205.12707 [hep-lat]

    2022 arXiv

  41. [49]

    On the phase diagram of QCD

    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. D58 (1998) 096007, arXiv:hep-ph/9804290 [hep-ph] . 8

    1998 arXiv

  42. [50]

    Critical behavior and net-charge fluctuations from lattice QCD

    F. Karsch, “Critical behavior and net-charge fluctuations from lattice QCD”,PoS CORFU2018 (2019) 163, arXiv:1905.03936 [hep-lat]

    2019 arXiv

  43. [51]

    Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

    C. S. Fischer, A. Maas, and J. A. Mueller, “Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)”, Eur. Phys. J. C 68 (2010) 165, arXiv:1003.1960 [hep-ph]

    2010 arXiv

  44. [52]

    The gluon propagator close to criticality

    A. Maas, J. M. Pawlowski, L. von Smekal, and D. Spielmann, “The gluon propagator close to criticality”, Phys. Rev. D 85 (2012) 034037, arXiv:1110.6340 [hep-lat]

    2012 arXiv

  45. [53]

    Baryon effects on the location of QCD’s critical end point

    G. Eichmann, C. S. Fischer, and C. A. Welzbacher, “Baryon effects on the location of QCD’s critical end point”, Phys. Rev. D 93 (2016) 034013, arXiv:1509.02082 [hep-ph]

    2016 arXiv

  46. [54]

    Quarks and light (pseudo-)scalar mesons at finite chemical potential

    P. J. Gunkel, C. S. Fischer, and P. Isserstedt, “Quarks and light (pseudo-)scalar mesons at finite chemical potential”, Eur. Phys. J. A 55 (2019) 169, arXiv:1907.08110 [hep-ph]

    2019 arXiv

  47. [55]

    Masses and decay constants of (axial-)vector mesons at finite chemical potential

    P. J. Gunkel and C. S. Fischer, “Masses and decay constants of (axial-)vector mesons at finite chemical potential”, Eur. Phys. J. A 57 no. 4, (2021) 147, arXiv:2012.01957 [hep-ph]

    2021 arXiv

  48. [56]

    Curvature of the pseudocritical line in qcd: Taylor expansion matches analytic continuation

    C. Bonati, M. D’Elia, F. Negro, F. Sanfilippo, and K. Zambello, “Curvature of the pseudocritical line in qcd: Taylor expansion matches analytic continuation”,Phys. Rev. D 98 no. 5, (2018) 054510,arXiv:1805.02960 [hep-lat]

    2018 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.