The transition temperature in QCD

C. Jung; C. Miao; C. Schmidt; E. Laermann; F. Karsch; J. van der Heide; K. Petrov; M. Cheng; N. H. Christ; O. Kaczmarek

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The transition temperature in QCD

M. Cheng, N. H. Christ, S. Datta, J. van der Heide, C. Jung, F. Karsch, O. Kaczmarek, E. Laermann

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R. D. Mawhinney, C. Miao, P. Petreczky, K. Petrov, C. Schmidt, T. Umeda

High Energy Physics - Lattice · Submitted 22 Aug 2006 · 28 references

Pith's verdict: A careful, well-documented lattice determination of Tc that mostly holds up; the continuum extrapolation from two spacings is the one place I'd push.

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arXiv IDhep-lat/0608013 (version 3)

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CitationC. Jung, C. Miao, C. Schmidt, E. Laermann, F. Karsch, J. van der Heide, K. Petrov, M. Cheng, N. H. Christ, O. Kaczmarek, P. Petreczky, R. D. Mawhinney, S. Datta, T. Umeda. "The transition temperature in QCD." arXiv:hep-lat/0608013 (2006). https://pith.science/paper/QTMOGLEH

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Editor's note

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This is the RBC-Bielefeld p4fat3 determination of the QCD transition temperature, and it's the version of that result worth reading. What's new relative to their earlier work and to MILC: much smaller light quark masses (down to m_l/m_s = 0.00325), a second temporal extent N_tau = 6, and RHMC sampling, which removes the finite-step-size worry that dogged the older hybrid-R runs. The result is Tc r0 = 0.457(7) at the physical point, Tc = 192(7)(4) MeV, about 10% above the number then in common use, with the shift attributed mostly to the newer r0 = 0.469(7) fm calibration. The paper is unusually transparent: full tables of raw condensates, susceptibilities and autocorrelation times in the appendix, explicit separation of statistical and systematic errors on the scale fits, volume checks at N_sigma = 8 through 32, and a strange-mass check at m_s = 0.1. They also state plainly that beta_c from the Polyakov loop and from the chiral susceptibility differ on small lattices, and they fold that difference into the error rather than picking a winner. That's the right instinct. Note the abstract classifier found no stated limitations; that's wrong, the authors do acknowledge the cutoff issue and call for a finer lattice in the Conclusions. The soft spot is the joint fit in Eq. 13: one shared mass coefficient A and one 1/N_tau^2 coefficient B across both spacings. The two ensembles don't cover the same mass range, the lightest N_tau = 6 point sits near m_ps r0 ~ 0.57 against 0.36 at N_tau = 4, so the finer lattice is being extrapolated over roughly a factor 1.8 in m_ps with A borrowed from the coarser one. With two spacings, B = 0.34(9) absorbs whatever curvature exists and the quoted 2% residual is an estimate, not a measured bound. Varying the chiral exponent d from 1 to 2 covers some of the mass-slope uncertainty but not the shared-A assumption. Second, smaller point: the scale interpolation in Eq. 12 draws six of its fourteen r0/a values from reference [15], listed as in preparation, so part of the fit rests on unpublished data. Neither of these overturns the central number, and the agreement with MILC's asqtad continuum result within errors is reassuring. This is for anyone who needs a Tc with a documented error budget, and for lattice people who want to see how the systematics were handled. Send it out.

Referee report

Significance

If it holds, this is a benchmark number: a continuum-extrapolated, physical-mass determination of the QCD transition temperature from first principles, with a fully tabulated raw data set (Tables A.1-A.9) covering lattice sizes, autocorrelation times, condensates, Polyakov loops and susceptibilities. The error budget is unusually explicit for this genre: statistical and systematic errors on r0/a and sqrt(sigma)a from 3- and 4-parameter Cornell fits, a systematic from the beta_c,L versus beta_c,l discrepancy, jackknife-based Ferrenberg-Swendsen reweighting for peak locations, and finite-volume checks at N_sigma = 8, 16, 24 and 32. The paper is also careful to separate the dimensionless result T_c r0, which does not depend on any physical scale, from the MeV conversion, which does. The observation that the light and strange sectors cross over at the same temperature to below the 1 MeV level is a useful, falsifiable statement for phenomenological models. The result is reproducible in principle from the stated action and parameters, and the external input is a single published scale from an independent collaboration.

