Critical point of QCD at finite T and \mu, lattice results for physical quark masses

S.D. Katz; Z. Fodor

REVIEW

Critical point of QCD at finite T and \mu, lattice results for physical quark masses

Z. Fodor, S.D. Katz

High Energy Physics - Lattice · Submitted 8 Feb 2004 · 30 references

Pith's verdict: A real physics update — the endpoint drops from 720 to 360 MeV at physical quark masses — but the reweighting overlap at the endpoint is argued, not measured, and the scale systematic is wider than the quoted error.

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CitationS.D. Katz, Z. Fodor. "Critical point of QCD at finite T and \mu, lattice results for physical quark masses." arXiv:hep-lat/0402006 (2004). https://pith.science/paper/SW4BQUXA

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The number to take away is mu_E = 360 +/- 40 MeV, down from the authors' own 720 MeV in the earlier larger-mass run. That is a genuine change in a quoted physical quantity, driven by lowering m_u,d by a factor of three to physical values, and it is what everyone expected qualitatively. They also grew the largest volume by a factor of three and got no volume trend, which is worth something. T_c = 164 +/- 2 MeV and the curvature C = 0.0032(1) come along with it. The Lee-Yang zero analysis is stated cleanly: zeros on the complex beta plane, beta_0(V) = beta_inf + zeta/V, jackknife over subsamples of the L_s = 6, 8, 10, 12 partition functions, mu_end = 0.1825(75) in lattice units. I could follow the chain from Table 1 to the quoted MeV without guessing, which is not nothing in this literature. They are also upfront that the continuum extrapolation is missing (abstract:s9, Section 4) — that is their own flag, not a discovery, and I would not hold it against them twice. On the stress-test concern: it lands, but softly. The reweighting weight is evaluated at the largest mu in the study and at a shifted beta, so both the gauge action and the determinant sit far from the sampled ensemble, and there is no effective sample size or weight histogram at mu_end. Volume-independence across L_s = 6-12 is necessary but blind to a bias common to all four volumes. That said, the method was validated in their earlier work, the imaginary-mu continuation agrees on the phase line, and the endpoint is not forced by construction. I would call this the standard, known soft spot of the approach rather than a defect specific to this paper. Two smaller things. The R_0 versus m_rho scales disagree by 10-15 percent by their own admission, and that spread does not obviously live inside the quoted errors; the 1.3 percent figure is the scale error, not the scale ambiguity. And the line-of-constant-physics correction is imported from the larger-mass run under a parallelism assumption that is not tested at m_u,d = 0.0092 — minor, and they say it only nudges the curvature. Read it as a well-motivated target with a systematic band of order ten percent, not a precision prediction. Worth a serious referee.

Referee report

Significance

If the result holds, this is the first lattice determination of the crossover-to-first-order boundary of 2+1 flavour QCD at physical quark masses, and it fixes a falsifiable target (mu_E ≈ 360 MeV, T_E ≈ 162 MeV) for heavy-ion searches and for independent lattice methods. The improvements over Ref. [8] are real and substantial: the light quark mass is reduced by a factor of three to approximately its physical value, the largest volume is increased by a factor of three, and the volume-independence of the extrapolated zeros across L_s = 6–12 is a meaningful consistency check. The agreement of the phase line with the imaginary-chemical-potential determinations of Refs. [18, 19] is a genuine, if indirect, cross-validation of the method. The paper is also commendably explicit about what it has not done, naming the missing continuum extrapolation in the abstract and in Section 4 rather than burying it.

Major objections (4)

