Event-by-event fluctuations of particle ratios in heavy-ion collisions

Tawfik, A.

doi:10.1007/s12648-012-0097-z

Cited by 16 publications

(7 citation statements)

References 26 publications

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“…( 28) with Eq. ( 27), we conclude that calculating higher order moments is associated with a gradual change in n. Expression (10) reflects almost the same behaviour, where higher order moments are associated with change in the coefficients.…”

Section: Higher Order Moments Of the Particle Multiplicitymentioning

confidence: 58%

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On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out, and QCD Critical Endpoint

Tawfik¹

2013

Advances in High Energy Physics

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We calculate the first six non-normalized moments of particle multiplicity within the framework of the hadron resonance gas model. In terms of the lower order moments and corresponding correlation functions, general expressions of higher order moments are derived. Thermal evolution of the first four normalized moments and their products (ratios) are studied at different chemical potentials , so that it is possible to evaluate them at chemical freeze out curve. It is found that a non-monotonic behaviour, reflecting the dynamical fluctuation and strong correlation of particles starts to appear from the normalized third order moment. We introduce novel conditions for describing the chemical freeze out curve. Although the hadron resonance gas model does not contain any information on the criticality related to the chiral dynamics and singularity in the physical observables, we are able find out the location of the QCD critical endpoint at µ ∼ 350 MeV and temperature T ∼ 162 MeV.Recently, the higher order multiplicity moments have gained prominence in high energy physics with a huge hope in pinpointing the QCD critical endpoint (CEP) [1] connecting the first order boundary separating the hadronic from the partonic matter at high density with the crossover boundary at low density [2,3]. It is clear that the hadron resonance gas partition function is an approximation to a non-singular part of the free energy of QCD in the hadronic phase. There are large theoretical uncertainties of its location and even its existence is not fully confirmed, yet [4][5][6]. The characteristic feature of CEP are critical dynamical fluctuations [7][8][9][10][11]. The higher order moments are conjectured to reflect the large fluctuations associating the hadronquark phase transition. This was the motivation of a remarkable number of experimental and theoretical studies [1,[12][13][14]. Recently, various calculations have shown that the higher order moments of the multiplicity distributions of some conserved quantities, such as net-baryon, net-charge, and net-strangeness, are sensitive to the correlation length ξ [15-17], which in turn is related to the higher order moments, themselves. In realistic heavy-ion collisions, the correlation length is found to remain finite.Apparently, it should not be an exception that the strongly interacting QCD matter undergoes phase transition(s) at extreme conditions, as almost all matter types suffer from such a critical change as the extreme conditions change. The Lattice QCD calculations predict that a cross-over takes place between the hadronic phase and the Quark Gluon Plasma (QGP) phase, when the temperature exceeds critical value of T c ≃ 150 − 190 MeV. As given in Ref. [3,18], depending on the different parameters (for instance, the quark favours and their masses) and on the lattice configurations, lattice QCD assigns different values to T c . Furthermore, the value of T c depends on the baryon chemical potential µ. With vanishing µ the lattice QCD calculations [19] show that the higher order suscepti...

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Section: Higher Order Moments Of the Particle Multiplicitymentioning

confidence: 58%

“…There are large theoretical uncertainties of its location and even its existence is not fully confirmed, yet [4][5][6]. The characteristic feature of CEP are critical dynamical fluctuations [7][8][9][10][11]. The higher order moments are conjectured to reflect the large fluctuations associating the hadronquark phase transition.…”

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confidence: 99%

On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out, and QCD Critical Endpoint

Tawfik¹

2013

Advances in High Energy Physics

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“…Their dependence on √ s is also non-monotonic. While fluctuations from K − /π − exponentially decrease with increasing √ s, fluctuations from Λ/π and Ξ + /π have minimum values at √ s ∼ 10 GeV [98].…”

Section: Dynamical Fluctuations Of Particle Ratiosmentioning

confidence: 93%

“…To find shear viscosity η, we put i = j in Eqs. (95) and (98). To find bulk viscosity ξ, we substitute i with j and T µν 0 with 3P .…”

