Static quark anti-quark free energy and the running coupling at finite temperature

F. Karsch; F. Zantow; O. Kaczmarek; P. Petreczky

REVIEW

Static quark anti-quark free energy and the running coupling at finite temperature

O. Kaczmarek, F. Karsch, P. Petreczky, F. Zantow

High Energy Physics - Lattice · Submitted 23 Jun 2004 · 24 references

Pith's verdict: Real lattice data and a quotable r_screen scaling law; the confinement-remnant headline is a gloss on a gauge-fixed correlator, not a derived result.

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arXiv IDhep-lat/0406036 (version 1)

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CitationF. Karsch, F. Zantow, O. Kaczmarek, P. Petreczky. "Static quark anti-quark free energy and the running coupling at finite temperature." arXiv:hep-lat/0406036 (2004). https://pith.science/paper/V3KJ3KJF

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Worth your time for the data, less for the headline. The solid part: they take the Necco-Sommer zero-temperature running-coupling machinery and run it at finite T on 32^3 x N_tau quenched lattices with N_tau = 4, 8, 16, 100-500 configurations per point, Symanzik-improved action, and the r_I correction for rotational symmetry. The short-distance result -- F1 tracks the T=0 potential and alpha_qq stays temperature-independent below r ~ 0.1 fm up to about 3 Tc -- is clean and I believe it. The r_screen = (0.48 fm) Tc/T scaling in Fig. 4 is a compact statement people will quote. Fig. 6 is the honest part of the paper: the two Debye fit parameters only converge around 6 Tc, which is a useful caution for anyone fitting screening masses out of F1. Where it is soft: the abstract's confinement-remnant line [abstract:s3] leans on the sign change of alpha_V and the rise of alpha_qq at r ~ 0.1-0.5 fm, and both are properties of the Coulomb-gauge-fixed Tr L L-dagger. Section II.A cites Vink-Wiese and Philipsen for the dressed-loop reading but never shows their dressing coincides with this gauge fixing, and the gluon cloud can plausibly generate structure right in the intermediate-distance window where the signal is read. The authors half-concede this themselves: at r >~ 0.1 fm they say the couplings 'merely reflect the non-perturbative properties of the observable used to define them.' So the interpretation is a gloss, not a derivation. Reasonable as a suggestion; do not quote it as established. Second soft spot: the T >= 6 Tc 'agreement with perturbation theory' uses a rescaling factor fitted to the same data, so it is a consistency check, not a test. Third: quenched. Named, not weighed, and the quarkonium motivation is unquenched. None of this breaks the quantitative claims, which are the reason to read it. For lattice people working on in-medium quarkonium and for anyone who needs a defensible number for where temperature starts to matter in the q-qbar force. Send it to referees; the short-distance and r_screen results will survive, and a referee should push on the gauge-fixing argument and the rescaled perturbative comparison.

Referee report

Significance

The paper provides a quantitative, well-documented lattice determination of the scale separating vacuum-like from screened physics in the quark–gluon plasma, with a complete simulation-parameter table, a continuum cross-check of the short-distance free energy at T = 1.5 Tc (Fig. 1b, Nτ = 4, 8, 16), and a genuinely falsifiable scaling law r_screen ∝ 1/T. The short-distance result — that the running coupling is temperature independent for r ≲ 0.1 fm up to T ≈ 3 Tc — is a clean and useful statement for heavy-quark and jet phenomenology in heavy-ion collisions, and the high-temperature consistency check of the two-loop running (only the overall normalization is fitted, the shape is fixed by Tc/Λ_MS taken from the literature) is a meaningful one-parameter test rather than a tautology. The interpretive conclusion is appropriately hedged as a suggestion, and the explicit comparison with the Shuryak–Zahed scenario is a useful contribution to that discussion.