[Section 3, scale-setting paragraph; Section 4 and Figure 2 caption] The error budget attached to the headline number does not appear to contain the dominant scale systematic. Section 3 states that R_0 (0.5 fm) and m_rho (770 MeV) give scales differing by 'approximately 10-15%', and that an average of the two is used; the Figure 2 caption then quotes 'an overall additional error of 1.3% ... from the error of the scale determination at T=0'. A 10-15% spread between the two scale-setting quantities is 36-54 MeV on mu_E = 360 MeV, i.e. comparable to or larger than the quoted ±40 MeV, and it is a systematic spread, not a statistical error, so the 1.3% figure does not cover it. The same applies to T_E and T_c. The authors should state explicitly whether the 10-15% spread is included anywhere in the quoted uncertainties, and if it is not, they should propagate it and revise the error bars accordingly, or justify why the average is the correct central value with a smaller assigned systematic.
[Table 1, Re(mu) = 0.20 row; Figure 1] The endpoint location is controlled by the zero crossing of Im(beta_0^inf) between Re(mu) = 0.16 and Re(mu) = 0.20, and at Re(mu) = 0.20 the extrapolated value is -0.39(77) while all four finite-volume values in that column (2.26(22), 0.98(12), 5.29(76) x 10^-3, 2.07(74) x 10^-3) are positive. The sign change is produced entirely by the linear 1/V fit, and the L_s = 6 point sits well off the trend of the L_s = 8, 10, 12 points in every column of the table, so the fit is dominated by the coarsest and least reliable volume. Since mu_end = 0.1825(75) is read off this crossing, the authors should demonstrate that the result is stable under the extrapolation ansatz: repeat the fit with 1/V^2, with the L_s = 6 point excluded, and with a fit to the three largest volumes only, and report the resulting spread in mu_end as a systematic. As it stands the reader cannot tell whether the quoted ±0.0075 reflects the data or the choice of fit form.
[Section 3, paragraph beginning 'Along the transition line beta decreases'; Section 4, curvature sentence] The line-of-constant-physics correction is imported rather than computed at the masses used here. The text states that 'we corrected for this effect by using our previous results at larger m_ud [8] and by following the observation that transition lines for slightly different quark masses are practically parallel', but the correction is applied at m_ud = 0.0092 whereas Ref. [8] was at a quark mass three times larger, and its magnitude is never quoted. This matters because the same correction is then invoked in Section 4 to explain why C = 0.0032(1) is smaller than the values of Refs. [8, 13, 14, 15, 18]: 'The small change of the mass parameter on the line of constant physics ... slightly decreases the curvature.' A correction that is large enough to move C away from four independent determinations needs to be shown, not asserted. Please give the size of the shift in C and in mu_end produced by this correction, and state how it was obtained from Ref. [8].
[Section 2, Eq. 2.1; Section 3] The reliability of the reweighting at the largest chemical potential is the load-bearing assumption of the paper, and no direct diagnostic of it is reported at mu_end. The support offered is qualitative (reweighting between two transition points overlaps better than reweighting from a hadronic ensemble, Refs. [7, 8]), a scaling argument for the reachable range of mu (mu ∝ V^gamma, Refs. [11, 12, 17]), and volume-independence of the results. The last is necessary but not sufficient: a bias common to all four volumes would not appear as a volume trend. Since the endpoint is extracted precisely where the weight mismatch between the sampled ensemble at (beta_w, mu = 0) and the target (beta, mu_end) is largest, the authors should report at least one quantitative overlap diagnostic at mu_end, for example the effective sample size or a histogram of the reweighting weights, and, if feasible, a comparison of Im(beta_0) at a common mu against an independent method such as the imaginary-chemical-potential continuation of Refs. [18, 19].

Minor objections (8)

[Abstract] The abstract describes the quark masses as 'physical', but Section 3 reports m_pi/m_rho = 0.188(2) against a physical 0.179 and m_pi/m_K = 0.267(1) against a physical 0.277. 'Approximately physical' would be more accurate and is what the body of the paper actually claims.
[Section 3, configuration generation] The text states that the determinant is evaluated every 50 trajectories and that 'our results are based on a few thousand independent configurations', but no autocorrelation analysis or integrated autocorrelation time is given, and the R-algorithm step size (half the light quark mass) is not accompanied by a step-size systematic check. Either soften 'independent' or support it.
[Table 1 caption] The caption should state that the row labelled infinity is the beta_0(V) = beta_0^inf + zeta/V extrapolation, give the fit form explicitly, and note that the entries in the L_s = 10 and L_s = 12 rows are quoted in units of 10^-3 while the L_s = 6 and L_s = 8 rows are in units of 10^-2, since the mixed units are easy to misread.
[Section 3, mu_end = 0.1825(75)] Please state explicitly that mu_end is the quark chemical potential in lattice units and that mu_B = 3 mu, so that the lattice and physical numbers in Section 4 can be connected without the reader having to infer the convention.
[Section 4, curvature] The definition T/T_c = 1 - C mu_B^2/T_c^2 is given, but the fit range in mu_B over which C = 0.0032(1) was extracted is not. Please state the range and whether the fit includes the region near the endpoint.
[Figure 1] The figure would be clearer with the units of Im(beta_0^inf) on the axis, the value of mu_end marked with its error band, and the individual L_s points shown alongside the extrapolated curve so that the reader can see the volume dependence that underlies the crossing.
[References] Reference [26] ('I. Montvay and G. Munster,') is incomplete: no title, publisher, or year. Please supply the full entry.
[Section 1 and Section 3] Typographical: 'phase digram' in Section 1 and 'dissappear' in the footnote to Section 3 should be corrected.

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The paper

The paper claims

The paper locates the QCD critical endpoint at $T_E=162$ MeV and baryon chemical potential $200$ MeV using lattice QCD with physical quark masses.

