Search Results (15)

We study the thermodynamic properties produced in symmetric p–p collisions at $\sqrt{s_{NN}}=0.9\mathrm{TeV}$ and $7\mathrm{TeV}$, based on experimental data by the ALICE collaboration at CERN. Particularly, we analyze the initial temperature $T_i$, effective temperature T, freeze-out temperature $T_0$, chemical potential $\mu$, mean transverse momentum $⟨p_T⟩$, freeze-out volume V, and transverse flow velocity ${\beta }_T$ of different hadrons such as $K_S^0$, $\Lambda$, ${\Xi }^{-}$, and $d/\overline{d}$. To effectively use the transverse momentum $p_T$ distributions of these hadrons, and to extract the thermodynamic parameters, the Single-Slope Standard Distribution with and without the chemical potential $\mu$, the Double-Slope Standard Distribution, and the modified Standard Distribution Functions are applied separately to fit the experimental data. The Modified Standard Distribution Function provides the most accurate description of the ALICE experimental data as compared to the Single-Slope (with and without $\mu$) and Double-Slope Standard Distribution Function. We have investigated the correlation between the extracted thermodynamic parameters and the measurements of mass and energy of particles of the collision, and we observed that the increase in $\sqrt{s_{NN}}$ is positively correlated with $T_i$, T, $T_0$, $⟨p_T⟩$, V, and negatively correlated with $\mu$. The comparison of p–p collisions with heavy-ion collisions (Au–Au collisions) suggests the possibility of collective-like dynamics even in small systems, which supports the hypothesis of thermalization and partial de-confinement in high-energy p–p collisions, indicating a transition towards a quark-gluon plasma (QGP)-like medium. Full article

Quark–Gluon plasma driven by the strong force is subject to the conservativeness of the baryon number, net electric charge, strangeness, etc. However, the fluctuations around their mean values at specific temperatures and chemical potentials can provide viable signals for the production of Quark–Gluon plasma. These fluctuations can be captured theoretically as moments of different orders in the expansion of pressure or the thermodynamic potential of the system under concern. Here, we look for possible explanations in the methodologies used for capturing them by using the framework of the Polyakov–Nambu–Jona-Lasinio (PNJL) model under the 2 + 1 flavor consideration with mean-field approximation. The various quantities thus explored can act to signify meaningfully near the phase transitions. Justifications are also made for some of the quantities capable of serving necessarily under experimental scenarios. Additionally, variations in certain quantities are also made for the different collision energies explored in the high-energy experiments. Rectification of the quantitative accuracy, especially in the low-temperature hadronic sector, is of prime concern, and it is also addressed. It was found that most of the observables stay in close proximity with the existing lattice QCD results at the continuum limit, with some artifacts still remaining, especially in the strange sector, which needs further attention. Full article

The local growth global reset (LGGR) dynamical model is reviewed and its performance in describing the hadron energy spectra in relativistic collisions is demonstrated. It is shown that even for dynamical processes a temperature-like quantity can be defined and distributions resembling statistical equilibrium can be reached. With appropriate growth and reset rates the LGGR model is capable of describing the right energy spectra. These findings draw a certain picture of quark–gluon plasma development with random hadronization and re-swallowing steps and signals the fact that observing an exponential spectrum does not necessarily prove thermal equilibrium in the experiment. Full article