Major objections (4)

[§II.A, abstract:s3] The headline interpretation rests on the intermediate-distance structure of F1(r,T) — the sign change of α_V and the rise and maximum of α_qq at r ≈ 0.1–0.5 fm — and F1 is built from the Coulomb-gauge-fixed correlator Tr L(x)L†(0). Section II.A defends this by citing Vink–Wiese [15] and Philipsen [16], but those constructions correspond to a specific dressing of the static sources, and the paper does not show that the Coulomb-gauge fixing used here (maximize Σ_i U_i per time slice, then make Σ_x U0 τ-independent) reproduces that dressing at the distances where the signal is read off. A concrete and feasible test is available in the authors' own data: the color-averaged free energy F(r,T) of Eqs. (1) and (3) is gauge invariant, and the paper already argues that F ≈ F1 at short distances. Showing that the intermediate-distance rise of α_qq, or at least the location of its maximum, is reproduced by the gauge-invariant combination would substantially secure the interpretation; if it is not, the sentence at abstract:s3 should be softened to a statement about the gauge-fixed singlet correlator. I want to be clear that this does not threaten the short-distance running-coupling result, which is protected by the gauge independence of leading one-gluon exchange and by the fact that the derivative in Eq. (8) removes the additive renormalization.
[§IV, Eq. (7) and Fig. 3] The statement that α_V changes sign at r ≈ 0.25 fm for Tc ≤ T ≲ 3 Tc is quoted as evidence for confinement remnants, but α_V = −(3r/4)F1 is linear in F1 and therefore inherits the additive renormalization constant in full. The constant is fixed by matching the short-distance part of F1 to the T = 0 potential of Ref. [10], and the paper notes that this fixes the large-distance behaviour completely; the location, and indeed the existence, of the zero crossing is then a property of that matching prescription rather than a renormalization-group-invariant statement. Please quantify the sensitivity: how far does the crossing radius move if the matching is performed at a different reference distance, and does the qualitative conclusion survive? The same question applies to the comparison between α_V and α_qq in the paragraph following Fig. 3.
[§V, Eq. (14) and Fig. 6] The large-distance fit uses three parameters, α(T), α̃(T) and c(T), against a function whose tail is a single exponential plus a constant, and the extracted ratio α/α̃ is central to the claim that the perturbative limit (Eq. 15) is reached for T ≳ 6 Tc. The manuscript does not report the fit window in rT, the χ²/dof, or the correlation between α and α̃ (and between α̃ and c), all of which are needed to judge whether the ratio is determined or is a parameter degeneracy. Please add these, and show the stability of α(T) and α̃(T) under variation of the fit range. Relatedly, the statement that the temperature dependence follows the two-loop logarithmic form should be stated precisely: since Λ_MS/Tc is taken from Refs. [8, 21] and only the overall factor 2.095(82) is fitted, this is a one-parameter shape test, and saying so explicitly would strengthen rather than weaken the claim.
[§IV, Fig. 4] The scaling law r_screen = (0.48 ± 0.01) fm · Tc/T is one of the two results advertised in abstract:s1, but the quoted uncertainty appears to be statistical only. The prefactor should carry a systematic error budget from the scale setting (√σ = 420 MeV), from the finite-difference approximation to dF1/dr, and from the scheme dependence of the maximum of α_qq, which the paper itself emphasizes. In addition, please state whether a maximum of α_qq is actually resolved within the accessible range of r at the highest temperature shown (12 Tc), or whether that point is an upper or lower bound on r_screen; if the maximum lies outside the simulated range, the point should be marked accordingly in Fig. 4.