The reading

The paper asks where, on the plane of temperature and baryon density, QCD stops changing smoothly and begins to jump. That location is the critical endpoint: below it the transition between hadrons and quark-gluon plasma is a crossover, above it a first-order transition, and near it long-wavelength fluctuations could leave experimental signatures in heavy-ion collisions. Using lattice QCD with 2+1 flavours of staggered quarks at approximately physical masses, the authors report the endpoint at $T_E=162$ MeV and baryon chemical potential $200$ MeV, together with a zero-density crossover temperature $T_c=164$ MeV. The result improves their earlier work by lowering the light quark masses by a factor of three and increasing the largest volume by a factor of three; the lower masses moved the endpoint down, while the volume change left it unchanged. The authors state that the continuum extrapolation is still missing, so the numbers are a controlled step rather than a final answer.

What carries the argument

The method is overlap-improving multi-parameter reweighting combined with Lee-Yang zeros. Configurations are generated at $200$ and at the zero-density transition temperature, where importance sampling works; each configuration is then given a Boltzmann weight for nonzero $200$ and for the lower transition temperature at that $200$, with the gauge coupling reweighted by the Ferrenberg-Swendsen procedure. The partition function is continued into the complex $200$ plane, and its Lee-Yang zeros are located. Their finite-volume scaling carries the argument: zeros that stay away from the real axis mean a crossover, zeros that approach it as $1/V$ mean a first-order transition, and the endpoint is the $200$ at which the extrapolated imaginary part vanishes. The physical scale is set from the Sommer scale $R_0$ and the $200$ mass.

Extended reading notes

Core claim

The central claim is that the QCD critical endpoint sits at $T_E=162$ MeV and $200$ MeV for 2+1-flavour QCD with physical quark masses on $L_t=4$ lattices. In lattice units the endpoint is $200$. The evidence comes from the infinite-volume extrapolation of Lee-Yang zeros of the reweighted partition function: at small $200$ the extrapolated imaginary part of the zero, $200$, is inconsistent with zero and the transition is a crossover; as $200$ increases it falls, and at the endpoint the crossover disappears and finite-volume scaling becomes consistent with a first-order transition. The paper also reports a crossover-line curvature $T/T_c=1-C200^2/T_c^2$ with $C=0.0032(1)$. The authors explicitly note that the continuum extrapolation has not been done.

Load-bearing premise

The load-bearing premise is that the reweighting from $200$ ensembles still samples the nonzero-density transition well enough at the endpoint for the Lee-Yang zeros to be reliable; the authors also acknowledge that the continuum extrapolation is still missing.

Editorial extensions

If this is right

Heavy-ion searches for critical-point signatures can target the region around $T\approx162$ MeV and baryon chemical potential $\approx360$ MeV rather than the much larger $\mu_E\approx700$ MeV suggested by earlier large-mass estimates.
The crossover line's small curvature, $C=0.0032(1)$, gives a concrete input for the QCD equation of state at small baryon density.
Because lowering the light quark masses moved $\mu_E$ down from about 720 MeV to 360 MeV, quark-mass effects must be controlled in any comparison between lattice endpoints and experiment.
The insensitivity to a threefold volume increase supports the reliability of the finite-volume Lee-Yang analysis, leaving the lattice spacing as the main systematic uncertainty.

Reading between the lines

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

A quantitative overlap diagnostic at the endpoint, such as the distribution of reweighting weights or an effective sample size, would test the method independently of the statistical error bars on the zeros.
Agreement between this reweighting result and an imaginary-$\mu$ analytic continuation at the same quark masses would be a strong cross-check, because the two methods fail in different ways.
Since $T_E$ and $T_c$ differ by only about 2 MeV, within errors, the data do not yet establish whether the endpoint lies exactly on the zero-density transition line or slightly below it.
Mapping $T$ and $\mu_B$ to heavy-ion collision energies requires a freeze-out model; the endpoint's location is a thermodynamic statement, not by itself a prediction of which beam energy will see critical fluctuations.

Original abstract

A critical point (E) is expected in QCD on the temperature (T) versus baryonic chemical potential (\mu) plane. Using a recently proposed lattice method for \mu \neq 0 we study dynamical QCD with n_f=2+1 staggered quarks of physical masses on L_t=4 lattices. Our result for the critical point is T_E=162 \pm 2 MeV and \mu_E= 360 \pm 40 MeV. For the critical temperature at \mu=0 we obtained T_c=164 \pm 2 MeV. This work extends our previous study [Z. Fodor and S.D.Katz, JHEP 0203 (2002) 014] by two means. It decreases the light quark masses (m_{u,d}) by a factor of three down to their physical values. Furthermore, in order to approach the thermodynamical limit we increase our largest volume by a factor of three. As expected, decreasing m_{u,d} decreased \mu_E. Note, that the continuum extrapolation is still missing

