Analytical derivation and numerical calculation of the $\alpha_s$-order correction to the non-perturbative equation of state for SU(3) gluon matter

M. Vasuth; V. Gogokhia

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Analytical derivation and numerical calculation of the $\alpha_s$-order correction to the non-perturbative equation of state for SU(3) gluon matter

V. Gogokhia, M. Vasuth

High Energy Physics - Phenomenology · Submitted 19 Dec 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We also explicitly derive and numerically calculate the first perturbative contribution of the $\alpha_s$-order to the non-perturbative part of the equation of state derived and calculated previously.

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arXiv ID1012.4157 (version 6)

Pith ID6U4PIVFZ, Pith's permanent record of this paper and its review

CitationM. Vasuth, V. Gogokhia. "Analytical derivation and numerical calculation of the $\alpha_s$-order correction to the non-perturbative equation of state for SU(3) gluon matter." arXiv:1012.4157 (2010). https://pith.science/paper/6U4PIVFZ

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.74 · mentions code or data availability 0.02.

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arXiv listing abstract v6. Results and the main claim are underlined; show every role.

In our previous works the effective potential approach for composite operators has been generalized to non-zero temperature in order to derive the analytical equation of state for pure SU(3) Yang-Mills fields without quark degrees of freedom. In the absence of external sources this is nothing but the vacuum energy density. The key element of this derivation is the introduction of a temperature dependence into the expression for the bag constant. The non-perturbative part of the analytical equation of state does not depend on the coupling constant, but instead introduces a dependence on the mass gap. This is responsible for the large-scale dynamical structure of the QCD ground state. The perturbative part of the analytical equation of state does depend on the QCD fine-structure coupling constant $\alpha_s$. Here we develop the analytical formalism, incorporating the perturbative part in a self-consistent way. It makes it possible to calculate the PT contributions to the equation of state in terms of the convergent series in integer powers of a small $\alpha_s$. We also explicitly derive and numerically calculate the first perturbative contribution of the $\alpha_s$-order to the non-perturbative part of the equation of state derived and calculated previously. The analytical equation of state or, equivalently, the gluon pressure is exponentially suppressed at low temperatures, while at temperature $T=T_c = 266.5 \ \MeV$ it has a maximum, if divided by $T^4/3$. It demonstrates a highly non-trivial dependence on the mass gap and the temperature near to $T_c$ and up to approximately $(3-4)T_c$. At very high temperatures its polynomial character is confirmed, containing the terms proportional to $T^2$ and $T$ with a non-analytical dependence on the mass gap.

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	In our previous works the effective potential approach for composite operators has been generalized to non-zero temperature in order to derive the analytical equation of state for pure SU(3) Yang-Mills fields without quark degrees of freedom.	background 0.99	0.70	0.04	asserted 1.00
s1	In the absence of external sources this is nothing but the vacuum energy density.	background 0.57	0.15	0.02	asserted 1.00
s2	The key element of this derivation is the introduction of a temperature dependence into the expression for the bag constant.	method 0.82	0.52	0.04	asserted 1.00
s3	The non-perturbative part of the analytical equation of state does not depend on the coupling constant, but instead introduces a dependence on the mass gap.	result 0.47	0.47	0.07	asserted 1.00
s4	This is responsible for the large-scale dynamical structure of the QCD ground state.	interpretation 0.97	0.23	0.04	asserted 1.00
s5	The perturbative part of the analytical equation of state does depend on the QCD fine-structure coupling constant $\alpha_s$.	background 0.93	0.33	0.05	asserted 1.00
s6	Here we develop the analytical formalism, incorporating the perturbative part in a self-consistent way.	contribution 0.96	0.93	0.08	asserted 1.00
s7	It makes it possible to calculate the PT contributions to the equation of state in terms of the convergent series in integer powers of a small $\alpha_s$.	method 0.64	0.81	0.11	asserted 0.77
s8	We also explicitly derive and numerically calculate the first perturbative contribution of the $\alpha_s$-order to the non-perturbative part of the equation of state derived and calculated previously.	contribution 0.96	0.96	0.43	asserted 1.00
s9	The analytical equation of state or, equivalently, the gluon pressure is exponentially suppressed at low temperatures, while at temperature $T=T_c = 266.5 \ \MeV$ it has a maximum, if divided by $T^4/3$.	result 1.00	0.80	0.20	asserted 0.99
s10	It demonstrates a highly non-trivial dependence on the mass gap and the temperature near to $T_c$ and up to approximately $(3-4)T_c$.	result 0.96	0.79	0.18	asserted 1.00
s11	At very high temperatures its polynomial character is confirmed, containing the terms proportional to $T^2$ and $T$ with a non-analytical dependence on the mass gap.	result 0.99	0.81	0.14	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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arXiv listing abstract v6