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons, measured by ALICE Collaboration at ten centrality classes of Pb + Pb collisions at $\sqrt{s_{nn}}$ = 5.02 TeV in the Large Hadron Collider (LHC, CERN, Switzerland), are successfully analyzed using combined minimum χ² fits with a thermodynamically non-consistent, as well as thermodynamically consistent, Tsallis function with transverse flow. The extracted non-extensivity parameter q decreases systematically for all considered particle species with increasing Pb + Pb collision centrality, suggesting an increase in the degree of system thermalization with an increase in collision centrality. The results for q suggest quite a large degree of thermalization of quark–gluon plasma (QGP) created in central Pb + Pb collisions at $\sqrt{s_{nn} }$= 5.02 TeV with the average number of participant nucleons $⟨N_{part}⟩$ > 160. The obtained significantly different growth rates of transverse flow velocity, $⟨{\beta }_T⟩$, in regions $⟨N_{part}⟩$ < 71 ± 7 and $⟨N_{part}⟩$ > 71 ± 7 with the temperature parameter T₀ remaining constant within uncertainties in region $⟨N_{part}⟩$ > 71 ± 7 probably indicates that $⟨N_{part}⟩$ ≈ 71 ± 7 (corresponding to $⟨d{N}_{ch}/d\eta ⟩$ ≈ 251 ± 20) is a threshold border value for a crossover transition from a dense hadronic state to the QGP phase (or mixed phase of QGP and hadrons) in Pb + Pb collisions at $\sqrt{s_{nn}}$ = 5.02 TeV. The threshold border value for transverse flow velocity $⟨{\beta }_T⟩$ ≈ 0.46 ± 0.03 (corresponding to $⟨N_{part}⟩$ ≈ 71 ± 7), estimated by us in Pb + Pb collisions at $\sqrt{s_{nn}}$ = 5.02 TeV, agrees well with the corresponding border value $⟨{\beta }_T⟩$ ≈ 0.44 ± 0.02, recently obtained in Xe + Xe collisions at $\sqrt{s_{nn} }$= 5.44 TeV, and with almost constant $⟨{\beta }_T⟩$ values extracted earlier in the Beam Energy Scan (BES) program of the Relativistic Heavy-Ion Collider (RHIC, Brookhaven, GA, USA) in central Au + Au collisions in the $\sqrt{s_{nn} }$= 7.7 − 39 GeV energy range, where the threshold for QGP production is achieved. The correlations between extracted T₀ and $⟨{\beta }_T⟩$ parameters are found to be greatly different in regions $⟨{\beta }_T⟩$ < 0.46 and $⟨{\beta }_T⟩$ > 0.46, which further supports our result obtained for the threshold border value in Pb + Pb collisions at $\sqrt{s_{nn}}$= 5.02 TeV. Full article

In this paper, we provide an account of analytical results related to the Tsallis thermodynamics that have been the subject matter of a lot of studies in the field of high-energy collisions. After reviewing the results for the classical case in the massless limit and for arbitrarily massive classical particles, we compute the quantum thermodynamic variables. For the first time, the analytical formula for the pressure of a Tsallis-like gas of massive bosons has been obtained. The study serves both as a brief review of the knowledge gathered in this area, and as original research that forwards the existing scholarship. The results of the present paper will be important in a plethora of studies in the field of high-energy collisions including the propagation of non-linear waves generated by the traversal of high-energy particles inside the quark-gluon plasma medium showing the features of non-extensivity. Full article

High-multiplicity proton-proton (pp) collisions at the Large Hadron Collider (LHC) energies have created a new domain of research to look for a possible formation of quark–gluon plasma in these events. In this paper, we estimate various thermal properties of the matter formed in pp collisions at the LHC energies, such as mean free path, isobaric expansivity, thermal pressure, and heat capacity using a thermodynamically consistent Tsallis distribution function. Particle species-dependent mean free path and isobaric expansivity are studied as functions of final state charged particle multiplicity for pp collisions at the center-of-mass energy $\sqrt{s}$ = 7 TeV. The effects of degree of non-extensivity, baryochemical potential, and temperature on these thermal properties are studied. The findings are compared with the theoretical expectations. Full article

In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark–gluon plasma takes place in the narrow temperature interval of 150–190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the $Z\left(3\right)$ center symmetry of the color $SU\left(3\right)$ group of QCD. We suggest a Polyakov-loop quark–gluon plasma model with $\mathcal{O}\left({\alpha }_s\right)$ virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures. Full article

We discuss thermodynamic properties of open confining strings introduced via static sources in the vacuum of Yang-Mills theory. We derive new sum rules for the chromoelectric and chromomagnetic condensates and use them to show that the presence of the confining string lowers the gluonic pressure in the bulk of the system. The pressure deficit of the gluon plasma is related to the potential energy in the system of heavy quarks and anti-quarks in the plasma. Full article

In this paper, we utilize known exact analytic solutions of perfect fluid hydrodynamics to analytically calculate the polarization of baryons produced in heavy-ion collisions. Assuming local thermodynamical equilibrium also for spin degrees of freedom, baryons get a net polarization at their formation (freeze-out). This polarization depends on the time evolution of the Quark-Gluon Plasma (QGP), which can be described as an almost perfect fluid. By using exact analytic solutions, we can thus analyze the necessity of rotation (and vorticity) for non-zero net polarization. In this paper, we give the first analytical calculations for the polarization four-vector. We use two hydrodynamical solutions; one is the spherically symmetric Hubble flow (a somewhat oversimplified model, to demonstrate the methodology); and the other solution is a somewhat more involved one that corresponds to a rotating and accelerating expansion, and is thus well-suited for the investigation of some of the main features of the time evolution of the QGP created in peripheral heavy-ion collisions (although there are still numerous features of real collision geometry that are beyond the scope of this simple model). Finally, we illustrate and discuss our results on the polarization. Full article