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,402 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.98 · human participants 0.01 · controlled comparison 0.20 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

A critical point (E) is expected in QCD on the temperature (T) versus baryonic chemical potential (\mu) plane. Using a recently proposed lattice method for \mu \neq 0 we study dynamical QCD with n_f=2+1 staggered quarks of physical masses on L_t=4 lattices. Our result for the critical point is T_E=162 \pm 2 MeV and \mu_E= 360 \pm 40 MeV. For the critical temperature at \mu=0 we obtained T_c=164 \pm 2 MeV. This work extends our previous study [Z. Fodor and S.D.Katz, JHEP 0203 (2002) 014] by two means. It decreases the light quark masses (m_{u,d}) by a factor of three down to their physical values. Furthermore, in order to approach the thermodynamical limit we increase our largest volume by a factor of three. As expected, decreasing m_{u,d} decreased \mu_E. Note, that the continuum extrapolation is still missing

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A critical point (E) is expected in QCD on the temperature (T) versus baryonic chemical potential (\mu) plane.	background 1.00	0.05	0.07	hedged possibility 0.88
s1	Using a recently proposed lattice method for \mu \neq 0 we study dynamical QCD with n_f=2+1 staggered quarks of physical masses on L_t=4 lattices.	method 0.85	0.89	0.04	asserted 0.94
s2	Our result for the critical point is T_E=162 \pm 2 MeV and \mu_E= 360 \pm 40 MeV.	result 1.00	0.97	0.86	asserted 1.00
s3	For the critical temperature at \mu=0 we obtained T_c=164 \pm 2 MeV.	result 1.00	0.97	0.09	asserted 1.00
s4	This work extends our previous study [Z.	contribution 0.58	0.43	0.02	asserted 0.82
s5	Fodor and S.D.Katz, JHEP 0203 (2002) 014] by two means.	background 0.51	0.32	0.02	asserted 0.67
s6	It decreases the light quark masses (m_{u,d}) by a factor of three down to their physical values.	contribution 0.61	0.89	0.03	asserted 0.99
s7	Furthermore, in order to approach the thermodynamical limit we increase our largest volume by a factor of three.	method 0.59	0.93	0.03	asserted 0.99
s8	As expected, decreasing m_{u,d} decreased \mu_E.	interpretation 0.67	0.85	0.06	asserted 0.97
s9	Note, that the continuum extrapolation is still missing	limitation 1.00	0.37	0.03	asserted 0.98

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** shows Im(β∞ 0 ) as a function of µ enlarged around the endpoint µend. The picture is simple and reflects the physical expectations. For small µ-s the extrapolated Im(β∞ 0 ) is inconsistent with a vanishing value, and the prediction is a crossover. Increasing µ the value of Im(β∞ 0 ) decreases, thus the transition becomes consistent with a first order phase transition. The statistical error was determined by a jackknife analysis using subsamples of the total Ls=6,8,10 and 12 partition functions. Our primary result in lattice units is µend = 0.1825(75)

**Figure 2.** The phase diagram in physical units. Dotted line illustrates the crossover, solid line the first order phase transition. The small square shows the endpoint. The depicted errors originate from the reweighting procedure. Note, that an overall additional error of 1.3% comes from the error of the scale determination at T=0. Combining the two sources of uncertainties one obtains TE = 162 ± 2 MeV and µE = 360 ± 40 MeV. The above result is a significant improvement on our previous analysis [8] by two means. We increased the physical volume by a factor of three and decreased the light…

Figures reproduced from arXiv:hep-lat/0402006 by the authors.

References

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hep-lat 2020-02 accept novelty 6.0 of 10

Continuum-extrapolated lattice QCD gives kappa2 = 0.0153(18) and kappa4 = 0.00032(67) for the QCD crossover line, with no sign of criticality up to muB of about 300 MeV.
Off-diagonal correlators of conserved charges from lattice QCD and how to relate them to experiment
hep-lat 2019-10 conditional novelty 6.0 of 10

Continuum-extrapolated lattice correlators of baryon number, charge, and strangeness are matched to ratios of measured net-kaon and net-Lambda variances, and the strangeness ratio favors a 165 MeV freeze-out temperature.
Cluster Expansion Model for QCD Baryon Number Fluctuations: No Phase Transition at $\mu_B / T < \pi$
hep-ph 2017-11 conditional novelty 6.0 of 10

A two-input cluster expansion fitted to lattice QCD at imaginary chemical potential reproduces baryon susceptibilities up to sixth order and places the nearest pressure singularity at |mu_B/T| >= pi.
Critical point in the phase diagram of primordial quark-gluon matter from black hole physics
nucl-th 2017-06 conditional novelty 6.0 of 10

