Three-loop free energy for pure gauge QCD

Arnold, Peter; Zhai, Chengxing

doi:10.1103/physrevd.50.7603

Cited by 292 publications

(537 citation statements)

References 12 publications

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“…Then, only the internal lines with zero Matsubara frequency (ω n = 0) can be soft, and require resummation [177,178]. Since in the static limit the HTL's collapse to the Debye mass term (cf.…”

Section: Some Applications Of Htl-resummed Perturbation Theorymentioning

confidence: 99%

The quark–gluon plasma: collective dynamics and hard thermal loops

Blaizot¹,

Iancu²

2002

Physics Reports

515

714

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We present a unified description of the high temperature phase of QCD, the so-called quark-gluon plasma, in a regime where the effective gauge coupling g is sufficiently small to allow for weak coupling calculations. The main focuss is the construction of the effective theory for the collective excitations which develop at a typical scale gT , which is well separated from the typical energy of single particle excitations which is the temperature T . We show that the short wavelength thermal fluctuations, i.e., the plasma particles, provide a source for long wavelength oscillations of average fields which carry the quantum numbers of the plasma constituents, the quarks and the gluons. To leading order in g, the plasma particles obey simple gauge-covariant kinetic equations, whose derivation from the general Dyson-Schwinger equations is outlined. By solving these equations, we effectively integrate out the hard degrees of freedom, and are left with an effective theory for the soft collective excitations. As a by-product, the "hard thermal loops" emerge naturally in a physically transparent framework. We show that the collective excitations can be described in terms of classical fields, and develop for these a Hamiltonian formalism. This can be used to estimate the effect of the soft thermal fluctuations on the correlation functions. The effect of collisions among the hard particles is also studied. In particular we discuss how the collisions affect the lifetimes of quasiparticle excitations in a regime where the mean free path is comparable with the range of the relevant interactions. Collisions play also a decisive role in the construction a Member of CNRS. E-mail: blaizot@spht.saclay.cea.fr b Member of CNRS. E-mail: iancu@spht.saclay.cea.fr c Laboratoire de la Direction des Sciences de la Matière du Commissariatà l'Energie Atomique of the effective theory for ultrasoft excitations, with momenta ∼ g 2 T , a topic which is briefly addressed at the end of this paper.

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Section: Some Applications Of Htl-resummed Perturbation Theorymentioning

confidence: 99%

The quark–gluon plasma: collective dynamics and hard thermal loops

Blaizot¹,

Iancu²

2002

Physics Reports

515

714

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“…However, it was well-known that this expansion is no longer calculable perturbatively at O(g 6 ) [29]. By now all calculable orders up to O(g 5 ln g) have been calculated [30]. Unfortunately it turned out that the information gained from this expansion is rather limited.…”

Section: The Qcd Equation Of Statementioning

confidence: 99%

“…In fact, even at T ≃ 4 Tc deviations from the ideal gas value are larger than 10%. This is too much to be understood in terms of weakly interacting gluons as they are described by ordinary high temperature perturbation theory [30]. Even at these high temperatures non-perturbative effects have to be taken into account which may be described in terms of interactions among quasi-particles [31,40].…”

Section: Thermodynamics Of the Su(3) Gauge Theorymentioning

confidence: 99%

“…We thus must expect that non-perturbative screening effects also have an influence on bulk thermodynamics properties (pressure, energy density) above Tc and even up to quite large temperatures. In fact, the calculations of the pressure and energy density in the SU (3) gauge theory and in QCD with light quarks, which we are going to discuss in the next section, show that at temperatures a few times Tc deviations from the ideal gas limit are still too large to be understood in terms of conventional high temperature perturbation theory, which converges badly at these temperatures just because of the large contribution arising from Debye screening [30]. The screening of static quark and anti-quark sources is commonly analyzed in terms of Polyakov-loop correlation functions, which define the heavy quark free energy introduced in Eq.…”

Section: Chiral Symmetry Restorationmentioning

confidence: 99%

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Lattice QCD at High Temperature and Density

Karsch

Lecture Notes in Physics

437

187

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After a brief introduction into basic aspects of the formulation of lattice regularized QCD at finite temperature and density we discuss our current understanding of the QCD phase diagram at finite temperature. We present results from lattice calculations that emphasize the deconfining as well as chiral symmetry restoring features of the QCD transition, and discuss the thermodynamics of the high temperature phase.

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“…For a thermal medium, the free energy in non-abelian gauge theories have been analytically computed up to O(g 4 ) [44,45], O(g 5 ) [46], O(g 6 ln(1/g)) [47] (where g is the coupling constant). However, the thermodynamic observables obtained by the addition of successive higher-order terms in the weak-coupling expansion oscillate haphazardly, as a result they have a small radius of convergence.…”

Section: Introductionmentioning

confidence: 99%

One-loop QCD thermodynamics in a strong homogeneous and static magnetic field

Rath

Patra

2017

J. High Energ. Phys.

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Abstract:We have studied how the equation of state of thermal QCD with two light flavors is modified in a strong magnetic field. We calculate the thermodynamic observables of hot QCD matter up to one-loop, where the magnetic field affects mainly the quark contribution and the gluon part is largely unaffected except for the softening of the screening mass. We have first calculated the pressure of a thermal QCD medium in a strong magnetic field, where the pressure at fixed temperature increases with the magnetic field faster than the increase with the temperature at constant magnetic field. This can be understood from the dominant scale of thermal medium in the strong magnetic field, being the magnetic field, in the same way that the temperature dominates in a thermal medium in the absence of magnetic field. Thus although the presence of a strong magnetic field makes the pressure of hot QCD medium larger, the dependence of pressure on the temperature becomes less steep. Consistent with the above observations, the entropy density is found to decrease with the temperature in the presence of a strong magnetic field which is again consistent with the fact that the strong magnetic field restricts the dynamics of quarks to two dimensions, hence the phase space becomes squeezed resulting in the reduction of number of microstates. Moreover the energy density is seen to decrease and the speed of sound of thermal QCD medium increases in the presence of a strong magnetic field. These findings could have phenomenological implications in heavy ion collisions because the expansion dynamics of the medium produced in non-central ultra-relativistic heavy ion collisions is effectively controlled by both the energy density and the speed of sound.

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Three-loop free energy for pure gauge QCD

Cited by 292 publications

References 12 publications

The quark–gluon plasma: collective dynamics and hard thermal loops

The quark–gluon plasma: collective dynamics and hard thermal loops

Lattice QCD at High Temperature and Density

One-loop QCD thermodynamics in a strong homogeneous and static magnetic field

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