The thermodynamic properties of weakly interacting quark-gluon plasma via the one-gluon exchange interaction

The thermodynamic properties of the quark-gluon plasma (QGP), as well as its phase diagram, are calculated as a function of baryon density (chemical potential) and temperature. The QGP is assumed to be composed of the light quarks only, i.e., the up and down quarks, which interact weakly, and the gluons which are treated as they are free. The interaction between quarks is considered in the framework of the one gluon exchange model which is obtained from the Fermi liquid picture. The bag model is used, with fixed bag pressure (B)for the nonperturbative part, and the quantum chromodynamics (QCD) coupling is assumed to be constant, i.e., with no dependence on the temperature or the baryon density. The effect of weakly interacting quarks on the QGP phase diagram are shown and discussed. It is demonstrated that the one-gluon exchange interaction for the massless quarks has considerable effect on the QGP phase diagram and it causes the system to reach to the confined phase at the smaller baryon densities and temperatures. The pressure of excluded volume hadron gas model is also used to find the transition phase diagram. Our results depend on the values of bag pressure and the QCD coupling constant. The latter does not have a dramatic effect on our calculations. Finally, we compare our results with the thermodynamic properties of strange quark matter and the lattice QCD prediction for the QGP transition critical temperature.     

QCD equation of state for heavy ion collisions

In this work, we calculate the equation of state(EoS) of quark gluon-plasma(QGP) using the CornwallJackiw-Tomboulis(CJT) effective action. We get the quark propagator by using the rank-1 separable model within the framework of the Dyson-Schwinger equations(DSEs). The results from CJT effective action are compared with lattice QCD data. We find that, when μ is small, our results generally fit the lattice QCD data when TT_c,but show deviations at and below T_c. It can be concluded that the EoS of CJT is reliable when TT_c. Then,by adopting the hydrodynamic code UVH2+1, we compare the CJT results of the multiplicity and elliptic flow v2 with the PHENIX data and the results from the original EoS in UVH2+1. While the CJT results of multiplicities generally match the original UVH2+1 results and fit the experimental data, the CJT results of v2 are slightly larger than the original UVH2+1 results for centralities smaller than 40% and smaller than the original UVH2+1 results for higher centralities.     

Physical mechanism of the (tri)critical point generation

We discuss some ideas resulting from a phenomenological relation recently declared between the tension of string connecting the static quark-antiquark pair and surface tension of corresponding cylindrical bag. This relation analysis leads to the temperature of vanishing surface tension coefficient of the QGP bags at zero baryonic charge density as T _?? = 152.9 ± 4.5 MeV. We develop the view point that this temperature value is not a fortuitous coincidence with the temperature of (partial) chiral symmetry restoration as seen in the lattice QCD simulations. Besides, we argue that T _?? defines the QCD (tri)critical endpoint temperature and claim that a negative value of surface tension coefficient recently discovered is not a sole result but is quite familiar for ordinary liquids at the supercritical temperatures.     

Equilibration in quark gluon plasma

The hydrodynamic expansion rate of quark gluon plasma (QGP) is evaluated and compared with the scattering rate of quarks and gluons within the system. Partonic scattering rates evaluated within the ambit of perturbative Quantum Choromodynamics (pQCD) are found to be smaller than the expansion rate evaluated with ideal equation of state (EoS) for the QGP. This indicate that during the space-time evolution the system remains out of equilibrium. Enhancement of pQCD cross sections and a more realistic EoS keep the partons closer to the equilibrium.     