A holographic model of dense quark matter, calibrated to lattice QCD at zero baryon density, places the QCD critical point at T = 89 MeV and baryon chemical potential 724 MeV, corresponding to collision energies of 2....
The QCD Equation of State to $\mathcal{O}(\mu_B^6)$ from Lattice QCD
hep-lat 2017-01 conditional novelty 6.0 of 10

Sixth-order lattice Taylor coefficients show the QCD equation of state is reliable up to a baryon chemical potential twice the temperature, and disfavor a critical point for mu_B/T <= 2 above T/Tc = 0.9.
The QCD equation of state at finite density from analytical continuation
hep-lat 2016-07 conditional novelty 6.0 of 10

Continuum-extrapolated Taylor coefficients of the QCD pressure through sixth order in baryon chemical potential, obtained by analytic continuation from imaginary chemical potential, extend the equation of state to mu_...
A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
hep-lat 2015-10 accept novelty 6.0 of 10

A Metropolis algorithm samples one Lefschetz thimble by mapping far points to a Gaussian region near the critical point, reproducing exact results for a solvable finite-density fermion model where a single thimble dominates.
Structure of Lefschetz thimbles in simple fermionic systems
hep-th 2014-12 accept novelty 6.0 of 10

In three solvable fermionic toy models the authors map the Lefschetz-thimble decomposition of the path integral and show the chiral limit is singular because competing thimbles must be summed.
Event-by-event mean $p_{\rm T}$ fluctuations in pp and Pb-Pb collisions at the LHC
nucl-ex 2014-07 accept novelty 6.0 of 10

Event-by-event mean transverse momentum fluctuations in pp and Pb-Pb collisions follow a power law in charged-particle multiplicity, and central Pb-Pb collisions show a marked suppression relative to the pp trend and ...
Thermal decoupling and the smallest subhalo mass in dark matter models with Sommerfeld-enhanced annihilation rates
hep-ph 2012-02 conditional novelty 6.0 of 10

A coupled treatment of chemical and kinetic decoupling shows that Sommerfeld-enhanced dark matter annihilation can continue past matter-radiation equality, lowering the relic density by up to two orders of magnitude a...
The QCD phase diagram at nonzero quark density
hep-lat 2011-02 conditional novelty 6.0 of 10

Continuum-extrapolated lattice QCD gives a crossover curvature of about 0.007 to 0.009 in units of the chemical potential squared over temperature squared, from two independent observables, with the transition width e...
A holographic critical point
hep-th 2010-12 conditional novelty 6.0 of 10

A holographic gravity model fitted to lattice QCD at zero chemical potential yields a first-order transition line ending at a critical point at 143 MeV and 783 MeV, with critical exponents close to mean-field values.
Using Higher Moments of Fluctuations and their Ratios in the Search for the QCD Critical Point
hep-ph 2010-06 conditional novelty 6.0 of 10

The paper derives the critical-fluctuation contribution to third and fourth cumulants of pion, proton, and mixed multiplicities and shows that five specific ratios of these cumulants equal one regardless of the correl...
Stochastic quantization at finite chemical potential
hep-lat 2008-07 conditional novelty 6.0 of 10

Complex Langevin dynamics reproduces exact results in solvable one-link models with a complex determinant, suggesting the sign problem need not block stochastic quantization at finite chemical potential.
The chiral critical line of N_f=2+1 QCD at zero and non-zero baryon density
hep-lat 2006-07 conditional novelty 6.0 of 10

On coarse N_t=4 lattices the chiral critical line of 2+1 flavour QCD is mapped with an exact algorithm, and its shift under imaginary chemical potential has the opposite sign to standard expectation, suggesting no QCD...
Elliptic flow of $\phi$ and $\Omega$ via quark recombination mechanism in relativistic heavy-ion collisions
nucl-th 2026-11 conditional novelty 5.0 of 10

A quark recombination model with viscous corrections describes phi and Omega elliptic flow from RHIC to LHC energies, and extracts the strange quark elliptic flow.
Magnetic susceptibility of a hot hadronic medium and quark degrees of freedom near the QCD cross-over point
hep-ph 2025-11 unverdicted novelty 5.0 of 10

A quark-meson model with lattice-fitted temperature-dependent quark masses and anomalous magnetic moments reproduces the magnetic susceptibility of hot hadronic matter up to the QCD crossover, showing quarks are activ...
Investigation of the Spectator Effect on Light Nuclei Production in Nucleus-Nucleus Collisions at High Baryon Density Region
hep-ph 2025-11 conditional novelty 5.0 of 10

Spectator nucleons enhance low-pT light-nucleus production in peripheral, forward-rapidity 3 GeV Au+Au collisions, so pT-integrated yields obtained by Blast-Wave extrapolation are underestimated.
Higher order fluctuations and correlations of conserved charges from lattice QCD
hep-lat 2018-05 conditional novelty 5.0 of 10