Major objections (3)

[Section V, Eq. (13), Tables III and IV] The joint fit of Eq. (13) assumes a single mass coefficient A shared between N_tau = 4 and N_tau = 6, but the two ensembles do not cover the same mass range. From Table III the lightest N_tau = 4 point sits at m_ps r0 = 0.1888 x 1.8915 = 0.357, while the lightest N_tau = 6 point sits at m_ps r0 = 0.2043 x 2.8030 = 0.573, against a physical value of 0.321. The chiral extrapolation on the finer lattice is therefore roughly a factor 1.8 in m_ps, and with a single shared A the fit cannot separate a cutoff dependence of the mass slope from the 1/N_tau^2 term B itself. Since the continuum value at the physical point is obtained precisely by combining the N_tau = 6 intercept with the shared slope, this degeneracy propagates directly into Eq. (15). A concrete and inexpensive test would be to refit with A allowed to differ between the two N_tau, or to fit each N_tau separately and compare the extracted slopes; reporting the resulting shift in T_c r0 at m_ps r0 = 0.321 would settle whether the common-A assumption is doing silent work.
[Section V, after Eq. (15), and Conclusions] The continuum extrapolation rests on two lattice spacings and a single leading 1/N_tau^2 correction. The authors are explicit that the residual higher-order cutoff uncertainty 'is not larger than 2%' is an estimate, and they call in the Conclusions for 'an additional calculation on an even finer lattice', so the limitation is acknowledged rather than hidden. What remains unresolved is the quantitative status of that 2%: with only two spacings, B = 0.34(9) absorbs whatever curvature exists and there is no lever arm to test a 1/N_tau^4 contribution. It would strengthen the paper to convert the estimate into a sensitivity statement, for example by adding a term C/N_tau^4 with C fixed at values that would be plausible on the basis of the observed N_tau = 4 to N_tau = 6 shift, and quoting the resulting excursion of T_c r0. As written, the asymmetric systematic +8/-2 in Eq. (15) does not appear to include any curvature component, and a reader cannot tell whether 2% is a bound or an expectation.
[Section IV.B, Table III, and Section V] The insensitivity of T_c r0 to the strange quark mass is established only at N_tau = 4, by comparing the ms = 0.1 and ms = 0.065 sets, where the kaon mass differs by about 20% and the results agree. At N_tau = 6 only ms = 0.04 is available, and Table III shows that this set gives m_K r0 = 1.25 at the physical pion mass, about 6% above the continuum value 1.177(18), while the N_tau = 4 set gives 1.12, about 6% below. The two ensembles entering the continuum extrapolation therefore sit on opposite sides of the physical kaon mass, and any residual ms dependence would be absorbed into the fitted cutoff coefficient B. Since the N_tau = 4 check is the only evidence that this does not happen, the paper should state explicitly how the ms = 0.1 versus 0.065 comparison at N_tau = 4 bounds the corresponding shift of the N_tau = 6 point, and fold that bound into the systematic error of Eq. (15).

Minor objections (8)

