The colourlessness partition function of the quantum quark-gluon gas

Gorenstein, M. I.; Lipskikh, S.I.; Petrov, V. K.; Zinovjev, G.

doi:10.1016/0370-2693(83)90988-7

Cited by 52 publications

(39 citation statements)

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“…Only in this limit can one indiscriminately use the GC or C descriptions. The results presented here do not rely on the system under consideration being of a relativistic nature and apply equally well to relativistic and nonrelativistic systems.There is an essential difference in the volume dependence of observables in the GC and C formulations [1][2][3]7,9]. Consequently, in the limit when V → ∞, some ratios of extensive quantities could in general converge to different In applications of statistical models to particle production in high energy collisions of elementary particles [13] and in heavy ion collisions [1,14], we are always dealing with small systems.…”

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confidence: 99%

Probability distributions in statistical ensembles with conserved charges

Cleymans¹,

Redlich²,

Turko³

2005

Phys. Rev. C

116

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The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken, then the canonical and grand canonical ensembles are equivalent. This equivalence is proven on the most general probability distribution level. Macroscopic data of an equilibrium state are described by means of statistical distributions of microscopic variables specific for a given ensemble. In the application to the description of particle production in high energy particle collisions, we are generally dealing with the grand canonical ensemble with respect to the particle number [1][2][3]. In the ultrarelativistic situation, energy conservation and particle number are usually controlled by the temperature of the system [4].Applications of statistical physics concepts to multiparticle production processes require, however, the implementation of internal symmetries [5,6] that result in associated conservation of quantum numbers. In the grand canonical formulation (GC), conservation of quantum numbers is applied to the average and is determined by the corresponding chemical potential. On the other hand, in the canonical ensemble (C) quantum number conservation is specifically treated.In general, the thermodynamic quantities calculated in the GC and C ensembles differ. This is particularly true when dealing with small systems [1][2][3][4]7,8]. Since relativistic heavy ion collisions correspond to a finite volume and to a given charge value, the canonical ensemble should be used whenever the GC and C formalisms give different answers [2,[8][9][10][11]. It is, however, to be expected that in the thermodynamic limit, the C and GC descriptions will provide the same answer for physical observables [2,9,10]. The thermodynamic limit is reached in large volume for a fixed density in C, and for a fixed average density in the GC ensemble. Only in this limit can one indiscriminately use the GC or C descriptions. The results presented here do not rely on the system under consideration being of a relativistic nature and apply equally well to relativistic and nonrelativistic systems.There is an essential difference in the volume dependence of observables in the GC and C formulations [1][2][3]7,9]. Consequently, in the limit when V → ∞, some ratios of extensive quantities could in general converge to different In applications of statistical models to particle production in high energy collisions of elementary particles [13] and in heavy ion collisions [1,14], we are always dealing with small systems. Thus, the model description of particle yields is in principle canonical with respect to the conservation laws. This is particularly evident in elementary particle and peripheral heavy ion collisions where, e.g., strangeness production is strongly suppressed due to canonical effects [11]. However, a detailed analysis of different particle yields [1,[9][10][11]14] has shown that in central heavy ion collisions the relative error between the C and G...

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confidence: 99%

Probability distributions in statistical ensembles with conserved charges

Cleymans¹,

Redlich²,

Turko³

2005

Phys. Rev. C

116

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“…We note that the ingredients of our rather simple calculation have been around for more than a decade [7][8][9][10][11], but to our knowledge no-one has checked these dramatic consequences explicitly before.…”

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“…The purpose of the present study is to reconsider the statistical themodynamical description of quantum gases consisting of quarks and antiquarks, in such a way that the underlying symmetry can amount to reordering of thermodynamic potential in terms of the color singlet multi-quark modes at any temperatures. We note that the ingredients of our rather simple calculation have been around for more than a decade [7][8][9][10][11], but to our knowledge no-one has checked these dramatic consequences explicitly before.…”

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confidence: 99%

“…The estimation of energy density and pressure [9,11] at moderately high temperatures show deviation from their ideal gas behaviour. In this context, it has been suggested [3] that the long distance behaviour of the high temperature phase can be characterised by the propagation of color singlet multi-quark structures.…”

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confidence: 99%

“…It is worth noting here that Eq. (7) represents the general structure of color projected partition function so far existing in the literature [7][8][9][10][11], and depending upon the nature of the problem it has been utilised accordingly. Now for convenience, we make a substitution ξ q = −iβµ q and after a little algebra, Eq.…”

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Hadronic modes in the quark plasma with an internal symmetry

Mustafa,

Sen,

Paria

1999

Eur. Phys. J. C

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We show that requiring the quark partition function to be color singlet of SU (3) color gauge group leads to reordering the thermodynamic potential in terms of the colorless multi-quark modes (qq, qqq,qqq, · · ·) at any given temperature. These color singlet structures are not bound states in real sense, rather they are combination of constituents quarks only. In accord with the "preconfinement" property of QCD, under a suitable confining mechanism, these could evolve into color singlet hadrons/baryons at low temperatures. At fairly high temperatures these multi-quark color singlet structures exist in the plasma like hadronic modes, just as in the more familiar low temperature phase. This suggests that there exists a strong color correlation in the plasma at all temperatures.PACS numbers: 24.85.+p, 12.38.Mh, 25.75.+r, 64.60.Qb The success of the quark model, the quantum chromodynamics (QCD), and the non-observability of the free partons (q,q, g) has entailed the concept of confinement. QCD, the theory of strong interactions, is not perturbative at large distances. Thus, the confinement itself can not be treated perturbatively. There are reasons to believe that the confinement of partons inside hadrons may not survive collisions between heavy nuclei at relativistic energies [1]. One of the most interesting predictions of QCD at high temperature is the transition from the confined/chirally broken phase to deconfined/chirally symmetric state of quasi-free quarks and gluons, the so called quark-gluon plasma. At very high temperatures, the bulk properties (energy density, pressure, and entropy etc.) of QCD matter, seem to be described by a gas of nearly free quarks and gluons. However, it is also known that long range, non-perturbative effects disrupt this simple picture even at fairly high temperatures [2].Lattice calculations [3] have provided ample evidence * Alexander von Humboldt Fellow, and on leave from Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Calcutta -700 064, India.that the long distance behaviour of high temperature phase is characterised by the propagation of color singlet objects like multi-quark structures. The determination of the plasma screening length shows evidence of a kind of correlations in the quark-gluon plasma at all temperatures. Now what these structures are and how they show up is not yet very clear theoretically. Quite sometime ago an indication was made as a "precursor" to the confinement property of QCD by Amati and Veneziano [4] where the cascading and fragmenting partons produced in hadronic collisions rearrange themselves into color singlet clusters which ultimately evolve into hadrons [5,6]. These considerations convince us that it is important to incorporate the dynamic requirement of color singletness of the quark-matter to take into account such 'interaction' which "tunnels" into hadronic matter phase space [6].The purpose of the present study is to reconsider the statistical themodynamical description of quantum gases consisting of quarks and antiquarks, in suc...

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