Imaginary-chemical-potential lattice QCD at physical quark masses yields sixth-order conserved-charge fluctuations and cumulant ratios whose Taylor extrapolation qualitatively reproduces the STAR net-proton trend.
Gravitational Waves from Hidden QCD Phase Transition
hep-ph 2017-09 conditional novelty 5.0 of 10

A scale-invariant hidden QCD sector with a first-order chiral transition at 0.3 to 9.5 TeV yields a stochastic gravitational wave signal near 10^-12 to 10^-13 at 0.01 to a few hertz, potentially visible to DECIGO.
Lefschetz-thimble analysis of the sign problem in one-site fermion model
hep-th 2015-09 conditional novelty 5.0 of 10

In a solvable one-site Hubbard model, reproducing the exact step-function density requires interference among many Lefschetz thimbles, not just the dominant one, and the number needed grows linearly with inverse temperature.
Energy loss, equilibration, and thermodynamics of a baryon rich strongly coupled quark-gluon plasma
hep-th 2015-07 conditional novelty 5.0 of 10

A holographic model fitted to zero-density lattice QCD predicts that heavy and light quark energy loss increases with baryon density and that equilibration is faster in a denser quark-gluon plasma.
Curvature of the chiral pseudo-critical line in QCD: continuum extrapolated results
hep-lat 2015-07 conditional novelty 5.0 of 10

Continuum-extrapolated lattice QCD simulations at imaginary chemical potential give a chiral pseudo-critical line curvature kappa = 0.0135(20), about twice earlier Taylor-expansion values.
Baryon number conservation and the cumulants of the net proton distribution
hep-ph 2012-03 conditional novelty 5.0 of 10

Global baryon-number conservation suppresses higher-order net-proton cumulants by large factors, and a specific combination of odd cumulants is constructed to be insensitive to this suppression.
Particle Models and the Small-Scale Structure of Dark Matter
astro-ph.CO 2009-03 conditional novelty 5.0 of 10

A full Boltzmann treatment of WIMP kinetic decoupling across about 400,000 supersymmetric models places the smallest dark matter protohalos between 10^-11 and 10^-3 solar masses, typically ten times heavier than earli...
The QCD phase diagram for three-flavor M\"obius domain-wall fermions
hep-lat 2026-06 unverdicted novelty 4.0 of 10

Lattice simulations with Möbius domain-wall fermions find the three-flavor QCD transition at mu_B=0 is a continuous crossover at pseudocritical quark masses of 184(10) MeV (Nt=6), 36-39 MeV (Nt=8), and 3.5-3.7 MeV (Nt...
Gravitational waves from holographic first-order QCD phase transition with magnetic field
hep-ph 2026-03 conditional novelty 4.0 of 10

In holographic QCD models, a stronger external magnetic field shifts the gravitational-wave peak from the first-order confinement transition to lower frequencies, with signals potentially visible to IPTA and SKA.
Study of the hottest droplet of fluid through correlations and fluctuations of collective variables
nucl-th 2025-05 conditional novelty 4.0 of 10

The thesis uses event-by-event fluctuations and correlations of collective flow and mean transverse momentum to propose new probes of the initial state, explain the ATLAS [pT]-variance fall, and constrain nuclear deformation.
The BEST framework for the search for the QCD critical point and the chiral magnetic effect
nucl-th 2021-08 accept novelty 4.0 of 10

The BEST Collaboration summarizes the modular modeling framework it has built to connect RHIC Beam Energy Scan measurements to the QCD critical point and the chiral magnetic effect.
Information theoretical view of QCD effective model with heavy quarks
hep-ph 2020-09 conditional novelty 4.0 of 10

The transfer mutual information in a 3D 3-state Potts model peaks at the confinement-deconfinement transition and distinguishes behavior below and above the Roberge-Weiss endpoint.
An Experimental Exploration of the QCD Phase Diagram: The Search for the Critical Point and the Onset of De-confinement
nucl-ex 2010-07 conditional novelty 4.0 of 10

STAR proposes a RHIC beam energy scan from 5 to 39 GeV, with event-count targets for critical-point and deconfinement measurements and test-run evidence that the detector performs at those energies.
New Forms of QCD Matter Discovered at RHIC
nucl-th 2004-05 conditional novelty 4.0 of 10

Published RHIC data are argued to show an equilibrated, nearly perfect-fluid quark gluon plasma whose initial state is a saturated color glass condensate.
The phase diagram of dense QCD
hep-ph 2010-05 accept novelty 3.0 of 10