[Section III, discussion of Fig. 5, versus Table II] The text quotes the largest discrepancy as beta_c,L - beta_c,l = 0.019(7) for the ml/ms = 0.2 set on the 16^3 x 6 lattice, but the corresponding entries in Table II are 3.4801(19) and 3.4595(19), which give 0.0206(27). Please reconcile the central value and the quoted error, or state which determination the 0.019(7) refers to.
[Section IV.A, Eq. (12)] The interpolation formula of Eq. (12), used to transport r0/a to the critical couplings, is fitted to 14 values that include data from Ref. [15], listed as 'in preparation'. Since the interpolation enters the scale determination for every entry of Table IV, it would help to state how much the fit parameters A, B, C, D, and hence T_c r0, change if only the eight Table III values are used. The interpolation ranges are small (Delta beta of order 0.006-0.01), so this is likely a small effect, but it should be quantified rather than left to the reader.
[Section V, Eqs. (14) and (15)] The asymmetric systematic errors +12/-3 and +8/-2 are not explained at the point of use. Please state in the text that the central value corresponds to d = 1.08 and that the lower and upper excursions correspond to d = 1 and d = 2 respectively, so that the convention is unambiguous without cross-referencing the preceding paragraph.
[Figure 7] The caption says the three parallel lines show fits based on Eq. (13) for N_tau = 4, 6 and N_tau -> infinity, but it is not stated whether the N_tau -> infinity line is the continuum extrapolation evaluated at each m_ps r0 or only anchored at the physical point. Clarifying this, and whether the lines share the fitted slope A, would make the figure self-contained.
[Table III caption] The caption should state that the (ms, ml) = (0.1, 0.05) row is excluded from the fit of Eq. (12), as is mentioned only in the body text. The second error quoted for r0/a and sqrt(sigma)a should also be identified in the caption as the fit-range and 4-parameter-fit systematic.
[Section V.A] The paper notes that r0 sqrt(sigma) = 1.11-1.13 is about 2% larger than the MILC value, and separately compares T_c r0 with the asqtad result of Ref. [3] converted via r0/r1 = 1.4795. Since a 2% discrepancy in this ratio feeds directly into that comparison, please state explicitly whether the comparison in Section V is affected, or whether it is made in a common scale.
[Abstract and body notation] The abstract uses N_t while the body uses N_tau, and the abstract writes m_l/m_s while the body uses hat{m}_l/hat{m}_s for bare masses. Please harmonize the notation between abstract and body.
[Section V.A and Acknowledgments] Two sentences appear garbled in the present text: 'the scale parameter r0, deduced from the bottomonium level splitting using NRQCD [13], see ms to be the best controlled lattice observable', and 'the transition temperature at the physical point, fixed by mpsr0r'. Please check these against the typeset version.

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The paper

The paper claims

The paper computes the temperature at which QCD turns into a quark-gluon plasma, using lattice simulations with two light quarks and a physical strange quark, and reports $T_c = 192(7)(4)$ MeV at the physical quark masses.

The reading

The paper sets out to compute, from first principles, the temperature at which strongly interacting matter stops being a gas of hadrons and becomes a quark-gluon plasma, for the quark masses that actually occur in nature: two light quarks plus a heavier strange one. The authors simulate the theory on space-time lattices with two different temporal extents, $N_𝜏 = 4$ and $6$, locate the crossover on each by watching where the chiral and Polyakov-loop susceptibilities peak, and convert lattice units into physical ones using the scale $r_0$ extracted from the zero-temperature static quark potential. Combining an extrapolation to vanishing light-quark mass with an extrapolation to vanishing lattice spacing gives $T_c r_0 = 0.457(7)$ at the physical point, which with $r_0 = 0.469(7)$ fm becomes $T_c = 192(7)(4)$ MeV. The number matters because it is a first-principles anchor for the whole picture of heavy-ion collisions: it says where the plasma forms, and it sits about 10 percent above the $175$ MeV value then in common use, largely because of a newer calibration of $r_0$.

What carries the argument

The load-bearing device is the joint fit in Eq. 13, $Y = Y_{0,m_s,\infty} + A(m_{ps} r_0)^d + B/N_𝜏^2$ with $Y = T_c r_0$ or $T_c/\sqrt{\sigma}$, which folds the light-quark extrapolation and the continuum extrapolation into one two-parameter-plus-offset form. The exponent $d = 2/\beta\delta \simeq 1.08$ comes from O(4) universal scaling; the authors bracket the systematic by repeating the fit with $d = 1$ and $d = 2$ (the first-order case) and quoting the spread. The critical coupling for each parameter set is the average of the peak positions in the Polyakov-loop susceptibility and the disconnected light-quark chiral susceptibility, with peaks located by Ferrenberg-Swendsen reweighting and errors from jackknife resampling; the split between the two peaks is added as a systematic. The scale $r_0$, defined by $r^2 dV_{\bar{q}q}/dr = 1.65$ at $r = r_0$, is obtained from Cornell-type fits to the static quark potential with lattice distortions handled by replacing the Euclidean distance with the lattice Coulomb potential of Eq. 8, and interpolated in coupling and quark mass through the renormalization-group-inspired ansatz of Eq. 12. Simulations use the p4fat3 improved staggered action with the exact RHMC algorithm, which removes the finite step-size errors of the earlier hybrid-R runs.