Revisiting the quasi-particle model of the quark–gluon plasma

The quasi-particle model of the quark–gluon plasma (QGP) is revisited here with a new method, different from earlier studies, one without the need of a temperature dependent bag constant and other effects such as confinement, effective degrees of freedom etc. Our model has only one system dependent parameter and shows a surprisingly good fit to the lattice results for the gluon plasma, and for 2-flavor, 3-flavor and (2+1)-flavor QGP. The basic idea is first to evaluate the energy density ε from the grand partition function of quasi-particle QGP, and then derive all other thermodynamic functions from ε. Quasi-particles are assumed to have a temperature dependent mass equal to the plasma frequency. Energy density, pressure and speed of sound at zero chemical potential are evaluated and compared with the available lattice data. We further extend the model to a finite chemical potential, without any new parameters, to obtain the quark density, quark susceptibility etc., and the model fits very well with the lattice results on 2-flavor QGP. PACS 12.38.Mh; 12.38.Gc; 05.70.Ce; 52.25.Kn     

Nonperturbative equation of state of quark-gluon plasma: Applications

The vacuum-driven nonperturbative factors L_i for quark and gluon Green’s functions are shown to define the nonperturbative dynamics of QGP in the leading approximation. EoS obtained recently in the framework of this approach is compared in detail with known lattice data for μ = 0 including P/T⁴, ε/T⁴, . The basic role in the dynamics at T ? 3T_c is played by the factors L_i which are approximately equal to the modulus of Polyakov line for quark L_fund and gluon L_adj. The properties of L_i are derived from field correlators and compared to lattice data, in particular the Casimir scaling property follows in the Gaussian approximation valid for small vacuum correlation lengths. Resulting curves for P/T⁴, ε/T⁴, are in a reasonable agreement with lattice data, the remaining difference points out to an effective attraction among QGP constituents.     

The interfacial surface tension of a quark-gluon plasma fireball in a hadronic medium

We calculate the interfacial surface tension of a QGP-fireball in a hadronic medium in the Ramanathan et al statistical model. The constancy of the ratio of the surface tension with the cube of the critical transition temperature is in overall accordance with lattice QCD findings. It is in complete agreement with a recent MIT bag model calculation of surface tension. The velocity of sound in the QGP droplet is predicted to be in the range (0.27 ± 0.02) times the velocity of light in vacuum and this value is independent of both the value of the transition temperature and the model parameters.      

Dissociation of 1P states in hot QCD Medium Using Quasi-Particle Model

We extend the analysis of a very recent work [1] to study the dissociation phenomenon of 1P states of the charmonium and bottomonium spectra (χ_c and χ_b) in a hot QCD medium using Quasi-Particle Model. This study employed a medium modified heavy quark potential which has quite different form in the sense that it has a lomg range Coulombic tail in addition to the Yukawa term even above the deconfinement temperature. Then we study the flavor dependence of their binding energies and explore the nature of dissociation temperatures by employing the Quasi-Particle debye mass for pure gluonic and full QCD case. Interestingly, the dissociation temperatures obtained by employing EoS1 and EoS2 with the Γ criterion, is closer to the upper bound of the dissociation temperatures which are obtained by the dissolution of a given quarkonia state by the mean thermal energy of the quasi-partons in the hot QCD/QGP medium.     

Nucleation rate of the quark-gluon plasma droplet at finite quark chemical potential

The nucleation rate of quark-gluon plasma (QGP) droplet is computed at finite quark chemical potential. In the course of computing the nucleation rate, the finite size effects of the QGP droplet are taken into account. We consider the phenomenological flow parameter of quarks and gluons, which is dependent on quark chemical potential and we calculate the nucleation rate of the QGP droplet with this parameter. While calculating the nucleation rate, we find that for low values of quark phenomenological parameter ?? _q , nucleation rate is negligible and when ?? _q increases, nucleation rate increases significantly.     

Analysis of K-prime equations of state

In the present communication, we introduce a new K-prime equation of state (EoS), which can be used to understand the interior of the Earth. The newly developed EoS is found to yield similar results as given by Stacey K-prime EoS and Keane EoS, in reference to the seismological data. However, the zero pressure and infinite pressure extrapolation of higher pressure derivatives of bulk modulus are found different for different K-prime EoS.     