A structured survey of the QCD phase diagram that separates firmly established results (lattice QCD at small baryon density, weak-coupling colour superconductivity at asymptotically high density) from conjectured phas...
Simulating QCD at finite density
hep-lat 2010-05 accept novelty 3.0 of 10

Lattice QCD at finite baryon density stays blocked by the sign problem; the three standard workarounds agree only at small chemical potential, and the existence of a QCD critical point remains undetermined.
Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment
nucl-ex 2004-10 conditional novelty 3.0 of 10

BRAHMS argues that the RHIC data, chiefly the factor 3 to 5 suppression of high-momentum hadrons in central gold-gold collisions, require partonic degrees of freedom, while conceding that no hadronic description has b...
Long Range Plan: Dense matter theory for heavy-ion collisions and neutron stars
nucl-th 2022-11 accept novelty 2.0 of 10

The US nuclear theory community's long-range plan argues that heavy-ion, neutron-star, and gravitational-wave data now demand a single coordinated theory program for dense matter, and lists the tools that program still lacks.
Lattice QCD and heavy ion collisions: a review of recent progress
hep-lat 2018-04 accept novelty 2.0 of 10

Lattice QCD, now run at physical quark masses in the continuum limit, reproduces heavy-ion freeze-out temperatures and the QCD equation of state, and this review documents where theory and data agree and where they st...
Properties of hot and dense matter from relativistic heavy ion collisions
nucl-th 2015-10 accept novelty 2.0 of 10

Collisions of heavy nuclei at RHIC and the LHC produce a locally thermalized, nearly perfect fluid whose equation of state, transport coefficients, and freeze-out conditions can be read off bulk observables.
Thermodynamics of strong-interaction matter from Lattice QCD
hep-lat 2015-04 accept novelty 2.0 of 10

First-principles lattice QCD fixes the crossover temperature of hot strong-interaction matter at 154 ± 9 MeV and its equation of state, with controlled but limited extensions to nonzero baryon density.
Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
hep-th 2012-05 accept novelty 2.0 of 10

Ultracold Fermi gases and the quark-gluon plasma both flow as nearly perfect liquids, with shear viscosity to entropy density near hbar/(4 pi k_B), the value holographic duality predicts for strongly coupled fluids.
Hadronic Fluctuations and Correlations
nucl-th 2008-10 accept novelty 2.0 of 10

Event-by-event fluctuations of conserved charges provide a measurable bridge between Lattice QCD susceptibilities and the search for the QCD critical point in heavy-ion collisions.
Finite-density lattice QCD and sign problem: current status and open problems
hep-lat 2021-08 conditional novelty 1.0 of 10

A critical survey of finite-density lattice QCD arguing that every current workaround for the sign problem is formally correct but degrades, often without warning, in the low-temperature high-density region.
Introductory lectures on lattice QCD at nonzero baryon number
hep-lat 2015-12 accept novelty 1.0 of 10

The notes explain the lattice QCD sign problem at nonzero chemical potential and review methods that partially evade it, without claiming a new solution.
Lattice QCD at non-zero temperature
hep-lat 2012-03 accept novelty 1.0 of 10

Lattice QCD places the chiral crossover at 154 ± 9 MeV at physical quark masses and finds no separate deconfinement temperature.

How later papers used it

160 later papers cite it

Evidence: substantial. 141 of the citing papers share no author with it, and 37 of those carry a confident label from Pith's citation classifier.

Pith read 27 of the 217 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 2 used its data or values.

Uses its data or values 2 of 20 papers with this label

Chose its mixed temperature and chemical potential parameter to reproduce a critical endpoint at μ_c=354 MeV and T_c=167 MeV for symmetric matter and zero net strangeness in accordance with this paper's lattice data.

Chiral Symmetry Restoration and Deconfinement to Quark Matter in Neutron Stars (2009) · 0.98 · paraphrased: the licence does not allow quoting
Took the position of the critical point in μ (at μ=360 MeV) from this paper's lattice QCD calculations.

Event-by-Event Fluctuations and the Search for the Critical Point within the NA49 Experiment (2009) · 0.92 · paraphrased: the licence does not allow quoting

How the literature uses it

130 arXiv papers cite this in 184 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 107 sentences without a confident label

Contests it 1 paper

Our results about the critical surface appear to be in qualitative contradiction with those of [ref] , [ref] , which both conclude for the existence of a critical point $(μ_E,T_E)$ at small chemical potential $μ_E/T_E 1$.

Exploring the QCD phase diagram · Discussion · contest 0.72

Builds on it 1 paper

Generalization to multi-parameter and joint expansion in $T,$.– Akin to multi-parameter reweighting [ref] in bare gauge coupling, $Δβ=β-β_0$, and quark mass, $Δm=m-m_0$, our resummation scheme also can be extended to obtain $_N(T,)$ starting from a different temperature $T_0(β_0)$ and bare quark mass $m_0$,

Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansion · Introduction · 0.84

Uses its method or tool 8 papers

In this manuscript we study Lee-Yang zeros, which offer a different approach to the study of the phase diagram [ref] , by means of a two-step extrapolation (see Ref. [ref] for a detailed explanation).