Minor objections (8)

[§II.B, Eq. (9)] Please state the sign convention for β(g) explicitly. As printed, the two forms in Eq. (9) differ by the sign of the β-function term, and the text below Fig. 3 states that α_V > α_qq at short distances; a reader checking the two against each other with β = dg/d ln μ versus β = dg/d ln r will not be able to reconcile them without the convention being spelled out.
[§III, Table I] The Nτ = 16 column contains only two entries (T/Tc = 1.5 and 3.0). Please state in the text whether these runs were used for a continuum extrapolation or only as a cross-check of cutoff effects, since Fig. 1b is the main evidence for the absence of cutoff dependence at short distances.
[§VI and abstract] The study is quenched throughout. Since the interpretive conclusion concerns the QCD plasma phase near Tc, where dynamical quarks are expected to matter most, a sentence in the summary on the expected direction and rough size of the quenching error would help the reader place the result.
[§II.A, Eq. (6)] The notation g(r) in the short-distance line and g(T) in the large-distance line of Eq. (6) should be defined once in the surrounding text, together with the statement that the exponent is the leading-order Debye mass μ = g(T)T; the footnote [24] covers the gauge invariance but not the notation.
[References [20] and [21]] These two entries appear to be the same paper (Beinlich, Karsch, Laermann, Peikert, Eur. Phys. J. C6 (1999) 133) listed twice; please merge them.
[Reference [12]] The arXiv identifier 'hep-th/031122' appears truncated; please check and give the complete number.
[Figs. 2 and 3 captions] The phrase 'the value s of the temperature' should read 'the values of the temperature'.
[§II.B] 'We will extent here' should read 'We will extend here', and 'additative' in §II.A should read 'additive'.

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The paper

The paper claims

The quark-antiquark force in a hot gluon plasma keeps its zero-temperature strength at short distances and only screens beyond a temperature-set length scale.

The reading

This paper asks how the force between a static quark and antiquark changes when the QCD vacuum is replaced by a gluon plasma, and which length scale controls the force's strength at each distance. Working in quenched SU(3) lattice gauge theory at temperatures from just above $T_c$ up to $12T_c$, the authors extract running couplings from the color-singlet free energy and compare them with the zero-temperature heavy quark potential and with two-loop perturbation theory. They find that below roughly $0.1$ fm the coupling is indistinguishable from its zero-temperature value for temperatures up to about $3T_c$, and that the crossover to screened, temperature-dominated behavior happens at a distance that shrinks inversely with temperature, $r_{screen} = (0.48 +- 0.01)$ fm $T_c/T$. The interpretive payoff is that the growth of the coupling at intermediate distances near $T_c$ is a leftover of the confining force rather than a thermally strengthened Coulomb interaction. That matters because it undercuts a picture in which the near-$T_c$ plasma hosts many Coulombically bound heavy-quark states.

What carries the argument

The load-bearing object is the color-singlet heavy quark free energy $F_1(r,T)$, obtained from the Coulomb-gauge-fixed Polyakov loop correlator $Tr L(x) L^†(0)$ and normalized by matching its short-distance part to the zero-temperature heavy quark potential. Two derived quantities carry the argument: the potential-scheme coupling $α_V = -(3r/4)F_1$, which is sensitive to the sign change that a confining linear term forces, and the force-scheme coupling $α_{qq} = (3r^2/4) dF_1/dr$, which stays positive and whose maximum locates the screening length. A lattice-spacing correction replaces the separation $r$ by $r_I$ defined through the Fourier transform of the tree-level improved gluon propagator, which removes most of the rotational-symmetry breaking at short distances and is what makes the $r < 0.1$ fm comparison with perturbation theory meaningful.