Working group report: Quark gluon plasma

The 10th Workshop on High Energy Physics Phenomenology (WHEPP-10) was held at the Institute of Mathematical Sciences, Chennai during January 2–13, 2008. One of our working grops (WG) is QCD and QGP. The discussions of QGP WG include matter at high density, lattice QCD, charmonium states in QGP, viscous hydrodynamics and jet quenching, colour factor in heavy ion collisions and RHIC results on photons, dileptons and heavy quark. There were two plenary talks and several working group talks with intense discussions regarding the future activities that are going to be persued.      

Direct hadron production in ultrarelativistic heavy-ion collisions

Hadrons emitted by the pre-surface layer of a quark-gluon plasma (QGP) before the phase transition into a hadronic gas are considered as possible sources of direct information about QGP. It is shown that if QGP is created in ultrarelativistic heavy-ion collisions, then these hadrons strongly contribute at soft p_t at SpS energy and dominate up to an order of magnitude at LHC energy.     

Matter radii and wave function admixtures in 2n halo nuclei

We analyze longitudinal pion spectra from $\ensuremath \sqrt{s_{NN}}=2$ GeV to $\ensuremath \sqrt{s_{NN}}=20$ GeV within Landau??s hydrodynamical model and the UrQMD hybrid approach. From the measured data on the widths of the pion rapidity spectra, we extract the sound velocity c _s ² in the dense stage of the reactions. It is found that the sound velocity has a local minimum (indicating the softest point in the equation of state, EoS) at $\ensuremath \sqrt{s_{NN}}=4\mbox{--}9$ GeV, an energy range accessible at the Facility for Antiproton and Ion Research (FAIR) as well as the RHIC-Beam Energy Scan (RHIC-BES). This softening of the EoS is compatible with the formation of a QGP at the onset of deconfinement. The extracted sound velocities are then used to calculate an excitation function for the mean transverse mass of pions from the hybrid model. We find that, above $\ensuremath \sqrt{s_{NN}} \approx 10$ GeV, even the lowest c _s ² gives a considerably larger $\ensuremath \langle m_T\rangle$ of pions compared to data.     

Directed flow of baryons from high-energy heavy-ion collisions

The collective motion of nucleons from high-energy heavy-ion collisions is analyzed within a relativistic two-fluid model for different equations of state (EoS). As function of beam energy the theoretical slope parameter F _y of the differential directed flow is in good agreement with experimental data, when calculated for the QCD-consistent EoS described by the statistical mixed-phase model. Within this model, which takes the deconfinement phase transition into account, the excitation function of the directed flow (P _x ) turns out to be a smooth function in the whole range from SIS till SPS energies. This function is close to that for pure hadronic EoS and exhibits no minimum predicted earlier for a two-phase bag-model EoS. Attention is also called to a possible formation of nucleon antiflow (F _y < 0) at energies ? 100 A·GeV.     

Effective-potential model for the self-interacting gluon gas

The thermodynamic behaviour of a pure gluon-plasma is investigated within the context of an effective-interaction model and the relativistic Landau theory of quantum liquids. Agreement is sought withSU (2) andSU (3) lattice computer simulations and asymptotic perturbation theory. For bothSU (2) andSU (3) the available data are fitted rather well by a logarithmically screened Coulomb potential. The difference in critical behaviour ofSU (2) andSU (3) can also be modelled. Contact is made with the Bare Bones bag model, yielding a bag pressure ofB ^1/4≈200 MeV.     

Bianchi type-III Dark Energy Model in f(R,T) Gravity

A dark energy model with EoS parameter is investigated in f(R,T) gravity in Bianchi type-III space-time in the presence of perfect fluid source. To obtain a determinate solution special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B 74:183, 1983) is used. We have also assumed that the scalar expansion is proportional to shear and the EoS parameter is proportional to skewness parameter. It is observed that the EoS parameter, skewness parameters in the model turn out to be functions of cosmic time. Some physical and kinematical properties of the model are also discussed.     