In this work, the nonequilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at a local thermodynamic equilibrium is revisited. This method, which was used to obtain the first “Kubo” formula of shear viscosity, is especially suitable to describe quantum effects in fluids. This feature makes it a viable tool to describe the physics of Quark–Gluon Plasma in relativistic nuclear collisions. Full article

We outline an approach to a unified equation of state for quark-hadron matter on the basis of a $\mathsf{\Phi }-$ derivable approach to the generalized Beth-Uhlenbeck equation of state for a cluster decomposition of thermodynamic quantities like the density. To this end we summarize the cluster virial expansion for nuclear matter and demonstrate the equivalence of the Green’s function approach and the $\mathsf{\Phi }-$ derivable formulation. As an example, the formation and dissociation of deuterons in nuclear matter is discussed. We formulate the cluster $\mathsf{\Phi }-$ derivable approach to quark-hadron matter which allows to take into account the specifics of chiral symmetry restoration and deconfinement in triggering the Mott-dissociation of hadrons. This approach unifies the description of a strongly coupled quark-gluon plasma with that of a medium-modified hadron resonance gas description which are contained as limiting cases. The developed formalism shall replace the common two-phase approach to the description of the deconfinement and chiral phase transition that requires a phase transition construction between separately developed equations of state for hadronic and quark matter phases. Applications to the phenomenology of heavy-ion collisions and astrophysics are outlined. Full article

Investigation of femtoscopic correlation functions in relativistic heavy ion reactions is an important tool to access the space-time structure of particle production in the strongly interacting Quark Gluon Plasma (sQGP). The shape of the source, and thus the shape of the correlation functions, is often assumed to be Gaussian, but experimental results found evidence for heavy tails in the source distribution of pions. Recent analysis revealed that the statistically correct assumption could be the so-called Lévy distribution. The detailed investigation of correlation functions in various systems may shed light on the location of the critical endpoint on QCD (Quantum Chromodynamics) phase diagram. It could also reveal if there is partially coherent pion production or could indicate the possible in-medium mass modification of the ${\eta }^{\prime }$ meson due to the (partial) restoration of the $U_{\mathrm{A}}\left(1\right)$ axial symmetry. These phenomena could depend on the system size and on the collision energy. A detailed centrality-dependent analysis could explore the multiplicity dependencies of the Lévy parameters, and thus the critical and thermodynamical properties of the sQGP, and could give information about the above mentioned processes. In this paper, we present the status of the centrality dependent measurements of two-pion Lévy Bose-Einstein correlation functions $\sqrt{s_{\mathrm{NN}}}=200$ GeV Au+Au collisions at PHENIX.
Full article

One important ingredient in the study of cosmological evolution is the equation of state of the primordial matter formed in the first stages of the Universe. It is believed that the first matter produced was of hadronic nature, probably the quark–gluon plasma which has been studied in high-energy collisions. There are several experimental indications of self-similarity in hadronic systems—in particular in multiparticle production at high energies. Theoretically, this property was associated with the dynamics of particle production, but it is also possible to relate self-similarity to the hadron structure—in particular to a fractal structure of this system. In doing so, it is found that the thermodynamics of hadron systems at equilibrium must present specific properties that are indeed supported by data. In particular, the well-known self-consistence principle proposed by Hagedorn 50 years ago is shown to be valid, and can correctly describe experimental distributions, mass spectrum of observed particles, and other properties of the hadronic matter. In the present work, a review of the theoretical developments related to the thermodynamical properties of hadronic matter and its applications in other fields is presented. Full article

This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an infra-red stable fixed point, and the correlation lengths of the stochastic Yang-Mills fields. Other non-perturbative applications of the world-line formalism presented in the review are devoted to the determination of the electroweak phase-transition critical temperature, to the derivation of a semi-classical analogue of the relation between the chiral and the gluon QCD condensates, and to the calculation of the free energy of the gluon plasma in the high-temperature limit. As a complementary result, we demonstrate Casimir scaling of k-string tensions in the Gaussian ensemble of the stochastic Yang-Mills fields. Full article

The equation of state associated with $\mathcal{N}=4$ supersymmetric Yang–Mills in four dimensions, for $SU\left(N\right)$ in the large N limit, is investigated using the AdS/CFT correspondence. An asymptotically AdS black-hole on the gravity side provides a thermal background for the Yang–Mills theory on the boundary in which the cosmological constant is equivalent to a volume. The thermodynamic variable conjugate to the cosmological constant is a pressure, and the $P-V$ diagram of the quark-gluon plasma is studied. It is known that there is a critical point where the heat capacity diverges, and this is reflected in the isothermal compressibility. Critical exponents are derived and found to be mean field in the large N limit. The same analysis applied to three- and six-dimensional conformal field theories again yields mean field exponents associated with the compressibility at the critical point. Full article