Extended reading notes

Core claim

The central claim is a controlled determination of the QCD transition temperature at physical quark masses. The authors report $T_c r_0 = 0.457(7)^{+8}_{-2}$ at $m_{ps} r_0 = 0.321(5)$, equivalently $T_c/\sqrt{\sigma} = 0.408(8)^{+3}_{-1}$, and $T_c r_0 = 0.444(6)^{+12}_{-3}$ in the chiral limit, about 3 percent lower. Converting with $r_0 = 0.469(7)$ fm gives $T_c = 192(7)(4)$ MeV, where the second error is the authors' estimate of residual cutoff effects. Three supporting observations carry the result: the $N_𝜏 = 6$ values sit systematically 3 to 4 percent below the $N_𝜏 = 4$ values at matched pion mass, as a nonzero lattice spacing should produce; results at $\hat{m}_s = 0.1$ and $0.065$ agree within errors even though the kaon mass differs by about 20 percent, so the answer is insensitive to the exact strange mass; and the peaks in the light and strange quark susceptibilities coincide to within about 1 MeV, so a single temperature describes both sectors. The authors also note that their $r_0/\sqrt{\sigma} \simeq 1.11$ implies $\sqrt{\sigma} \simeq 465$ MeV, roughly 10 percent above the string tension used in earlier scale settings, which is where most of the upward shift from 175 MeV comes from.

Load-bearing premise

The continuum extrapolation rests on only two lattice spacings, $N_𝜏 = 4$ and $6$, fitted with a single $1/N_𝜏^2$ term, so the claimed 2 percent residual cutoff uncertainty is an estimate that no third spacing is available to check.

Editorial extensions

If this is right

A single transition temperature governs both the light and strange sectors: the peaks in the two susceptibilities agree to within about 1 MeV, so phenomenological models that split the two crossover temperatures are not supported at this precision.
The chiral-limit value is about 3 percent below the physical-point value, so any comparison with experiment should use $T_c r_0 = 0.457(7)$ rather than the easier-to-compute chiral number.
The ratio $T_c/\sqrt{\sigma} = 0.408(8)$ is independent of any experimental calibration, so it survives even if the fm conversion is later revised.
Since the fit gives $B \approx 1/3$, results on $N_𝜏 = 4$ lattices run about 5 percent high and $N_𝜏 = 6$ about 2 percent high, which sets the correction future coarse-lattice work should expect.
Combined with freeze-out temperatures below 170 MeV inferred from particle yields at RHIC, a transition at 192 MeV leaves room for an intermediate hadronic stage between the crossover and chemical freeze-out.

Reading between the lines

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

The headline shift from roughly 175 MeV to 192 MeV is driven mostly by the $r_0$ calibration rather than by the lattice data, so the more durable output of this paper is the dimensionless $T_c r_0$; any future revision of $r_0$ moves the MeV number proportionally and should be read as a scale recalibration, not a contradiction of this result.
With only two lattice spacings, a $1/N_𝜏^2$ term and a $1/N_𝜏^4$ term are indistinguishable; a single $N_𝜏 = 8$ run with the same action would be the cheapest decisive test, and the sign and size of the shift it produces would calibrate how much to trust the quoted 2 percent residual-cutoff estimate elsewhere.
The fit's weak preference for $d \approx 0.6$, below the O(4) value of 1.08, is plausibly a symptom of the coarse light-quark masses rather than evidence against O(4) scaling; extending the light-mass range downward would sharpen the exponent and, incidentally, test whether the transition stays a crossover at the physical strange mass.
The 2 percent continuum-extrapolation error is an estimate rather than a measured quantity, so downstream users who fold this $T_c$ into error budgets for, say, hydrodynamic models of heavy-ion collisions should treat the total uncertainty as somewhat larger than the quoted $(7)(4)$ MeV.