Extended reading notes

Core claim

The authors compute the color-singlet free energy $F_1(r,T)$ of a static quark-antiquark pair in quenched QCD on $32^3 x N_τ$ lattices with $N_τ = 4, 8, 16$ and a tree-level Symanzik-improved gauge action, renormalizing it by matching the short-distance part to the zero-temperature heavy quark potential. From it they build two couplings, $α_V(r,T) = -(3r/4) F_1(r,T)$ and $α_{qq}(r,T) = (3r^2/4) dF_1(r,T)/dr$, and find that for $r <~ 0.1$ fm both agree with the zero-temperature lattice potential and with the two-loop perturbative force, with no visible temperature dependence up to $T ≃ 3T_c$; above that, thermal effects reach even into the short-distance regime. Beyond $r ≃ 0.1$ fm non-perturbative physics takes over: $α_V$ changes sign for $T_c <= T <~ 3T_c$, exactly as a linearly rising confining potential would force it to, while $α_{qq}$ rises and then peaks. The location of that peak defines the screening scale, and across the whole temperature range it obeys $r_{screen} = (0.48 +- 0.01)$ fm $T_c/T$. At large distances the authors fit $F_1$ with a Debye-screened Coulomb form containing two independent couplings, $α(T)$ and $ã(T)$; their ratio approaches one only for $T >~ 6T_c$ and reaches about five near $T_c$, so a temperature-dependent coupling is badly scheme dependent for $T_c <= T <~ 2T_c$. For $T >= 6T_c$ a single rescaled two-loop coupling, $α(T) = 2.095(82) α_{pert}(T)$, describes both the Coulomb strength and the screening mass. The conclusion the authors draw is that the near-$T_c$ plasma is better described by remnants of confinement than by a strong Coulombic force.

Load-bearing premise

The argument depends on the Coulomb-gauge-fixed Polyakov loop correlator being a faithful stand-in for a physical, gauge-invariant singlet free energy at the distances and temperatures studied, since if that identification only approximately holds, the extracted coupling describes a gauge-dependent quantity rather than the plasma.

Editorial extensions

If this is right

Short-distance observables at separations below about $0.1$ fm in a quark-gluon plasma up to $3T_c$ can be computed with vacuum QCD input, without thermal corrections to the coupling.
The relation $r_{screen} = (0.48 +- 0.01)$ fm $T_c/T$ gives a concrete criterion for when medium effects begin to modify a process of a given spatial extent.
For $T >= 6T_c$, a single constant rescaling of the two-loop running coupling describes both the Coulomb strength and the screening mass extracted from the singlet free energy, so higher-order and non-perturbative corrections appear as an overall factor there.
Near $T_c$, models that trace the plasma's non-perturbative behavior to a large Coulomb coupling are attributing the effect to the wrong source; the relevant physics is residual confinement at intermediate distances.
Any quoted temperature-dependent coupling for $T_c <= T <~ 2T_c$ is scheme dependent at the level of a factor of several, so such couplings should not be transported between different observables without conversion.

Reading between the lines

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

If the remnant-confinement reading is right, fitting $F_1$ near $T_c$ with a linear-plus-Coulomb form should yield an effective string tension that decreases smoothly with temperature and vanishes only gradually, which is a check the paper does not perform directly.
The whole short-distance result rests on a gauge-fixed correlator standing in for a gauge-invariant singlet free energy; a cross-check with a genuinely gauge-invariant dressed-Polyakov-loop operator, or in a different gauge, would test whether the reported temperature independence of the slope is physical rather than an artifact of the Coulomb-gauge choice.
For quarkonium phenomenology this implies a specific ordering: the Coulombic binding of a heavy quark pair should be essentially unmodified until the screening length falls below the bound-state radius, so medium modification of the lowest-lying states should set in at a calculable temperature rather than gradually from $T_c$.
Because the ratio $α(T)/ã(T)$ varies from about five near $T_c$ to one near $6T_c$, anyone extracting a Debye mass or a plasma coupling from lattice free energies in the intermediate temperature range should report which of the two fitted parameters they mean; tabulating the ratio as a function of temperature would make the ambiguity usable rather than merely noted.

Original abstract

We analyze the free energy of a static quark anti-quark pair in quenched QCD at short and large distances. From this we deduce running couplings, g^2(r,T), and determine the length scale that separates at high temperature the short distance perturbative regime from the large distance non-perturbative regime in the QCD plasma phase. Ambiguities in the definition of a coupling beyond the perturbative regime are discussed in their relation to phenomenological considerations on heavy quark bound states in the quark gluon plasma. Our analysis suggests that it is more appropriate to characterize the non-perturbative properties of the QCD plasma phase close to T_c in terms remnants of the confinement part of the QCD force rather than a strong Coulombic force.