Status of Quark-Gluon Plasma

I review the current status of the experimental searches for a Quark-Gluon Plasma in heavy ion collisions. The brief introduction covers important results of finite temperature lattice QCD and the intuitive Bjorken picture of Quark-Gluon Plasma (QGP) formation. Global features of the data, such as transverse energy distributions and the various signatures of QGP such asJ/ϕ-suppression, ψ-enhancement as well as thermal dileptons and photons are then discussed.     

Field localization and particle confinement effects on pair creation by Schwinger’s mechanism

Solutions of the Dirac equation in the presence of a static uniform electric fieldɛ in thez-direction and a linear confining potentialAz, are obtained. Generalized reflection and transmission coefficients are derived for such divergent potentials forɛ >A/e. The eigenspectrum and corresponding localized eigenfunctions forɛ <A/e are obtained from the reflection coefficient and the continuum solutions respectively. The rate for the electric field to decay into pairs is derived from the transmission coefficient. Neglecting nonabelian effects in quantum chromodynamics we identify the fieldɛ with a colour electric field and the produced particles with a quark and an antiquark. By considering a cylindrical geometry, we thus obtain a generalization of Schwinger’s formula, for the fieldɛ in a finite spatial region with the quark (antiquark) being confined in thez direction by the linear potentialAz and in the perpendicular direction by the MIT bag boundary condition. The result is used to qualitatively study Schwinger’s mechanism of quark-gluon plasma (QGP) formation in ultrarelativistic heavy ion collisions. It is found that the critical strength of the field required to create pairs is enhanced,ɛ _c(A) >ɛ _c(A = 0). The rate of pair creation for constantɛ, decreases for non-zeroA, implying longer QGP formation times. Because ofɛ _c(A) >ɛ _c(0), QGP is predicted to be formed in the early stages of the nuclear collision. The finite size effects and the MIT bag boundary condition effects on QGP formation are also discussed.     

Recent observational constraints on generalized Chaplygin gas in UDME scenario

Recent observational predictions suggest that our Universe is passing through an accelerating phase in the recent past. This acceleration may be realized with the negatively pressured dark energy. Generalized Chaplygin gas may be suitable to describe the evolution of the Universe as a candidate of unified dark matter energy (UDME) model. Its EoS parameters are constrained using (i) dimensionless age parameter (H ₀ t ₀) and (ii) the observed Hubble (H(z)?z) data (OHD) + baryon acoustic oscillation (BAO) data + cosmic microwave background (CMB) shift data + supernovae (Union2.1) data. Dimensionless age parameter puts loose bounds on the EoS parameters. Best-fit values of the EoS parameters H ₀, A _s and α (A _s and α are defined in the energy density for generalized Chaplygin gas (GCG) and in EoS) are then determined from OHD + BAO + CMB + Union2.1 data and contours are drawn to obtain their allowed range of values. The present age of the Universe (t ₀) and the present Hubble parameter (H ₀) have been estimated with 1σ confidence level. Best-fit values of deceleration parameter (q), squared sound speed (\(c_{\mathrm {s}}^{2}\)) and EoS parameter (ω) of this model are then determined. It is seen that GCG satisfactorily accommodates an accelerating phase and structure formation phase.     

Holographic Dark Energy (DE) Cosmological Models with Quintessence in Bianchi Type-V Space Time

In this paper, author studied homogeneous and anisotropic Bianchi type-V universe filled with matter and holographic dark energy (DE) components. The exact solutions to the corresponding Einstein’s field equations are obtained for exponential and power-law volumetric expansion. The holographic dark energy (DE) EoS parameter behaves like constant, i.e. ω _Λ =?1, which is mathematically equivalent to cosmological constant (Λ) for exponential expansion of the model, whereas the holographic dark energy (DE) EoS parameter behaves like quintessence for power-law expansion of the model. A correspondence between the holographic dark energy (DE) models with the quintessence dark energy (DE) is also established. Quintessence potential and dynamics of the quintessence scalar field are reconstructed, which describe accelerated expansion of the universe. The statefinder diagnostic pair {r,s} is adopted to characterize different phases of the universe.