Original abstract

We present a detailed calculation of the transition temperature in QCD with two light and one heavier (strange) quark mass on lattices with temporal extent N_t =4 and 6. Calculations with improved staggered fermions have been performed for various light to strange quark mass ratios in the range, 0.05 <= m_l/m_s <= 0.5, and with a strange quark mass fixed close to its physical value. From a combined extrapolation to the chiral (m_l -> 0) and continuum (aT = 1/N_t -> 0) limits we find for the transition temperature at the physical point T_c r_0 = 0.457(7) where the scale is set by the Sommer-scale parameter r_0 defined as the distance in the static quark potential at which the slope takes on the value, (dV_qq(r)/dr)_r=r_0 = 1.65/r_0^2. Using the currently best known value for r_0 this translates to a transition temperature T_c = 192(7)(4)MeV. The transition temperature in the chiral limit is about 3% smaller. We discuss current ambiguities in the determination of T_c in physical units and also comment on the universal scaling behavior of thermodynamic quantities in the chiral limit.

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.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.58 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.20 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We present a detailed calculation of the transition temperature in QCD with two light and one heavier (strange) quark mass on lattices with temporal extent N_t =4 and 6. Calculations with improved staggered fermions have been performed for various light to strange quark mass ratios in the range, 0.05 <= m_l/m_s <= 0.5, and with a strange quark mass fixed close to its physical value. From a combined extrapolation to the chiral (m_l -> 0) and continuum (aT = 1/N_t -> 0) limits we find for the transition temperature at the physical point T_c r_0 = 0.457(7) where the scale is set by the Sommer-scale parameter r_0 defined as the distance in the static quark potential at which the slope takes on the value, (dV_qq(r)/dr)_r=r_0 = 1.65/r_0^2. Using the currently best known value for r_0 this translates to a transition temperature T_c = 192(7)(4)MeV. The transition temperature in the chiral limit is about 3% smaller. We discuss current ambiguities in the determination of T_c in physical units and also comment on the universal scaling behavior of thermodynamic quantities in the chiral limit.

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	We present a detailed calculation of the transition temperature in QCD with two light and one heavier (strange) quark mass on lattices with temporal extent N_t =4 and 6.	contribution 0.96	0.96	0.06	asserted 0.98
s1	Calculations with improved staggered fermions have been performed for various light to strange quark mass ratios in the range, 0.05 <= m_l/m_s <= 0.5, and with a strange quark mass fixed close to its physical value.	method 0.93	0.89	0.02	asserted 0.99
s2	From a combined extrapolation to the chiral (m_l -> 0) and continuum (aT = 1/N_t -> 0) limits we find for the transition temperature at the physical point T_c r_0 = 0.457(7) where the scale is set by the Sommer-scale parameter r_0 defined as the distance in the static quark potential at which the slope takes on the value, (dV_qq(r)/dr)_r=r_0 = 1.65/r_0^2.	result 1.00	0.97	0.84	asserted 1.00
s3	Using the currently best known value for r_0 this translates to a transition temperature T_c = 192(7)(4)MeV.	result 1.00	0.88	0.48	asserted 1.00
s4	The transition temperature in the chiral limit is about 3% smaller.	result 1.00	0.89	0.06	asserted 0.94
s5	We discuss current ambiguities in the determination of T_c in physical units and also comment on the universal scaling behavior of thermodynamic quantities in the chiral limit.	interpretation 0.68	0.25	0.03	unclear 0.77

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

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sources read

arXiv listing abstract v3

not examined

full text
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levels run

P abstract

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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.** FIG. 1: Time history of the light and strange quark chiral con

**Figure 2.** FIG. 2: The light quark chiral condensate in units of

**Figure 3.** FIG. 3: The disconnected part of the light quark chiral susce

**Figure 4.** FIG. 4: The disconnected part of the light quark chiral susce

**Figure 5.** FIG. 5: The difference of gauge couplings at the location of pe

**Figure 6.** FIG. 6: The square of the kaon mass in units of

Showing 6 of the paper's 7 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-lat/0608013 by the authors.