High-precision baryon number cumulants from lattice QCD in a finite box: cumulant ratios, Lee-Yang zeros and critical endpoint predictions · Introduction · 0.80
Using the multi-parameter reweighting technique [ref] we studied dynamical QCD with $n_f$=2+1 staggered quarks of physical masses on $N_t$=4 lattices [ref] .

Recent Result in QCD Thermodynamics from the Lattice · Results at non-vanishing baryonic chemical potential · 0.97
In this paper, as in Refs. [ref] , we adopt the following prescription.

Lattice simulations of the QCD chiral transition at real baryon density · B.1. Staggered rooting at finite chemical potential · 0.99

Uses its data or values 17 papers

There is as yet no complete agreement as to the location of the quark matter critical endpoint, as obtained from lattice studies: in [ref] one finds a discussion of various proposed points in the phase diagram, such as one (see [ref] ) with coordinates $(μ_B^CEP/T^CEP, T^CEP/T^C_0) ≈(1.68, 0.94)$, where $T^C_0$ is the crossover temperature at $μ_B = 0$, for which we follow [ref] and take the value $≈$ 150 MeV; but also another with coordinates $(μ_B^CEP/T^CEP, T^CEP/T^C_0) ≈(2.2, 0.99)$ (see [ref] ).

The Trajectory of the Cosmic Plasma Through the Quark Matter Phase Diagram · Section · 0.80
The lattice data includes a first order phase transition at $T=270$ MeV and a pressure functional P(T) similar to Refs. [ref] at $μ=0$ for pure gauge, a crossover at vanishing chemical potential with a transition temperature of $171$ MeV (determined as the peak of the change of the chiral condensate and $Φ$) and the location of the critical end-point (at $μ_c=354$ MeV , $T_c=167$ MeV for symmetric matter in accordance with one of the existent calculations [ref] ).

A Novel Approach to Model Hybrid Stars · Introduction · 0.97
The case of physical quark masses, after conversion to continuum units, is shown in [ref] (right) [ref] .

Status of Lattice Studies of the QCD Phase Diagram · Calculations at finite density · 0.92

Compares with it 9 papers

As can be seen in that Figure, the leading Fisher zero extrapolates to a point on the real line at around $μ_B/T=2.4$, in agreement with the result of Ref. [ref] .

New approach to lattice QCD at finite density: reweighting without an overlap problem · Unimproved action at $N_τ=4$ · 0.99
The obtained expression is in excellent agreement with numerical computations [ref] .

Phase Transitions, theta Behavior and Instantons in QCD and its Holographic Model · conclusion · 0.96
Indeed, this must happen if one wishes to reconcile our result with that of Fodor and Katz [ref] , whose critical point Fig. [ref] lies at $μ/T ∼0.7$ for mass parameters similar to eq.

Simulating QCD at finite density · The curvature of the critical surface · 0.94

Cites it as support 1 paper

In particular, it includes: $∙$ lattice computations of topological susceptibility in the vicinity of the phase transition [ref] ; $∙$ lattice computations of the critical temperature $T_c(μ)$ as a function of $μ$ at small $μ$ [ref] ; $∙$ analysis of the holographic models of QCD in vicinity of the phase transition at nonzero temperature [ref] .

Confinement- Deconfinement Phase Transition in Hot and Dense QCD at Large N · Confinement- Deconfinement Phase Transition in hot QCD at large $N$. · 1.00

Cites it as background 39 papers

A number of approaches have been proposed to side-step this problem, such as reweighting [ref] , Taylor expansion around zero chemical potential [ref] , analytic continuation from purely imaginary chemical potentials [ref] , or the complex Langevin approach [ref] .

New approach to lattice QCD at finite density: reweighting without an overlap problem · Introduction · 0.98
It is well known that at vanishing chemical potentials, QCD exhibits a cross-over phase transition [ref] near the pseudo-critical temperature $T_c∼155$ MeV, passing gradually from hadronic degrees of freedom below $T_c$ to quarks and gluons above.

Magnetic susceptibility of a hot hadronic medium and quark degrees of freedom near the QCD cross-over point · Introduction · 0.90
Though there have been attempts in extracting information about the location of the supposed CEP from lattice simulations [ref] , these attempts face great difficulties, as extrapolation-type methods have the property that they give reliable results mostly in the immediate vicinity of $μ_B=0$.

The QCD crossover at finite chemical potential from lattice simulations · Introduction · 0.91

Discussion

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