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, 3,717 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.67 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.13 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We analyze the free energy of a static quark anti-quark pair in quenched QCD at short and large distances. From this we deduce running couplings, g^2(r,T), and determine the length scale that separates at high temperature the short distance perturbative regime from the large distance non-perturbative regime in the QCD plasma phase. Ambiguities in the definition of a coupling beyond the perturbative regime are discussed in their relation to phenomenological considerations on heavy quark bound states in the quark gluon plasma. Our analysis suggests that it is more appropriate to characterize the non-perturbative properties of the QCD plasma phase close to T_c in terms remnants of the confinement part of the QCD force rather than a strong Coulombic force.

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 analyze the free energy of a static quark anti-quark pair in quenched QCD at short and large distances.	contribution 0.99	0.94	0.03	asserted 0.89
s1	From this we deduce running couplings, g^2(r,T), and determine the length scale that separates at high temperature the short distance perturbative regime from the large distance non-perturbative regime in the QCD plasma phase.	result 0.73	0.96	0.15	asserted 1.00
s2	Ambiguities in the definition of a coupling beyond the perturbative regime are discussed in their relation to phenomenological considerations on heavy quark bound states in the quark gluon plasma.	interpretation 0.45	0.42	0.04	unclear 0.54
s3	Our analysis suggests that it is more appropriate to characterize the non-perturbative properties of the QCD plasma phase close to T_c in terms remnants of the confinement part of the QCD force rather than a strong Coulombic force.	interpretation 0.99	0.86	0.72	hedged possibility 1.00

What kind of paper the classifier reports this is: simulation study 0.89 · evidence from simulation or computation 0.87.

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.** FIG. 1: Heavy quark free energies in the singlet channel cal

**Figure 2.** FIG. 2: The running coupling in the

**Figure 4.** FIG. 4: The location of the maximum in

**Figure 5.** FIG. 5: The singlet free energy versus

Showing 4 of the paper's 5 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-lat/0406036 by the authors.

References

Works cited (24)

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O. Philipsen, Phys. Lett. B535 (2002) 138

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S. Necco and R. Sommer, Phys. Lett. B 523 (2001) 135

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for a diﬀerent renormalization scheme see, A. Dumitru, Y. Hatta, J. Lenaghan, K. Orginos and R. D. Pisarski, hep-th/031122

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B. Beinlich, F. Karsch, E. Laermann, A. Peikert, Eur.Phys.J. C6 (1999) 133

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B. Beinlich, F. Karsch, E. Laermann and A. Peikert, Eur. Phys. J. C 6 (1999) 133

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[24]

Although this is usually called the leading order pertu r- bative result in the high temperature phase the screened potential already involves summation of an inﬁnite set of ladder diagrams which leads to the screening mass µ(T ) = g(T )T . We note, that this leading order per- turbative result is gauge invariant

View on Pith

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An updated potential-model calculation of bottomonium suppression in 2.76 TeV lead-lead collisions reproduces the shape of preliminary CMS suppression data versus centrality, rapidity, and transverse momentum, and fav...
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...
Gauge/String Duality, Hot QCD and Heavy Ion Collisions
hep-th 2011-01 accept novelty 2.0 of 10

The review synthesizes a decade of work showing that strongly coupled plasma calculations from gauge/string duality give a coherent, quantitatively useful picture of hot QCD matter and heavy ion observables.
Heavy-flavor production and medium properties in high-energy nuclear collisions - What next?
nucl-th 2016-12 accept novelty 1.0 of 10

The heavy-flavor community's 2016 consensus roadmap names B-meson suppression near 10 GeV, open charm and bottom cross sections to 10 percent accuracy, and quarkonium feed-down measurements as the priorities for the n...