References

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hep-lat 2011-11 accept novelty 6.0 of 10

Continuum-extrapolated lattice QCD gives a chiral crossover temperature of 154 +/- 9 MeV at physical quark masses, defined by the peak of the chiral susceptibility under O(4) scaling.
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.
Thermodynamics of the brane
hep-th 2007-01 conditional novelty 6.0 of 10

For probe D7 and D6 branes in black D3 and D4 backgrounds, the authors compute the fundamental matter's free energy, entropy, energy density and speed of sound, and find tachyonic brane modes exactly where the thermod...
Lightest sterile neutrino abundance within the nuMSM
hep-ph 2006-12 conditional novelty 6.0 of 10

A first-principles calculation of sterile neutrino production in the early universe caps the Dodelson-Widrow dark matter sterile neutrino at roughly 3.5 keV, and at 6 keV under the most conservative treatment of hadro...
Scaling functions in the soft-wall AdS/QCD models
hep-ph 2025-07 conditional novelty 5.0 of 10

Soft-wall AdS/QCD models reproduce mean-field chiral scaling functions and follow a T_c scaling law whose slope, tuned by a modified potential, can approach Dyson-Schwinger results.
Effect of the QCD equation of state and strange hadronic resonances on multiparticle correlations in heavy ion collisions
nucl-th 2017-11 conditional novelty 5.0 of 10

Replacing the outdated S95n-v1 equation of state with continuum lattice QCD equations of state plus updated hadronic resonances changes the shear viscosity fitted to LHC flow data by up to 88 percent.
Interacting hadron resonance gas meets lattice QCD
nucl-th 2012-01 conditional novelty 5.0 of 10

Giving every hadron a hard-core radius of 0.3 fm removes the Hagedorn divergence of the hadron resonance gas and brings its energy density, pressure, entropy density and trace anomaly into agreement with lattice QCD u...
Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III
hep-lat 2010-05 accept novelty 5.0 of 10

The QCD crossover temperature discrepancy between the Wuppertal-Budapest and hotQCD collaborations is attributed to lattice discretization artifacts and heavier-than-physical quark masses in the hotQCD simulations, no...
The QCD transition temperature: results with physical masses in the continuum limit II.
hep-lat 2009-03 accept novelty 5.0 of 10

Using finer lattices and physical quark masses, the Wuppertal-Budapest collaboration confirms a QCD crossover temperature near 150 to 155 MeV and reports an unresolved 20 to 35 MeV discrepancy with the hotQCD collaboration.
Comparing the drag force on heavy quarks in N=4 super-Yang-Mills theory and QCD
hep-th 2006-11 conditional novelty 5.0 of 10

Matching the static quark-antiquark force to lattice QCD and comparing at fixed energy density raises the AdS/CFT drag prediction for charm quarks from about 0.6 fm/c to about 2.1 fm/c at T = 250 MeV.
Causal Viscous Hydrodynamics for Relativistic Heavy Ion Collisions
nucl-th 2009-08 conditional novelty 4.0 of 10

Causal viscous hydrodynamics in 2+1 dimensions with shear viscosity near the KSS bound suppresses elliptic flow by roughly 30%, making v2 a sensitive diagnostic of the quark-gluon plasma shear viscosity to entropy ratio.
The phase diagram of nuclear and quark matter at high baryon density
hep-ph 2013-01 conditional novelty 3.0 of 10

The review argues that a third regime, quarkyonic matter, sits between confined nuclear matter and deconfined quark matter in large-Nc QCD, with pressure scaling as O(Nc).
The QCD equation of state from the lattice
hep-lat 2012-07 accept novelty 3.0 of 10

Lattice QCD simulations now give a controlled, near-continuum equation of state for hot quark matter at physical quark masses, with residual systematic errors concentrated in the staggered-fermion rooting question and...
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...
The phase diagram of quantum chromodynamics
hep-ph 2009-08 accept novelty 2.0 of 10

Lattice QCD places the zero-density confinement transition at roughly 151 to 175 MeV and finds it to be an analytic crossover, while the nonzero-density critical point remains unlocated.
Charmonium from Statistical Hadronization of Heavy Quarks -- a Probe for Deconfinement in the Quark-Gluon Plasma
nucl-th 2009-01 conditional novelty 2.0 of 10

The statistical hadronization model predicts that charmonium yields scale with the square of the charm-quark number, so central LHC Pb-Pb collisions should show enhanced rather than suppressed J/psi production.
Theta dependence of SU(N) gauge theories in the presence of a topological term
hep-th 2008-03 accept novelty 2.0 of 10

Lattice measurements of the topological susceptibility and its theta-expansion coefficients in SU(N) gauge theory agree with large-N scaling and the Witten-Veneziano explanation of the U(1)_A problem.
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

64 later papers cite it

Evidence: substantial. 61 of the citing papers share no author with it, and 15 of those carry a confident label from Pith's citation classifier.