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The paper

Original abstract

In our previous works the effective potential approach for composite operators has been generalized to non-zero temperature in order to derive the analytical equation of state for pure SU(3) Yang-Mills fields without quark degrees of freedom. In the absence of external sources this is nothing but the vacuum energy density. The key element of this derivation is the introduction of a temperature dependence into the expression for the bag constant. The non-perturbative part of the analytical equation of state does not depend on the coupling constant, but instead introduces a dependence on the mass gap. This is responsible for the large-scale dynamical structure of the QCD ground state. The perturbative part of the analytical equation of state does depend on the QCD fine-structure coupling constant $\alpha_s$. Here we develop the analytical formalism, incorporating the perturbative part in a self-consistent way. It makes it possible to calculate the PT contributions to the equation of state in terms of the convergent series in integer powers of a small $\alpha_s$. We also explicitly derive and numerically calculate the first perturbative contribution of the $\alpha_s$-order to the non-perturbative part of the equation of state derived and calculated previously. The analytical equation of state or, equivalently, the gluon pressure is exponentially suppressed at low temperatures, while at temperature $T=T_c = 266.5 \ \MeV$ it has a maximum, if divided by $T^4/3$. It demonstrates a highly non-trivial dependence on the mass gap and the temperature near to $T_c$ and up to approximately $(3-4)T_c$. At very high temperatures its polynomial character is confirmed, containing the terms proportional to $T^2$ and $T$ with a non-analytical dependence on the mass gap.

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2 arXiv papers cite this in 28 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 · 24 sentences without a confident label

Uses its data or values 1 paper

For the numerical values of the exponents $ν_i, i=1,2,3,4,5$ see our work [ref] , where the low-temperature expansion (5.5) has been analytically derived (for the explicit expressions of $ω'_eff$, $ω̅_eff$ and $ω̃_eff$ see below).

Analytic description of SU(3) lattice thermodynamics in the whole temperature range within the mass gap approach · The gluon pressure $P_g(T)$ · 0.85

Cites it as support 2 papers

It is worth emphasizing that all the series which arise from the initial term (4.1) in integer powers of a small $x(ω^2, ω^2_n)$ (or, equivalently, $α_s$) are convergent [ref] .

The Hagedorn-type structure of the non-perturbative gluon pressure within the mass gap approach to QCD · Thermal PT · 0.99
Analytically this cancelation at high temperatures (above $T_c$) has been shown in [ref] , where it has also been shown that the massless (but not free) gluons may be present at low temperatures (below $T_c$) in the GM.

Analytic description of SU(3) lattice thermodynamics in the whole temperature range within the mass gap approach · The full GP EoS · 0.96

Cites it as background 1 paper

II, III, and IV, in which we briefly describe our results obtained earlier in [ref] , especially taking into account that the book [ref] is not freely available.

The Hagedorn-type structure of the non-perturbative gluon pressure within the mass gap approach to QCD · The gluon pressure at non-zero temperature · 0.82

What it cites · 33 sentences without a confident label

Builds on 2 papers

We also explicitly derive and numerically calculate the first PT contribution of the $α_s$-order to the NP part of the GM EoS derived and calculated previously [ref] .

The non-perturbative analytical equation of state for the gluon matter. I · Introduction · 0.98
The key element in this program was the extension of our paper [ref] to non-zero temperature [ref] .

Vacuum Energy Density in the Quantum Yang - Mills Theory · Introduction · 0.90

Uses the method or tool of 1 paper

In this integral the summation over the Matsubara frequencies can be performed analytically (i.e., exactly) with the help of the expression explicitly given in [ref] .

The non-perturbative analytical equation of state for the gluon matter. I · $P_PT(Δ^2; T)$ contribution · 1.00

Uses data or values from 2 papers

[equation] where $ω_eff=1$ and the mass gap $Δ^2= 0.4564 ^2$ for $SU(3)$ gauge theory are fixed [ref] .

The non-perturbative analytical equation of state for the gluon matter. I · $P_NP(T)$ contribution · 0.95
[equation] where $ω_eff=1$ and the mass gap $Δ^2= 0.4564 ^2$ for $SU(3)$ gauge theory are fixed [ref] .

Vacuum Energy Density in the Quantum Yang - Mills Theory · $P_NP(T)$ contribution · 0.95

Cites as background 3 papers

Recently it underwent a rapid progress ( [ref] and references therein).

Equation of state and more from lattice regularized QCD · Introduction · 0.90
Recently it underwent a rapid progress ( [ref] and references therein).

The QCD Equation of State with almost Physical Quark Masses · Introduction · 0.90
Recently it underwent a rapid progress ( [ref] and references therein).

The QCD EoS from simulations on BlueGene L Supercomputers at LLNL and NYBlue · Introduction · 0.90

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