How later papers used it

51 later papers cite it

Evidence: substantial. 40 of the citing papers share no author with it, and 24 of those carry a confident label from Pith's citation classifier.

Pith read 25 of the 85 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

7 later papers by other authors are listed below: 6 used its data or values and 1 cited it as support. 2 more papers by the same authors are listed: 2 used its data or values.

Uses its data or values 8 of 14 papers with this label · 2 by the same authors

Used the potential U(r,T) evaluated by this paper from lattice QCD results and re-parameterised it.

Semi-classical approach to $J/\psi$ suppression in high energy heavy-ion collisions (2013) · 0.84 · paraphrased: the licence does not allow quoting
Estimated a scale as that at which this paper's lattice calculations of the running coupling coincide with the perturbative expression at a given temperature.

Bulk viscosity of QCD matter near the critical temperature (2007) · 0.86 · paraphrased: the licence does not allow quoting
Additionally, we show lQCD estimates: quenched QCD $N_f = 0$ results (grey circles) are taken from Ref. [ref] , $N_f = 2$ (black inverted triangles) from Ref. [ref] and $N_f = 2+1$ (brown squares) from Ref. [ref] (from Fig. 7).

Extraction of the microscopic properties of quasi-particles using deep neural networks (2023) · Results: $g^2, m, γ$ and transport coefficients. · 0.96
Adjusted the leading-order Debye mass by a factor of (1.4)^2 to account for higher-order corrections determined using this paper's lattice calculations.

Bottomonia Suppression in Heavy Ion Collisions from AdS/CFT (2017) · 0.91 · paraphrased: the licence does not allow quoting
Adjusted the isotropic leading-order Debye mass by a factor of (1.4)^2 to account for higher-order corrections measured in this paper's lattice simulations.

Thermal Bottomonium Suppression at RHIC and LHC (2011) · 0.85 · paraphrased: the licence does not allow quoting
The lattice results for quenched QCD, $N_f = 0$ (blue circles) are taken from Ref. [ref] , for $N_f = 2$ (orange inverted triangles) from Ref. [ref] , and for $N_f = 2+1$ (red triangles) from Ref. [ref] .

Inelastic and elastic parton scatterings in the strongly interacting quark-gluon plasma (2023) · Quasiparticle properties · 0.88

By the same authors

Assumed a large-distance form for V(r,T) with coefficients determined in this paper.

Can quarkonia survive deconfinement ? (2007) (same authors) · 0.96 · paraphrased: the licence does not allow quoting
Estimated a scale as that at which this paper's lattice calculations of the running coupling coincide with the perturbative expression at a given temperature.

Universal properties of bulk viscosity near the QCD phase transition (2007) (same authors) · 0.93 · paraphrased: the licence does not allow quoting

Cites it as support 1 paper

Said its conclusion is supported by this paper's calculations of the static quark-antiquark potential.

Prediction of a Photon Peak in Heavy Ion Collisions (2008) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

47 arXiv papers cite this in 80 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 · 36 sentences without a confident label

Builds on it 1 paper

Following [ref] we can generalize this approach to the free energy and singlet free energy and obtain the corresponding effective couplings.

Color screening in (2+1)-flavor QCD · The effective coupling · 0.94

Uses its method or tool 4 papers

In this expression, $μ= G(ξ,θ) m_D$ [ref] is the anisotropic Debye mass, where $G$ is a function which depends on the degree of plasma momentum-space anisotropy $ξ$, the angle of the line connecting the quark-antiquark pair with respect to the beamline direction $θ$, and the isotropic Debye mass $m_D = 1.4 √(1+N_f/6) g_s T$ [ref] .[In the limit $ξ→0$, one has $G = 1$ and the real part of the potential above reduces to the internal energy derived from the original Karsch-Mehr-Satz potential [ref] .].