Pith read 15 of the 74 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

1 later paper by other authors is listed below: 1 used its data or values. 1 more paper by the same authors is listed: 1 used its data or values.

Uses its data or values 2 of 10 papers with this label · 1 by the same authors

Cited this paper's value of 0.22 GeV^2 among recent calculations of the string tension, giving an estimate of 0.19 ± 0.03.

The Thermal Production of Strange and Non-Strange Hadrons in e+e- Collisions (2008) · 0.95 · paraphrased: the licence does not allow quoting

By the same authors

Estimated the shift in T_c expected when the light quark mass is reduced to its physical value by examining the dependence of T_c on the light quark mass found in this paper's N_t=6 staggered fermion calculations.

The finite temperature QCD using 2+1 flavors of domain wall fermions at N_t = 8 (2009) (same authors) · 0.86 · paraphrased: the licence does not allow quoting

How the literature uses it

53 arXiv papers cite this in 63 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

From a combined extrapolation to the chiral (m_l -> 0) and continuum (aT -> 0) limits we obtain for the transition temperature at the physical point T_c = 192(7)(4) MeV.

Transition temperature in QCD with physical light and strange quark masses · 0.99

Papers citing it · 34 sentences without a confident label

Uses its data or values 9 papers

Our strategy is linearly map $(∙)_q, SB$ to the corresponding quantities of the $g_q = 37 + 14.25$ ideal gas model, and map the $f_q = f_h$ and $s_q = s_h$ horizontal lines in Fig. [ref] and [ref] to the $g_h = 3 + 14.25$ ideal gas model, where $g_q$ and $g_h$ are the degrees of freedom of the real world at $T = T_dec ≃192 MeV$ [ref] before and after the confinement/deconfinement phase transition.

AdS/CFT aspects of the cosmological QCD phase transition · The Nucleation Rate · 0.91
At $T=0$ and $μ_B=0$, $$ can be evaluated by QCD sume rules [ref] : $≃0.012 ±0.006$ GeV$^4$ [ref] , corresponding to a typical scale $≃()^1/4 = 330$ MeV.

Unruh thermalization, gluon condensation and freeze-out · 2. String tension and gluon condensate at finite density · 0.92
Here one finds the average value $σ≃0.19 ±0.03$ GeV$^2$ [ref] , which with eq.

Hadron Freeze-Out and Unruh Radiation · Introduction · 0.99

Compares with it 6 papers

For comparison we also show the fit function of [ref] .

Finite temperature Lattice QCD with two flavors of improved Wilson fermions · Critical temperature · 1.00
It is of considerable interest to compare this result with those obtained in two recent large-scale studies using staggered fermions [ref] .

The finite temperature QCD using 2+1 flavors of domain wall fermions at N_t = 8 · Conclusion and Outlook · 1.00
Finally, we compare the quenched results to dynamical results using $p4fat3$ fermions with improved gauge action and quark masses $m_q$=0.0065 and $m_s$=0.065, see Ref. [ref] .

The Polyakov Loop and the Eigenvalues of the Dirac Operator · Data · 0.99

Cites it as support 1 paper

It has been established by lattice calculations that at the physical values of light and strange quark masses at zero baryon chemical potential the transition from the hadronic into the deconfined phase of QCD is a rapid crossover rather than a genuine phase transition [ref] .

Lattice QCD at Non-Zero Temperature · Chiral crossover · 0.96

Cites it as background 12 papers

In spite of enormous computational efforts [ref] , the answer to this question has remained controversial.

Probing the finite temperature phase transition with Nf=2 nonperturbatively improved Wilson fermions · Introduction · 0.93
Recently, the most detailed studies of the transition temperature have been performed with different variants of the staggered fermion action [ref] .

The finite temperature QCD using 2+1 flavors of domain wall fermions at N_t = 8 · Introduction · 0.99
At present, for QCD with $2+1$ light flavors, these simulations provide us with results, near the continuum limit, for the behavior of QCD in thermodynamic equilibrium [ref] .

Chiral matrix model of the semi-Quark Gluon Plasma in QCD · Introduction · 0.89

Discussion

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