Section: B Relaxation Time Approximationmentioning

confidence: 99%

Equilibrium statistical–thermal models in high-energy physics

Tawfik

2014

Int. J. Mod. Phys. A

211

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We review some recent highlights from the applications of statistical-thermal models to different experimental measurements and lattice QCD thermodynamics, that have been made during the last decade. We start with a short review of the historical milestones on the path of constructing statistical-thermal models for heavy-ion physics. We discovered that Heinz Koppe formulated in 1948 an almost complete recipe for the statistical-thermal models. In 1950, Enrico Fermi generalized this statistical approach, in which he started with a general cross-section formula and inserted into it simplifying assumptions about the matrix element of the interaction process that likely reflects many features of the high-energy reactions dominated by density in the phase space of final states. In 1964, Hagedorn systematically analysed the high-energy phenomena using all tools of statistical physics and introduced the concept of limiting temperature based on the statistical bootstrap model. It turns to be quite often that many-particle systems can be studied with the help of statistical-thermal methods. The analysis of yield multiplicities in high-energy collisions gives an overwhelming evidence for the chemical equilibrium in the final state. The strange particles might be an exception, as they are suppressed at lower beam energies. However, their relative yields fulfil statistical equilibrium, as well. We review the equilibrium statistical-thermal models for particle production, fluctuations and collective flow in heavy-ion experiments. We also review their reproduction of the lattice QCD thermodynamics at vanishing and finite chemical potential. During the last decade, five conditions have been suggested to describe the universal behavior of the chemical freeze out parameters. The higher order moments of multiplicity have been discussed. They offer deep insights about particle production and to critical fluctuations. Therefore, we use them to describe the freeze out parameters and suggest the location of the QCD critical endpoint. Various extensions have been proposed in order to take into consideration the possible deviations of the ideal hadron gas. We highlight various types of interactions, dissipative properties and location-dependences (spacial rapidity). Furthermore, we review three models combining hadronic with partonic phases; quasi-particle model, linear σ-model with Polyakov-loop potentials and compressible bag model. PACS numbers: 12.40.Ee,24.60.-k,05.70.Fh,12.40.-y Keywords: Statistical models of strong interactions, Statistical physics of nuclear reactions, Phase transition in statistical mechanics and thermodynamics, Models of strong interactions Contents * http://atawfik.net/ † Electronic address: atawfik@cern.ch 65 3. Chiral phase transition 69 4. Confinement-deconfinement phase diagram 72 V. Higher order moments in statistical-thermal models 74 A. Non-normalized higher order moments 74 B. Normalized higher order moments 77 C. Products of higher order moments 78 D. Experimental higher order moments of particle yie...

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“…For instance, at chemical equilibrium, the entropy and number of produced particles are fixed. Thus, statistical-thermal approaches can be applied in order to estimate various thermodynamic quantities [35][36][37][38][39]. The agreement with the lattice calculations was found excellent [40][41][42][43][44].…”

Section: Remarks On Proposed Estimatementioning

confidence: 99%

An estimate of the thermodynamic pressure in high-energy collisions

Tawfik

2015

Int. J. Mod. Phys. A

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We introduce a novel approach to estimate the thermodynamic pressure from heavy-ion collisions based on recently measured higher-order moments of particle multiplicities by the STAR experiment.We start with fitting the experimental results in the most-central collisions. Then, we integrate them back to lower ones. For example, we find that the first-order moment, the mean multiplicity, is exactly reproduced from the integral of variance, the second-order moment. Therefore, the zero-order moment, the thermodynamic pressure, can be estimated from the integral of the mean multiplicity. the possible comparison between such a kind of pressure (deduced from the integral of particle multiplicity) and the lattice pressure and the relating of Bjorken energy density to the lattice energy density are depending on lattice QCD at finite baryon chemical potential and first-principle estimation of the formation time of the quark-gluon plasma (QGP).

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Event-by-event fluctuations of particle ratios in heavy-ion collisions

Cited by 16 publications

References 26 publications

On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out, and QCD Critical Endpoint

On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out, and QCD Critical Endpoint

Equilibrium statistical–thermal models in high-energy physics

An estimate of the thermodynamic pressure in high-energy collisions

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