Using bottomonium production as a tomographic probe of the quark-gluon plasma · Methodology · 0.87
According to the definitions provided in lattice QCD [ref] , the running coupling constant is defined in the so-called qq-scheme as [equation] For Figs. [ref], [ref] (a), [ref] (a), and [ref] (a) of different systems at varying temperatures with $μ=0$, we observed that before reaching the critical temperature of each system, the running coupling constant increases with the quark separation distance.

The Potential Energy of Heavy Quarkonium in Flavor-Dependent Systems from a Holographic Model · Running coupling constant · 0.81
Similarly to papers [ref] we fix the renormalization constant $c'(μ)$ through the matching condition for $Ω_1(r, μ)$ at short distances to the short distance behavior of the interaction potential $V(r)$.

Lattice study of static quark-antiquark interactions in dense quark matter · The grand potential of a static quark-antiquark pair in dense quark matter · 0.90

Uses its data or values 13 papers

We choose to lead this study with the potential $U(r⃗,T)$, evaluated by Kaczmarek et al. [ref] from lQCD results and re-parameterised by us.

Semi-classical approach to $J/\psi$ suppression in high energy heavy-ion collisions · The color screened potentials and temperature scenarios · 0.84
At large distances, $rT > 1.25$ we assume that $V(r,T)$ has the form [equation] where $α_1$ and $α̃_1$ were determined in [ref] .

Can quarkonia survive deconfinement ? · Screening above deconfinement · 0.96
Thus by estimating their dependences on temperature by using quenched (pure Yang-Mills) lattice QCD simulations [ref] , we finally get the temperature dependences of the condensates.

Charmonium ground and excited states at finite temperature from complex Borel sum rules · Finite temperature effects · 0.86

Compares with it 9 papers

This picture qualitatively agrees with lattice result in Ref. [ref] .

Thermodynamics of deformed AdS$_5$ model with a positive/negative quadratic correction in graviton-dilaton system · The heavy quark potential · 0.98
The static energy given by Eq. ([ref]) coincides with the leading-order result [ref] of the so-called singlet free energy first introduced by Nadkarni [ref] (the heavy quark-antiquark free energy was defined by McLerran and Svetitsky in [ref] ) and also studied in lattice QCD (see e.g. [ref] and [ref] for reviews).

Static quark-antiquark pairs at finite temperature · Singlet static energy for $1/r ∼m_D$ · 0.96
The resulting $α_s (T)$ is displayed in the Panel (a) of Fig. [ref] and compared with QCD-lattice coupling deduced from a short-distance behavior of the singlet free energy [ref] and from spectral density of heavy-quark correlator [ref] .

Color path-integral Monte-Carlo simulations of quark-gluon plasma: Thermodynamic and transport properties · Simulations of QGP · 0.98

Cites it as support 1 paper

This conclusion is supported by calculations of both the static quark-antiquark potential [ref] and of Minkowski-space spectral functions in lattice-regularized QCD [ref] .

Prediction of a Photon Peak in Heavy Ion Collisions · Introduction · 1.00

Cites it as background 10 papers

After proper renormalization the expectation value of the renormalized Polyakov loop is related to the free energy, $F_Q$, of a static quark [ref] [equation] The renormalized Polyakov loop, or equivalently the free energy of a static charge $F_Q$ has been studied in SU(N) gauge theories in a wide temperature interval [ref] .

Polyakov loop in 2+1 flavor QCD from low to high temperatures · Introduction · 0.85
In the literature there are several ways to fix this constant [ref] .

QCD Thermodynamics · The renormalized static potential in the continuum limit · 0.84
A related topic of investigation on the lattice consists of calculating the quark-antiquark potential as a function of temperature [ref] .

Toward Large N Thermal QCD from Dual Gravity: The Heavy Quarkonium Potential · Introduction · 0.94

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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